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The asymptotic efficiency of a generalized likelihood ratio test proposed by Cox is studied under the large deviations framework for error probabilities developed by Chernoff. In particular, two separate parametric families of hypotheses are considered [Cox, 1961, 1962]. The significance level is set such that the maximal type I and type II error probabilities for the generalized likelihood ratio test decay exponentially fast with the same rate. We derive the analytic form of such a rate that is also known as the Chernoff index [Chernoff, 1952], a relative efficiency measure when there is no preference between the null and the alternative hypotheses. We further extend the analysis to approximate error probabilities when the two families are not completely separated. Discussions are provided concerning the implications of the present result on model selection.
We study the absolute penalized maximum partial likelihood estimator in sparse, high-dimensional Cox proportional hazards regression models where the number of time-dependent covariates can be larger than the sample size. We establish oracle inequali
Two-sample tests have been one of the most classical topics in statistics with wide application even in cutting edge applications. There are at least two modes of inference used to justify the two-sample tests. One is usual superpopulation inference
We consider the problem of estimating the predictive density of future observations from a non-parametric regression model. The density estimators are evaluated under Kullback--Leibler divergence and our focus is on establishing the exact asymptotics
Few methods in Bayesian non-parametric statistics/ machine learning have received as much attention as Bayesian Additive Regression Trees (BART). While BART is now routinely performed for prediction tasks, its theoretical properties began to be under
We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective equation d