Abstract
One of the most noticeable features of sign-based statistical procedures is an opportunity to build an exact test for simple hypothesis testing of parameters in a regression model. In this article, we expanded a sing-based approach to the nonlinear case with dependent noise. The examined model is a multi-quantile regression, which makes it possible to test hypothesis not only of regression parameters, but of noise parameters as well.
Highlights
Sign-based statistical procedures [1,2,3,4] are known to be more robust for outliers than the least squares and to have a possibility to control a precise significance level for finite samples when testing a simple hypothesis
In this article, we have obtained exact and asymptotic sign-based tests for simple hypothesis (3) H0 :υ = υ0 concerning the parameters of multi-quantile regression model (1) with stationary Markov noise εt, In theorem 1, we showed that despite the nonparametric problem statement, we can obtain expressions for the gradient of likelihood for signs ∇P( s υ )
These expressions for the gradient do not depend on the parametrization method of distribution P( s υ )
Summary
Sign-based statistical procedures [1,2,3,4] are known to be more robust for outliers than the least squares and to have a possibility to control a precise significance level for finite samples when testing a simple hypothesis. Since the problem is considered in a nonparametric setting, each fixed values of parameters μ and Q correspond to a class of finite-dimensional distributions of initial process εt. In the problem of testing simple hypothesis H0 :υ = υ0 , it gives the opportunity to build a test based on the principle of the maximal likelihood ratio. We consider the problem of calculating the critical values to provide the desired significance level with any accuracy for finite samples, as well as the critical values based on the asymptotic distribution of the test statistic. The obtained tests can be used as a basis for estimating parameters υ by the principle of maximal p-values [7], as well as for the development of tests for the linear hypothesis
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