Statistical inference on restricted partially linear additive errors-in-variables models

As a useful extension of partially linear models and additive models, partially linear additive model has been paid considerable attention in recent years. This paper considers statistical inference for the semiparametric model when the covariates in the linear part are measured with additive error. To test hypothesis on the parametric component, we propose a novel test statistic based on the difference between the corrected residual sums of squares under the null and alternative hypotheses, and show that its limiting distribution is that of a weighted sum of independent standard <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\chi_{1}^{2}$</EquationSource> </InlineEquation>. We also develop an adjusted test statistic, which has an asymptotically standard chi-squared distribution. Some simulation studies are conducted to illustrate our approaches. Copyright Sociedad de Estadística e Investigación Operativa 2012