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학술

arXiv 등 학술 논문. CC-BY 라이선스로 자유 재사용 가능 — 출처표시 시 상업 사용 OK.

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Augmenting goodness-of-fit tests with sequentially calibrated secondary statistics

arXiv:2607.15015v1 Announce Type: new Abstract: Goodness-of-fit statistics may have markedly different power against different types of alternatives. We propose a sequential procedure for augmenting a primary goodness-of-fit statistic with an ordered collection of secondary statistics. At each stage, the acceptance region of the current statistic is calibrated under the null distribution conditional on acceptance at all preceding stages. This conditional calibration gives a simple multiplicative decomposition of the overall Type~I error and allows the primary-stage level to be adjusted explicitly after the secondary-stage levels have been selected. The disjoint stagewise rejection regions also provide an ordered first-rejection decomposition of power. We illustrate the method by augmenting the Kolmogorov--Smirnov statistic with sample variance and sample skewness. In simulations under a standard normal null, the resulting chain procedures retain nearly all of the primary test's power against location alternatives while substantially improving power against scale, heavy-tailed, and asymmetric alternatives. Reversing the order of the secondary statistics produces nearly identical total power in the experiment, although the stagewise attribution of power can change considerably.

arXiv Stat

Flood risk estimation via geometric extremal graphical models

arXiv:2607.15000v1 Announce Type: new Abstract: We exploit the new framework of multivariate geometric extreme value theory for the statistical analysis of river flow extremes at multiple locations on a river network. Current methodologies within the geometric framework are limited to a relatively low number of dimensions. This is insufficient for the purposes of flood risk estimation, since the number of gauging stations on a river network is often of the order $10-20+$. In order to create a parsimonious model in higher dimensions, we translate recent theoretical work on geometric extremal graphical models into statistical practice. We define the gauge function, a key object in geometric extremes, in a structured way using block graphs, which are a natural way of expressing the river network. We introduce both simple models, and more complex ones that can accommodate both simultaneous and non-simultaneous flows, and apply them to extreme flows at 10 locations on a river network around Preston, in north-west England. The models are shown to fit well and indicate strong extrapolation performance. We also introduce a correction coefficient for the geometric framework to address potential over- or under-estimation of marginal probabilities. The overall utility of our approach is illustrated through calculation of probabilities of simultaneous flooding at four locations on the network.

arXiv Stat

Statistical Modelling of Planetary Boundary Layer Height and Its Measurement Uncertainty Using GRUAN Profiles

arXiv:2607.14960v1 Announce Type: new Abstract: The Planetary Boundary Layer (PBL) governs the exchange of energy and moisture and hosts the highest concentrations of pollutants before they mix into the free troposphere. The height of the PBL (PBLH) is therefore a key variable in meteorological and air-quality applications. Despite the wide range of methods available to derive PBLH from atmospheric observations, the associated uncertainties are rarely quantified. This study presents a methodology for propagating radiosonde measurement uncertainty into PBLH estimates obtained from state-of-the-art retrieval methods, including the parcel method, gradient-based methods, and the Richardson-number method. The framework relies on three components. First, it uses the GCOS Reference Upper-Air Network (GRUAN) Data Product, which provides traceable uncertainty estimates for all variables required in PBLH retrievals. Second, it employs a state-space model that captures the structure of atmospheric profiles and enables the generation of physically plausible simulated vertical profiles consistent with both observations and their uncertainties. Third, a Monte Carlo approach is used to propagate measurement uncertainty into the PBLH estimates, refining the retrieval and quantifying its uncertainty. Beyond providing uncertainty estimates, the methodology also shows preliminary signs of increased robustness in PBLH detection across several case studies, particularly in situations where standard gradient-based methods exhibit sensitivity to measurement uncertainty.

