Sample and Hypothesis Testing

Large Sample Estimation and Hypothesis Testing*

Two Sample Hypothesis Testing for Functional Data

A nonparametric testing procedure is proposed for testing the hypothesis that two samples of curves observed at discrete grids and with noise have the same underlying distribution. Our method relies on representing the curves using a common orthogonal basis expansion. The approach reduces the dimension of the testing problem in a way that enables the application of traditional nonparametric uni...

Sample Complexity of Testing the Manifold Hypothesis

The hypothesis that high dimensional data tends to lie in the vicinity of a low dimensional manifold is the basis of a collection of methodologies termed Manifold Learning. In this paper, we study statistical aspects of the question of fitting a manifold with a nearly optimal least squared error. Given upper bounds on the dimension, volume, and curvature, we show that Empirical Risk Minimizatio...

HYPOTHESIS TESTING FOR AN EXCHANGEABLE NORMAL DISTRIBUTION

Consider an exchangeable normal vector with parameters ????2, and ?. On the basis of a vector observation some tests about these parameters are found and their properties are discussed. A simulation study for these tests and a few nonparametric tests are presented. Some advantages and disadvantages of these tests are discussed and a few applications are given.

LINEAR HYPOTHESIS TESTING USING DLR METRIC

Several practical problems of hypotheses testing can be under a general linear model analysis of variance which would be examined. In analysis of variance, when the response random variable Y , has linear relationship with several random variables X, another important model as analysis of covariance can be used. In this paper, assuming that Y is fuzzy and using DLR metric, a method for testing ...