Goodness-of-fit tests in linear EV regression with replications

Weijia Jia and Weixing Song ()
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Weijia Jia: Kansas State University
Weixing Song: Kansas State University

Metrika: International Journal for Theoretical and Applied Statistics, 2018, vol. 81, issue 4, No 2, 395-421

Abstract: Abstract This paper proposes a goodness-of-fit test for checking the adequacy of parametric forms of the regression error density functions in linear errors-in-variables regression models. Instead of assuming the distribution of the measurement error to be known, we assume that replications of the surrogates of the latent variables are available. The test statistic is based upon a weighted integrated squared distance between a nonparametric estimator and a semi-parametric estimator of the density functions of certain residuals. Under the null hypothesis, the test statistic is shown to be asymptotically normal. Consistency and local power results of the proposed test under fixed alternatives and local alternatives are also established. Finite sample performance of the proposed test is evaluated via simulation studies. A real data example is also included to demonstrate an application of the proposed test.

Keywords: Errors-in-variables; Goodness-of-fit; Replication; Consistency and local power; Primary 62F35; Secondary 62F10 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00184-018-0648-1

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