arXiv Stat

Optimal Self-Distillation for Rectified Flow via Linear Probing

arXiv:2607.14947v1 Announce Type: new Abstract: Modern generative models are increasingly trained using model-generated signals, creating both opportunities for self-improvement and risks of collapse. We study optimal self-distillation (SD) for rectified flow (RF): given a suboptimal teacher velocity field, can a student trained on a mixture of true RF velocities and teacher velocities provably improve the teacher? For linear RF with ridge regularization on fixed interpolation pairs, we prove an exact affine path identity, derive the optimal mixing coefficient in closed form, and show strict improvement in integrated velocity risk whenever the teacher risk is nonstationary along the regularization path. The optimal coefficient obeys a sign rule: positive mixing corrects under-regularized teachers, while negative mixing corrects over-regularized teachers. We also give one-shot generalized cross-validation (GCV) and validation tuning procedure that avoids grid search over mixing weights and repeated refitting. Combining this theorem with RF Wasserstein convergence bounds, we show that optimal self-distillation improves the velocity estimation terms controlling continuous-time and finite-step generation error. Experiments with Gaussian models, Gaussian mixtures, and image data show that optimal self-distillation improves velocity risk, mode recovery, and finite-step generation relative to both the teacher and pure distillation.

arXiv Stat

Assing Preferential Sampling in Retail Survival Data: A Bayesian Joint LGCP and Spatial Probit Model for Mini-Supermarket Closure in Tokyo

arXiv:2607.14860v1 Announce Type: new Abstract: Retail store locations are strategically selected rather than randomly distributed, potentially inducing preferential sampling when the latent spatial factors governing placement also affect store survival. We propose a Bayesian hierarchical model that jointly combines a log-Gaussian Cox process for store locations with a probit regression for binary survival outcomes. The two components share a Gaussian process spatial effect, with a loading parameter measuring the association between the latent drivers of store placement and survival. To enable efficient inference for approximately 1,000 observations, we use a nearest-neighbor Gaussian process approximation and a Metropolis-within-Gibbs algorithm. We apply the model to 999 mini-supermarkets in Tokyo's 23 special wards, including 897 operating and 102 closed stores, using seven spatial covariates and a 3,471-point integration grid. The estimated loading is close to zero, with its credible interval including zero, providing no clear evidence of residual preferential sampling. Regression estimates are also stable across models with and without preferential sampling. Simulations show that the method can distinguish absent from strong preferential sampling. Proximity to full-scale supermarkets is the most robust predictor of closure risk, consistent with competitive substitution.

arXiv Stat

Mixed-Frequency Time Series Forecasting via Depth-Separable Neural Networks

arXiv:2607.14771v1 Announce Type: new Abstract: To better forecast mixed-frequency time series, it is the key to choose a suitable way for frequency alignment. However, the existing methods are all limited to linear transformations, and this may overlook the possible nonlinearity, leading to a worse prediction. We alternatively consider a deep neural network for each frequency alignment, and hence a depth-separable neural network. Moreover, a parameter-sharing mechanism is adopted across the alignment at each stage, making possible a deeper network for a large set of higher-frequency predictors. This paper establishes an approximation theory for the proposed depth-separable network, and a non-asymptotic prediction error bound is also derived. Simulation studies demonstrate the finite-sample performance of the proposed method, and an empirical application to forecasting U.S. quarterly macroeconomic variables using monthly and daily indicators, highlights its superior predictive accuracy over existing mixed-frequency methods.

arXiv Stat

Testing equivalence to binary generalized linear models with application to logistic regression

arXiv:2607.14724v1 Announce Type: new Abstract: We introduce a new equivalence test to show sufficiently good agreement of observed data with a binary generalized linear model (GLM). The test statistic is constructed via the minimum distance method. The test is developed for the important special case where all covariates are categorical. The critical values can be calculated using an asymptotic approximation or by means of bootstrapping. The application of the test to logistic regression is illustrated on two real data sets. The finite sample performance of the proposed test is studied by simulations which are based on these two data sets.

arXiv Stat

Exact Computation of Non-Gaussian Mismatch Penalties in Wiener-Hermite Cross-Correlation Identification

arXiv:2607.14699v1 Announce Type: new Abstract: Wiener-Hermite cross-correlation identification represents a polynomial response in the Hermite basis. Under Gaussian excitation the basis is orthogonal and a diagonal rule recovers it exactly; under non-Gaussian excitation the same basis is kept, but its Gram matrix gains off-diagonal terms and the diagonal rule is no longer the population projection. We give the exact finite-order excess $L^2(P)$ risk of this mismatch: a moment quadratic form from two Hankel-Cholesky factorizations and one diagonal solve, at $O(s^3)$ cost from moments to order $2s$. Closed cumulant forms at orders three and four expose which non-Gaussian features drive it; symmetry protects the Gaussian basis only through order two. A bootstrap decides, from data, whether a matched basis is worth building; on a Wiener-Hammerstein benchmark it separates a near-Gaussian channel (penalty $\approx 10^{-4}$) from a skewed output (penalty $0.05$). The computation is a weighted-$L^2$ projection whose core normal-system correspondence is machine-checked in Lean 4.

