The Generalization of Student’s Ratio

By H. Hotelling. 1931

Subfields: Statistics and Probability, Statistical Learning Theory

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Citations in the corpus

On the (Statistical) Detection of Adversarial Examples (2017, background): “Instead of simply having inputs classified in a wrong class, the attacker can also target a particular class.”
Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing (2015, methodology): “Two-sample testing is a fundamental decision-theoretic problem, having a long history in statistics - for example, the past century has seen a wide adoption of the t-statistic by Hotelling [1931] to decide if two samples have different population means (MDA).”
Statistical Query Lower Bounds for Robust Estimation of High-Dimensional Gaussians and Gaussian Mixtures (2016, methodology): “) The classical test for this task is Hotelling’s T-squared statistic [47], which is unfortunately not defined when the sample size is smaller than the dimen-”
Robust Trend Inference with Series Variance Estimator and Testing-Optimal Smoothing Parameter (2011, background): “…k s iidN(0; Ip) and PK k=1 k 0 k is a Wishart distribution Wp(Ip;K): Hence the limiting distribution of FT;OLS is Hotelling s T-square distribution (Hotelling (1931)): FT;OLS !d T 2(p;K): Since for K p; K p+ 1 pK T 2(p;K) s Fp;K p+1; we have (K p+ 1) pK FT;OLS !d Fp;K p+1 := 2p=p 2K p+1= (K p+ 1)…”
On the High-dimensional Power of Linear-time Kernel Two-Sample Testing under Mean-difference Alternatives (2014, background): “1); Simaika (1941); Anderson (1958); Salaevskii (1971)) that if P;Q are Gaussians, then the uniformly most powerful test in the xed-dimension setting under fairly general conditions, is the T-test by Hotelling (1931) : T H:= (m P m Q) TS 1(m P m Q) where m P;m Qand Sare the usual empirical estimator”
Classification Accuracy as a Proxy for Two Sample Testing (2016, background): “…, Q are Gaussians with equal covariance, this boils down to Two-sample testing is a fundamental decision-theoretic problem, having a long history in statistics – for example, the past century has seen a wide adoption of the t-statistic by [4] to decide if two samples have diﬀerent population means.”
Data-driven Soft Sensors in the process industry (2009, methodology): “Commonly, process monitoring techniques are based on multivariate statistical techniques like PCA, or more precisely on Hotelling's T 2 (Hotelling, 1931) and Q-statistics (Jackson and Mudholkar, 1979).”