Asymptotic properties for the estimators in heteroscedastic semiparametric EV models with α-mixing errors

ABSTRACT

In this paper, the heteroscedastic semiparametric errors-in-variables (EV) model, $y_i={\xi }_i\text{β}+g\left(t_i\right)+{ϵ}_i,x_i={\xi }_i+{\mu }_i,1\le i\le n$, is considered, where ${ϵ}_i={\sigma }_i{e}_i,{\sigma }_i^2=f\left(u_i\right)$, β is an unknown parameter to be estimated and $g(\cdot )$ and $f(\cdot )$ are unknown functions to be estimated. Under some suitable conditions, asymptotic properties for the estimators of β, $g(\cdot )$ and $f(\cdot )$ are presented based on α-mixing random errors. In addition, finite sample behavior of the estimators is provided via simulations to verify the validity of the theoretical results.

Keywords:

• Semiparametric EV regression model
• α-mixing errors
• least squares estimator
• strong consistency

2010 Mathematical Subject Classifications:

• 62J12
• 62G20

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Supported by the National Natural Science Foundation of China (11671012, 11871072), the Natural Science Foundation of Anhui Province (1908085QA01, 1908085QA07), the Provincial Natural Science Research Project of Anhui Colleges (KJ2019A0003) and the Project on Reserve Candidates for Academic and Technical Leaders of Anhui Province (2017H123).