arXiv Stat

Multiverse analysis, abdication of responsibility and manufacturing of doubt

arXiv:2607.14623v1 Announce Type: new Abstract: I argue that multiverse analysis is highly suited to two undesirable uses: abdication of researcher's responsibility for their conclusion and manufacturing of doubt. A review of multiverse analyses published in 2025 provides tentative empirical support that abdication of responsibility is present in the literature and I mention anecdotal evidence that multiverse has been used for manufacturing of doubt about Covid-19 precautions. To mitigate negative effects if multiverse analysis becomes widely used I suggest the community adopts two conventions for evaluating multiverse analyzes: evaluating multiverses by the single worst universe they contain and considering large size of a multiverse as a sign of weakness rather than a praiseworthy achievement.

arXiv Stat

Custom-made Gauss quadrature: an introduction for statisticians

arXiv:2607.14511v1 Announce Type: new Abstract: An $n$-point Gauss quadrature rule approximates the weighted integral of a function by a weighted average of $n$ evaluations of this function and is exact for polynomials of degree at most $2n-1$. Such rules can be highly accurate with relatively few evaluations. For weight functions that are associated with classical orthogonal polynomials of a continuous variable (such as Legendre, Hermite and Laguerre), these rules are readily available. We suppose that this is not the case, so that these rules must be custom-made. The two most easily understood methods for the computation of these rules are (a) moment determinants and (b) the Stieltjes procedure. We implement them in the Julia package CustomGaussQuadrature, which uses type-generic numerical programming and adaptive high-precision arithmetic to assess the approximation error due to roundoff. We describe access from R via JuliaConnectoR.

arXiv Stat

Improving interpretation of latent class models for diagnostic tests by recognizing their measurands via directed acyclic graphs (DAGs)

arXiv:2607.14473v1 Announce Type: new Abstract: Summary: In the absence of a perfect diagnostic test for a target condition, multiple imperfect tests may be used to arrive at a clinical diagnosis. Latent class analysis can be used to model such data with the objective of estimating test accuracy and target condition prevalence. Such models typically assume two latent classes - target condition positive and target condition negative. However, as we will illustrate in this manuscript, this would be an oversimplification if the different tests do not share the target condition as their measurand. We show how a Directed Acyclic Graph (DAG) can be used to illustrate the relationships between the relevant variables - the observed imperfect test results, their latent measurands, the latent target condition of interest and observed covariates - revealing any conditional dependence relations. The DAG helps determine the number of latent classes, underlying the observed data, and their labels. We show how the likelihood function changes due to incorporating the measurand of each test. We study the impact on identifiability of the model. Using simulation studies we show how ignoring the measurand of an imperfect test, when it is distinct from the target condition, can lead to biased estimates of test accuracy and prevalence. We illustrate the value of the proposed approach by re-analyzing two datasets used in previously published latent class analyses of tests for pediatric tuberculosis and leptospirosis.

arXiv Stat

Admissibility and Complete Classes for False Discovery Rate Control with E-values

arXiv:2607.14380v1 Announce Type: new Abstract: The false discovery rate (FDR) is the most widely used error metric in modern multiple testing. We provide the first comprehensive analysis of the admissibility of e-value-based procedures with FDR control. We consider both simultaneous and point procedures and introduce strong and weak notions of dominance. We show that every simultaneous procedure is strongly, and hence weakly, dominated by an admissible weighted-mean closed e-Benjamini-Hochberg ($\overline{\mathrm{eBH}}$) procedure, so weighted-mean $\overline{\mathrm{eBH}}$ procedures form a complete class. Moreover, every constant-free weighted-mean $\overline{\mathrm{eBH}}$ procedure is admissible at every level. Within the symmetric class, the usual mean $\overline{\mathrm{eBH}}$ procedure is the largest element if and only if the FDR level is small enough; otherwise this class has no largest element. We also obtain results on the admissibility of symmetric $\overline{\mathrm{eBH}}$ procedures with non-zero constant terms, and give guidance on the choice of the constant terms. Point e-testing procedures have a parallel theory for admissibility, where point weighted-mean $\overline{\mathrm{eBH}}$ procedures form a complete class. These results highlight the central role of weighted-mean $\overline{\mathrm{eBH}}$ procedures in multiple testing.

