An Infinite-Dimensional Approximation for Nearest Neighbor Goodness of Fit Tests

The Comparison Between Goodness of Fit Tests for Copula

‎Copula functions as a model can show the relationship between variables‎. ‎Appropriate copula function for a specific application is a function that shows the dependency between data in a best way‎. ‎Goodness of fit tests theoretically are the best way in selection of copula function‎. ‎Different ways of goodness of fit for copula exist‎. ‎In this paper we will examine the goodness of fit test...

Goodness-of-fit Tests for high-dimensional Gaussian linear models

Let (Y, (Xi)1≤i≤p) be a real zero mean Gaussian vector and V be a subset of {1, . . . , p}. Suppose we are given n i.i.d. replications of this vector. We propose a new test for testing that Y is independent of (Xi)i∈{1,...p}\V conditionally to (Xi)i∈V against the general alternative that it is not. This procedure does not depend on any prior information on the covariance of X or the variance of...

Goodness of fit tests for high-dimensional linear models

In this work we propose a framework for constructing goodness of fit tests in both low and high-dimensional linear models. We advocate applying regression methods to the scaled residuals following either an ordinary least squares or Lasso fit to the data, and using some proxy for prediction error as the final test statistic. We call this family Residual Prediction (RP) tests. We show that simul...

Random projections and goodness-of-fit tests in infinite-dimensional spaces

In this paper we provide conditions under which a distribution is determined by just one randomly chosen projection. Then we apply our results to construct goodnessof-fit tests for the one and two-sample problems. We include some simulations as well as the application of our results to a real data set. Our results are valid for every separable Hilbert space.

On Goodness-of-fit Tests