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

Fuxia Cheng () and Hira L. Koul ()
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Fuxia Cheng: Illinois State University
Hira L. Koul: Michigan State University

Metrika: International Journal for Theoretical and Applied Statistics, 2023, vol. 86, issue 1, No 2, 27-56

Abstract: 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 $$L_2$$ L 2 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.

Keywords: Fixed jump size; SETAR time series; Asymptotic normality; $$L_2$$ L 2 global alternatives; Primary 62J02; Secondary 62G10; 62G20 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00184-022-00861-6

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