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Many modern data analyses benefit from explicitly modeling dependence structure in data -- such as measurements across time or space, ordered words in a sentence, or genes in a genome. A gold standard evaluation technique is structured…

Machine Learning · Statistics 2020-12-02 Soumya Ghosh , William T. Stephenson , Tin D. Nguyen , Sameer K. Deshpande , Tamara Broderick

We conduct a non asymptotic study of the Cross Validation (CV) estimate of the generalization risk for learning algorithms dedicated to extreme regions of the covariates space. In this Extreme Value Analysis context, the risk function…

Statistics Theory · Mathematics 2024-09-12 Anass Aghbalou , Patrice Bertail , François Portier , Anne Sabourin

There is a wide literature on change point tests, but the case of variables with infinite variances is essentially unexplored. In this paper we address this problem by studying the asymptotic behavior of trimmed CUSUM statistics. We show…

Statistics Theory · Mathematics 2012-01-06 István Berkes , Lajos Horváth , Johannes Schauer

We consider a one-dimensional Gaussian process having exponential covariance function. Under fixed-domain asymptotics, we prove the strong consistency and asymptotic normality of a cross validation estimator of the microergodic covariance…

Statistics Theory · Mathematics 2017-07-26 Francois Bachoc , Agnes Lagnoux , Thi Mong Ngoc Nguyen

Cross-validation is a popular non-parametric method for evaluating the accuracy of a predictive rule. The usefulness of cross-validation depends on the task we want to employ it for. In this note, I discuss a simple non-parametric setting,…

Methodology · Statistics 2019-09-27 Stefan Wager

Cross-validation (CV) is one of the most popular tools for assessing and selecting predictive models. However, standard CV suffers from high computational cost when the number of folds is large. Recently, under the empirical risk…

Methodology · Statistics 2023-05-30 Yuetian Luo , Zhimei Ren , Rina Foygel Barber

As a technique that can compactly represent complex patterns, machine learning has significant potential for predictive inference. K-fold cross-validation (CV) is the most common approach to ascertaining the likelihood that a machine…

Machine Learning · Statistics 2026-04-24 Juan M Gorriz , R. Martin Clemente , F Segovia , J Ramirez , A Ortiz , J. Suckling

A new method of bandwidth selection for kernel density estimators is proposed. The method, termed indirect cross-validation, or ICV, makes use of so-called selection kernels. Least squares cross-validation (LSCV) is used to select the…

Methodology · Statistics 2008-12-02 Olga Y. Savchuk , Jeffrey D. Hart , Simon J. Sheather

Two new test statistics are introduced to test the null hypotheses that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. These statistics are empirical L_1-type distances between the isotonic estimates,…

Statistics Theory · Mathematics 2015-03-17 Piet Groeneboom , Geurt Jongbloed

The paper discusses the estimation of a continuous density function of the target random field $X_{\bf{i}}$, $\bf{i}\in \mathbb {Z}^N$ which is contaminated by measurement errors. In particular, the observed random field $Y_{\bf{i}}$,…

Statistics Theory · Mathematics 2014-07-21 Jiexiang Li

Models like LASSO and ridge regression are extensively used in practice due to their interpretability, ease of use, and strong theoretical guarantees. Cross-validation (CV) is widely used for hyperparameter tuning in these models, but do…

Machine Learning · Statistics 2022-11-03 William T. Stephenson , Zachary Frangella , Madeleine Udell , Tamara Broderick

Many versions of cross-validation (CV) exist in the literature; and each version though has different variants. All are used interchangeably by many practitioners; yet, without explanation to the connection or difference among them. This…

Machine Learning · Statistics 2022-05-31 Waleed A. Yousef

Model selection is a crucial issue in machine-learning and a wide variety of penalisation methods (with possibly data dependent complexity penalties) have recently been introduced for this purpose. However their empirical performance is…

Machine Learning · Statistics 2012-12-11 Charanpal Dhanjal , Nicolas Baskiotis , Stéphan Clémençon , Nicolas Usunier

The Pickands estimator for the extreme value index is beneficial due to its universal consistency, location, and scale invariance, which sets it apart from other types of estimators. However, similar to many extreme value index estimators,…

Statistics Theory · Mathematics 2024-07-29 Yizhou Li , Pawel Polak

Cross-validation (CV) is one of the most widely used techniques in statistical learning for estimating the test error of a model, but its behavior is not yet fully understood. It has been shown that standard confidence intervals for test…

Methodology · Statistics 2023-10-10 Min Woo Sun , Robert Tibshirani

K-fold cross-validation (CV) with squared error loss is widely used for evaluating predictive models, especially when strong distributional assumptions cannot be taken. However, CV with squared error loss is not free from distributional…

Methodology · Statistics 2021-08-10 Assaf Rabinowicz , Saharon Rosset

We consider the problem of detecting a rectangle of activation in a grid of sensors in d-dimensions with noisy measurements. This has applications to massive surveillance projects and anomaly detection in large datasets in which one detects…

Statistics Theory · Mathematics 2014-09-26 James Sharpnack , Ery Arias-Castro

Risk sensitive decision making finds important applications in current day use cases. Existing risk measures consider a single or finite collection of random variables, which do not account for the asymptotic behaviour of underlying…

Risk Management · Quantitative Finance 2024-05-24 Shivam Patel , Vivek Borkar

We employ random matrix theory to establish consistency of generalized cross validation (GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling efficient and consistent tuning of regularization and sketching…

Statistics Theory · Mathematics 2024-03-21 Pratik Patil , Daniel LeJeune

We prove that the convex least squares estimator (LSE) attains a $n^{-1/2}$ pointwise rate of convergence in any region where the truth is linear. In addition, the asymptotic distribution can be characterized by a modified invelope process.…

Statistics Theory · Mathematics 2018-01-30 Yining Chen , Jon A. Wellner