Asymptotic properties of wavelet estimators in partially linear errors-in-variables models with long-memory errors

In this paper, we consider the generalized semiparametric model (GSPM) y i = h(x T i β) + f (t i) + e i , 1≤ i ≤ n, where h(•) is a known function, e i are dependent errors. We obtain an estimator of the parametric component β for the model by a difference-based M-estimator. In addition, we prove the asymptotic normality of the proposed estimator and investigate the weak convergence rate of the wavelet estimator of f (•). Furthermore, we apply these results to a partially linear model with dependent errors.

show abstract

“…Condition (C5) is quite mild and can be easily satisfied. Conditions (C6)-(C9) are used by Hu et al [38].…”

Section: Difference-based M-estimationmentioning

confidence: 99%

Difference-based M-estimator of generalized semiparametric model with NSD errors

Zeng

Liu

2019

J Inequal Appl

View full text Add to dashboard Cite

show abstract

“…Condition (C1) is standard and often imposed in the estimator of partial linear models, once can refer to Zhao et al [ 31 ]. Conditions (C2)–(C5) are used by Hu et al [ 29 ]. Therefore, our conditions are very mild and can easily be satisfied.…”

Section: Preliminary Conditions and Lemmasmentioning

confidence: 99%

“…Choose the Daubechies scaling function as in Hu et al [ 29 ]. Figures 3 and 4 show that the distribution of is closer and closer to with the increasing sample size.…”

Section: A Simulation Examplementioning

confidence: 99%

See 1 more Smart Citation

A difference-based approach in the partially linear model with dependent errors

Zeng

Liu

2018

J Inequal Appl

View full text Add to dashboard Cite

We study asymptotic properties of estimators of parameter and non-parameter in a partially linear model in which errors are dependent. Using a difference-based and ordinary least square (DOLS) method, the estimator of an unknown parametric component is given and the asymptotic normality of the DOLS estimator is obtained. Meanwhile, the estimator of a nonparametric component is derived by the wavelet method, and asymptotic normality and the weak convergence rate of the wavelet estimator are discussed. Finally, the performance of the proposed estimator is evaluated by a simulation study.

show abstract

Robust Nonparametric Function Estimation for Errors-in-variables Models

Yuan

Cui

2020

Acta Math. Appl. Sin. Engl. Ser.

View full text Add to dashboard Cite

Asymptotic properties of wavelet estimators in partially linear errors-in-variables models with long-memory errors

Cited by 3 publications

References 43 publications

Difference-based M-estimator of generalized semiparametric model with NSD errors

Difference-based M-estimator of generalized semiparametric model with NSD errors

A difference-based approach in the partially linear model with dependent errors

Robust Nonparametric Function Estimation for Errors-in-variables Models

Contact Info

Product

Resources

About