An analog of Bickel–Rosenblatt test for fitting an error density in the two phase linear regression model View Full Text


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Article Info

DATE

2022-02-23

AUTHORS

Fuxia Cheng, Hira L. Koul

ABSTRACT

This paper discusses a test of goodness-of-fit of a known error density in a two phase linear regression model in the case jump size at the phase transition point is fixed or tends to zero with the increasing sample size. The proposed test is based on an integrated square difference between a nonparametric error density estimator obtained from the residuals and its expected value under the null error density when the underlying regression parameters are known. The paper establishes the asymptotic normality of the proposed test statistic under the null hypothesis and under certain global L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_2$$\end{document} alternatives. The asymptotic null distribution of the test statistic is the same as in the case of the known regression parameters. Under the chosen alternatives, unlike in the linear autoregressive time series models with known intercept, it depends on the parameters and their estimates in general. We also describe the analogous results for the self-exciting threshold autoregressive time series model of order 1. More... »

PAGES

1-30

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00184-022-00861-6

DOI

http://dx.doi.org/10.1007/s00184-022-00861-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1145783252


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