Related papers: A Higher-Order Kolmogorov-Smirnov Test
In this paper, we analyze a multivariate counterpart of the generalized weighted Kolmogorov-Smirnov statistic, which is the supremum of weighted locally stationary chi-square process over non-compact interval. The boundedness and the exact…
We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…
We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions $P_0$ and $P_1$ and we would like to decide which hypothesis is true using a sequential test. It…
We consider the residual empirical process in random design regression with long memory errors. We establish its limiting behaviour, showing that its rates of convergence are different from the rates of convergence for to the empirical…
We present nonasymptotic concentration inequalities for sums of independent and identically distributed random variables that yield asymptotic strong Gaussian approximations of Koml\'os, Major, and Tusn\'ady (KMT) [1975,1976]. The constants…
We consider a binary statistical hypothesis testing problem, where $n$ independent and identically distributed random variables $Z^n$ are either distributed according to the null hypothesis $P$ or the alternate hypothesis $Q$, and only $P$…
The integrated conditional moment (ICM) test is a classical and widely used method for assessing the adequacy of regression models. Although it performs well in fixed-dimension settings, its behavior changes dramatically when the predictor…
We introduce an estimation method for the scaled skewness coefficient of the sample mean of short and long memory linear processes. This method can be extended to estimate higher moments such as curtosis coefficient of the sample mean. Also…
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…
We give simplify the proofs of the 2 results in Marius Zimand's paper "Kolmogorov complexity version of Slepian-Wolf coding, proceedings of STOC 2017, p22--32". The first is a universal polynomial time compression algorithm: on input…
We establish inequalities that compare the p-Wasserstein distance to distances which are built as suprema of box measures. More precisely, when the measures are supported on $[0,1]^d$, we obtain sharp upper-bounds of the $p$-Wasserstein…
Inference on the parametric part of a semiparametric model is no trivial task. If one approximates the infinite dimensional part of the semiparametric model by a parametric function, one obtains a parametric model that is in some sense…
We propose a new asymptotic test for the separability of a covariance matrix. The null distribution is valid in wide matrix elliptical model that includes, in particular, both matrix Gaussian and matrix $t$-distribution. The test is fast to…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
First and second kind modifications of usual confidence intervals for estimating the expectation and of usual local alternative parameter choices are introduced in a way such that the asymptotic behavior of the true non-covering…
This paper deals with order identification for nested models in the i.i.d. framework. We study the asymptotic efficiency of two generalized likelihood ratio tests of the order. They are based on two estimators which are proved to be…
The Universal Similarity Metric (USM) has been demonstrated to give practically useful measures of "similarity" between sequence data. Here we have used the USM as an alternative distance metric in a K-Nearest Neighbours (K-NN) learner to…
This paper investigates improved testing inferences under a general multivariate elliptical regression model. The model is very flexible in terms of the specification of the mean vector and the dispersion matrix, and of the choice of the…
A class of nonparametric two-sample tests has been proposed in this article. As a generalization of the original \v{S}id\'aks' test, the proposed test statistic is developed as the sum of the maximal precedence and maximal exceedance…
Hidden Markov models (HMMs) are one of the most widely used statistical methods for analyzing sequence data. However, the reporting of output from HMMs has largely been restricted to the presentation of the most-probable (MAP) hidden state…