arXiv Stat

A Leave-One-Out Influence Statistic for Density-Based Outlier Detection

arXiv:2607.14335v1 Announce Type: new Abstract: We propose a density-based leave-one-out influence score for unsupervised outlier detection. The motivation is that outliers are naturally associated with regions of very small probability density, but direct leave-one-out density refitting can be computationally prohibitive. We use the Linear-Blend Frequency Polygon (LBFP) estimator and define a score that compares the full-sample fitted density at an observation with the fitted density obtained after removing that observation, while keeping the grid and bandwidth fixed. The resulting statistic measures a relative density perturbation at the observation's own location. For the LBFP estimator, this score has an exact closed-form update, so the density estimator does not need to be refitted for each observation. This preserves a direct density interpretation while making the method computationally efficient for large samples. We study the score under contamination and show that regular positive-density observations and contamination-driven observations have distinct asymptotic orders. Simulations over a broad range of contamination models illustrate these theoretical regimes, show competitive performance relative to standard benchmarks, and document computing time. A credit-card fraud application with 29 variables illustrates that the method works well on a large real data set.

arXiv Stat

Parsimonious Mixtures of Skewed Bilinear Factor Analyzers

arXiv:2607.14297v1 Announce Type: new Abstract: Mixture models which cluster skewed random matrices can often suffer from over-parameterization in the absence of performing dimension reduction. Even with the use of bilinear factor analyzers, further parameter reduction can be achieved by constraining parameters over clusters. In this manuscript propose a parsimonious family of 256 models for mixtures of skewed matrix variate bilinear factor analyzers, specifically in the case of the skew t distribution. An AECM algorithm for parameter estimation is discussed in detail. Further, extensive simulations are performed, and the method is considered in the case of the MNIST dataset and the Olivetti faces dataset.

arXiv Stat

Analysis of Public Schools Educational Performance Based on Causal Models and Hierarchical Clustering

arXiv:2607.14124v1 Announce Type: new Abstract: The increasing availability of large-scale educational datasets has expanded the use of quantitative methods for investigating school performance. However, institutional heterogeneity among schools and the structural complexity of educational data pose substantial challenges to traditional statistical modeling approaches. This study investigates the existence of school typologies based on structural, pedagogical, and demographic characteristics, and examines how these typologies relate to performance in the Brazilian Basic Education Assessment System (Saeb). Using data from the Brazilian School Census and Saeb, data preprocessing and normalization procedures are applied followed by hierarchical clustering to identify groups of schools with similar structural profiles. After the identification of these typologies, causal analysis techniques are employed to investigate potential causal relationships between school characteristics and educational outcomes. The results reveal the presence of distinct school profiles and statistically significant differences in average performance among them. The causal analysis provides insights into the structural and contextual factors that may influence educational performance, contributing to a better understanding of the mechanisms associated with school effectiveness.

arXiv Econ

Automated Trading System for Straddle-Option Based on Deep Q-Learning

arXiv:2509.07987v2 Announce Type: replace-cross Abstract: Straddle Option is a financial trading tool that explores volatility premiums in high-volatility markets without predicting price direction. Although deep reinforcement learning has emerged as a powerful approach to trading automation in financial markets, existing work mostly focused on predicting price trends and making trading decisions by combining multi-dimensional datasets like blogs and videos, which led to high computational costs and unstable performance in high-volatility markets. To tackle this challenge, we develop automated straddle option trading based on reinforcement learning and attention mechanisms to handle unpredictability in high-volatility markets. Firstly, we leverage the attention mechanisms in Transformer-DDQN through both self-attention with time series data and channel attention with multi-cycle information. Secondly, a novel reward function considering excess earnings is designed to focus on long-term profits and neglect short-term losses over a stop line. Thirdly, we identify the resistance levels to provide reference information when great uncertainty in price movements occurs with intensified battle between the buyers and sellers. Through extensive experiments on the Chinese stock, Brent crude oil, and Bitcoin markets, our attention-based Transformer-DDQN model exhibits the lowest maximum drawdown across all markets, and outperforms other models by 92.5\% in terms of the average return excluding the crude oil market due to relatively low fluctuation.

