Partially linear models with p-order autoregressive skew-normal errors

Abstract

This paper proposes partially linear models with random errors following p-order autoregressive (AR) with skew-normal errors. The maximum likelihood estimators are derived from the Expectation-Maximization algorithm, which have analytic expressions for the M and E-steps. The estimation of the effective degrees of freedom concerning the nonparametric component are obtained based on a linear smoother. The conditional quantile residuals are used for the construction of simulated confidence bands to assess departures from the error assumptions, as well as autocorrelation and partial autocorrelation graphs are considered to check adequacy of the AR error structure. A simulation study is carried out to evaluate the efficiency of the EM algorithm. Finally, the methodology is illustrated by a real data set on cardiovascular mortality.