Berry-esseen Bounds In A Partly Linear EV Model With Heteroscedastic Errors

The partly linear regression model includes both parametric and non-parametric parts, so it combines the advantages of both and overcome their faults. Due to the partly linear EV mo-del has applied in many fields such as economics, surveying and so on, so it has attracted incr-easing attention by statisticians. Although, it has get a lot of results, but the Berry-Esseen bou-nds are not researched.In this paper, we investigate a fixed design heteroscedastic partly linear errors-in-variabl-es(EV) model, yi=xiβ+g(ti)+σiεi,Xi= xi+Si,i=1,2,...,n, where the random errors{εi,i= 1,2,...,n}with Eεi=O and E(εi2)= 1.{xi}are the measured err-ors and can not directly observed. Instead,{xi} are get through Xi= xi+Si and{Si} are the mea-surement errors with E Si= O and Var(Si)= σ2S.Further,{Si} are independent identically distrib-ution random sequence and are assumed to be independent of{εi} for each i.In the paper, using weighted functions and modified least-squares methods, we investiga-te a fixed design heteroscedastic partly linear errors-in-variables(EV) model and get the esti-mators of β, g (t) and σi2.Further, Berry-Esseen bounds of the estimators are given.The paper is divided into two parts as follows.In the first part, we obtains Berry-Esseen bounds of the parametric parts and nonparam-etric parts under α-mixing sequence errors, and generalizes some conclusions such as Zhang and Liang(2011),Yang(2007),Li and Guo(2009) and so on.In the second part, we gets Berry-Esseen bounds of a heteroscedastic part under in dep-endence sequence errors, and generalizes the conclusion of Zhang and Liang(2011).