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Register a new userRank tests for corrupted linear models
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Jana Jure\\v{c}kov\\'a
Publication date
2015
fields
Mathematical Statistics
and research's language is
English
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For some variants of regression models, including partial, measurement error or error-in-variables, latent effects, semi-parametric and otherwise corrupted linear models, the classical parametric tests generally do not perform well. Various modifications and generalizations considered extensively in the literature rests on stringent regularity assumptions which are not likely to be tenable in many applications. However, in such non-standard cases, rank based tests can be adapted better, and further, incorporation of rank analysis of covariance tools enhance their power-efficiency. Numerical studies and a real data illustration show the superiority of rank based inference in such corrupted linear models.
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Let $(Y,(X_i)_{iinmathcal{I}})$ be a zero mean Gaussian vector and $V$ be a subset of $mathcal{I}$. Suppose we are given $n$ i.i.d. replications of the vector $(Y,X)$. We propose a new test for testing that $Y$ is independent of $(X_i)_{iin mathcal{I}backslash V}$ conditionally to $(X_i)_{iin V}$ 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 $Y$ and applies in a high-dimensional setting. It straightforwardly extends to test the neighbourhood of a Gaussian graphical model. The procedure is based on a model of Gaussian regression with random Gaussian covariates. We give non asymptotic properties of the test and we prove that it is rate optimal (up to a possible $log(n)$ factor) over various classes of alternatives under some additional assumptions. Besides, it allows us to derive non asymptotic minimax rates of testing in this setting. Finally, we carry out a simulation study in order to evaluate the performance of our procedure.
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