arXiv Econ

Coordinating Treatment Allocation and Recommendation

arXiv:2606.21120v2 Announce Type: replace Abstract: We study a model in which a sender allocates limited treatment to agents with heterogeneous quality and later recommends selected agents to a receiver, seeking to maximize the number of agents accepted by the receiver. All agents value treatment, which improves agents' quality, but treatment must be allocated before the sender observes agents' initial quality; recommendation occurs only after quality is learned. A natural benchmark is to design the two instruments separately: allocate treatment randomly first, and then recommend agents from the top down afterward. Our main result shows that the sender can do strictly better by coordinating treatment allocation with recommendations. In the optimal joint mechanism, treatment is non-monotone in quality: an intermediate group has a lower treatment probability than both higher- and lower-quality agents, but is compensated with a guaranteed recommendation when treatment is realized. We provide an implementation through contracts that induce self-selection and discuss applications to education, industrial policy, and startup incubation. The takeaway is simple: coordinate treatment allocation and recommendation.

arXiv Econ

Variance Estimation with Dependence and Heterogeneous Means

arXiv:2603.11497v2 Announce Type: replace Abstract: This paper develops a framework for variance estimation under dependence and heterogeneous means. This paper shows that consistent estimation of the variance target is impossible in general, and characterizes necessary and sufficient conditions for conservative variance estimation using dual cones. To choose among the valid estimators, this paper formulates three criteria -- minimal correction, pointwise level estimand, and pointwise MSE -- and shows how an eigenvalue truncation solution is optimal under all three criteria. This characterization and solution allow us to assess if existing variance estimators are valid and optimal in their respective settings, and construct the first optimal variance estimator that is simultaneously robust to heterogeneous means and cross-cluster serial correlation.

arXiv Econ

Making Event Study Plots Honest: A Functional Data Approach to Causal Inference

arXiv:2512.06804v3 Announce Type: replace Abstract: Event study plots are the centerpiece of Difference-in-Differences (DiD) analysis, but current plotting methods cannot provide honest causal inference when the parallel trends and/or no-anticipation assumptions fail. We introduce a novel functional data approach to DiD that directly enables honest causal inference via event study plots. Our DiD estimator converges to a Gaussian process in the Banach space of continuous functions, enabling powerful simultaneous confidence bands. This theoretical contribution allows us to turn an event study plot into a rigorous honest causal inference tool through equivalence and relevance testing: Honest reference bands can be validated using equivalence testing in the pre-treatment period, and honest causal effects can be tested using relevance testing in the post-treatment period. We demonstrate the performance of our method in simulations and two case studies.

arXiv Econ

"Rich-Get-Richer"? Platform Attention and Earnings Inequality using Patreon Earnings Data

arXiv:2509.26523v3 Announce Type: replace Abstract: Using monthly Patreon earnings, we quantify how platform attention algorithms shape earnings concentration across creator economies. Patreon is a tool for creators to monetize additional content from loyal subscribers but offers little native distribution, so its earnings proxy well for the attention creators capture on external platforms (Instagram, Twitch, YouTube, Twitter/X, Facebook, and ``Patreon-only''). Fitting power-law tails to test for a highly unequal earnings distribution, we have three key findings. First, across years and platforms the earnings tail and distribution exhibits a Pareto exponent around $\alpha \approx 2$, closer to concentrated capital income than to labor income and consistent with a compounding, ``rich-get-richer'' dynamic (Barabasi and Albert 1999). Second, when algorithms tilt more attention toward the top, the gains are drawn disproportionately from the creator ``middle class''. Third, over time, creator inequality across social media platforms converge toward similarly heavy-tailed (and increasingly concentrated) distributions, plausibly as algorithmic recommendations rises in importance relative to user-filtered content via the social graph. While our Patreon-sourced data represents a small subset of total creator earnings on these platforms, it provides unique insight into the cross-platform algorithmic effects on earnings concentration.

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