The Consistency of Estimators in a Heteroscedastic Partially Linear Model with <i>ρ</i><sup>−</sup>-Mixing Errors
This paper studies a heteroscedastic partially linear model based on <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>ρ</mi> <mo>−</mo></msup></mrow></semantics></math></inline-formula>...
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doaj-4dcf874d7b6c482fb35b63f8870641fe2020-11-25T03:59:50ZengMDPI AGSymmetry2073-89942020-07-01121188118810.3390/sym12071188The Consistency of Estimators in a Heteroscedastic Partially Linear Model with <i>ρ</i><sup>−</sup>-Mixing ErrorsYu Zhang0Xinsheng Liu1State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaDepartment of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaThis paper studies a heteroscedastic partially linear model based on <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>ρ</mi> <mo>−</mo></msup></mrow></semantics></math></inline-formula>-mixing random errors, stochastically dominated and with zero mean. Under some suitable conditions, the strong consistency and <inline-formula> <math display="inline"> <semantics> <mi>p</mi></semantics></math></inline-formula>-th <inline-formula> <math display="inline"> <semantics> <mrow> <mrow> <mo>(</mo> <mrow> <mi>p</mi> <mo>></mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> mean consistency of least squares (LS) estimators and weighted least squares (WLS) estimators for the unknown parameter are investigated, and the strong consistency and <inline-formula> <math display="inline"> <semantics> <mi>p</mi></semantics></math></inline-formula>-th <inline-formula> <math display="inline"> <semantics> <mrow> <mrow> <mo>(</mo> <mrow> <mi>p</mi> <mo>></mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> mean consistency of the estimators for the non-parametric component are also studied. These results include the corresponding ones of independent, negatively associated (NA), and <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>ρ</mi> <mo>*</mo></msup></mrow></semantics></math></inline-formula>-mixing random errors as special cases. At last, two simulations are presented to support the theoretical results.https://www.mdpi.com/2073-8994/12/7/1188<i>ρ</i><sup>−</sup>-mixing random variablesheteroscedasticpartially linear modelLS estimatorsWLS estimatorsstrong consistency |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Yu Zhang Xinsheng Liu |
spellingShingle |
Yu Zhang Xinsheng Liu The Consistency of Estimators in a Heteroscedastic Partially Linear Model with <i>ρ</i><sup>−</sup>-Mixing Errors Symmetry <i>ρ</i><sup>−</sup>-mixing random variables heteroscedastic partially linear model LS estimators WLS estimators strong consistency |
author_facet |
Yu Zhang Xinsheng Liu |
author_sort |
Yu Zhang |
title |
The Consistency of Estimators in a Heteroscedastic Partially Linear Model with <i>ρ</i><sup>−</sup>-Mixing Errors |
title_short |
The Consistency of Estimators in a Heteroscedastic Partially Linear Model with <i>ρ</i><sup>−</sup>-Mixing Errors |
title_full |
The Consistency of Estimators in a Heteroscedastic Partially Linear Model with <i>ρ</i><sup>−</sup>-Mixing Errors |
title_fullStr |
The Consistency of Estimators in a Heteroscedastic Partially Linear Model with <i>ρ</i><sup>−</sup>-Mixing Errors |
title_full_unstemmed |
The Consistency of Estimators in a Heteroscedastic Partially Linear Model with <i>ρ</i><sup>−</sup>-Mixing Errors |
title_sort |
consistency of estimators in a heteroscedastic partially linear model with <i>ρ</i><sup>−</sup>-mixing errors |
publisher |
MDPI AG |
series |
Symmetry |
issn |
2073-8994 |
publishDate |
2020-07-01 |
description |
This paper studies a heteroscedastic partially linear model based on <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>ρ</mi> <mo>−</mo></msup></mrow></semantics></math></inline-formula>-mixing random errors, stochastically dominated and with zero mean. Under some suitable conditions, the strong consistency and <inline-formula> <math display="inline"> <semantics> <mi>p</mi></semantics></math></inline-formula>-th <inline-formula> <math display="inline"> <semantics> <mrow> <mrow> <mo>(</mo> <mrow> <mi>p</mi> <mo>></mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> mean consistency of least squares (LS) estimators and weighted least squares (WLS) estimators for the unknown parameter are investigated, and the strong consistency and <inline-formula> <math display="inline"> <semantics> <mi>p</mi></semantics></math></inline-formula>-th <inline-formula> <math display="inline"> <semantics> <mrow> <mrow> <mo>(</mo> <mrow> <mi>p</mi> <mo>></mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> mean consistency of the estimators for the non-parametric component are also studied. These results include the corresponding ones of independent, negatively associated (NA), and <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>ρ</mi> <mo>*</mo></msup></mrow></semantics></math></inline-formula>-mixing random errors as special cases. At last, two simulations are presented to support the theoretical results. |
topic |
<i>ρ</i><sup>−</sup>-mixing random variables heteroscedastic partially linear model LS estimators WLS estimators strong consistency |
url |
https://www.mdpi.com/2073-8994/12/7/1188 |
work_keys_str_mv |
AT yuzhang theconsistencyofestimatorsinaheteroscedasticpartiallylinearmodelwithirisupsupmixingerrors AT xinshengliu theconsistencyofestimatorsinaheteroscedasticpartiallylinearmodelwithirisupsupmixingerrors AT yuzhang consistencyofestimatorsinaheteroscedasticpartiallylinearmodelwithirisupsupmixingerrors AT xinshengliu consistencyofestimatorsinaheteroscedasticpartiallylinearmodelwithirisupsupmixingerrors |
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