A goodness-of-fit test for a polynomial errors-in-variables model

Abstract

Polynomial regression models with errors in variables are considered. A goodness-of-fit test is constructed, which is based on an adjusted least-squares estimator and modifies the test introduced by Zhu et al. for a linear structural model with normal distributions. In the present paper, the distributions of errors are not necessarily normal. The proposed test is based on residuals, and it is asymptotically chi-squared under null hypothesis. We discuss the power of the test and the choice of an exponent in the exponential weight function involved in test statistics.

Consistent estimation and testing in heteroscedastic polynomial errors-in-variables models

“…2, goodness-of-fit should be checked. In future work we will address this point, elaborating a test similar to one constructed by Cheng and Kukush (2004). The power of the tests in Sect.…”

“…Indeed, this problem seems not even being mentioned, as can be inferred from important references on the subject, such as Chan and Mak (1985), Fuller (1987), Moon and Gunst (1993), Cheng and Schneeweiss (1998), Schneeweiss and Nittner (2001), Cheng and Schneeweiss (2002), Kuha and Temple (2003), and Kukush et al (2005). A goodness-of-fit test is presented in Cheng and Kukush (2004). The cases focused are the case σ 2 u known (most frequent), the knowledge of the ratio of variances (σ 2 e /σ 2 u ) (Chan and Mak, 1985), and the situation where the covariance matrix in (3) is fully or partially known, with σ eu = cov(e i , u i ) not necessarily null.…”

Consistent estimator in multivariate errors-in-variables model in the case of unknown error covariance structure

“…In this section, we also assume that m ( k ) vary according to (9). Moreover, we assume that these numbers increase regularly in the following sense:…”

An Adaptive-to-Model Test for Parametric Single-Index Errors-in-Variables Models

“…A score-type lack-of-fitness test was proposed based on this fact. This testing procedure has been extended to polynomial EiV models by Cheng & Kukush (2004) and Zhu et al (2003) independently. Hall & Ma (2007) proposed a test based on deconvolution methods assuming that the distribution of the measurement error vector U is known.…”