Search

This paper is concerned with inference of panel data varying-coefficient partially linear models with a one-way error structure. The model is a natural extension of the well-known panel data linear model (due to Baltagi 1995) to the setting of semiparametric regressions. The authors propose a weighted profile least squares estimator (WPLSE) and a weighted local polynomial estimator (WLPE) for the parametric and nonparametric components, respectively. It is shown that the WPLSE is asymptotically more efficient than the usual profile least squares estimator (PLSE), and that the WLPE is also asymptotically more efficient than the usual local polynomial estimator (LPE). The latter is an interesting result. According to Ruckstuhl, Welsh and Carroll (2000) and Lin and Carroll (2000), ignoring the correlation structure entirely and "pretending" that the data are really independent will result in more efficient estimators when estimating nonparametric regression with longitudinal or panel data. The result in this paper shows that this is not true when the design points of the nonparametric component have a closeness property within groups. The asymptotic properties of the proposed weighted estimators are derived. In addition, a block bootstrap test is proposed for the goodness of fit of models, which can accommodate the correlations within groups. Some simulation studies are conducted to illustrate the finite sample performances of the proposed procedures. [ABSTRACT FROM AUTHOR]

Abstract Consider a repeated measurement partially linear regression model with an unknown vector parameter ß1, an unknown function g(·), and unknown heteroscedastic error variances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of ß, we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that it improves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given to determine the number of iterations. We also show that when the number of replicates is less than or equal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of those in [2] to the case of semiparametric regressions. [ABSTRACT FROM AUTHOR]

Consider a partially linear regression model with an unknown vector parameter Β, an unknown function g(·), and unknown heteroscedastic error variances. In this paper we develop an asymptotic semiparametric generalized least squares estimation theory under some weak moment conditions. These moment conditions are satisfied by many of the error distributions encountered in practice, and our theory does not require the number of replications to go to infinity. [ABSTRACT FROM AUTHOR]

Consider a partially linear regression model with an unknown vector parameter ß, an unknown function g(·), and unknown heteroscedastic error variances. Chen, You [23] proposed a semiparametric generalized least squares estimator (SGLSE) for ß, which takes the heteroscedasticity into account to increase efficiency. For inference based on this SGLSE, it is necessary to construct a consistent estimator for its asymptotic covariance matrix. However, when there exists within-group correlation, the traditional delta method and the delete-1 jackknife estimation fail to offer such a consistent estimator. In this paper, by deleting grouped partial residuals a delete-group jackknife method is examined. It is shown that the delete-group jackknife method indeed can provide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations. This result is an extension of that in [21]. [ABSTRACT FROM AUTHOR]

Consider the partly linear regression model % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca % WG5bWaaSbaaSqaaiaadMgaaeqaaOGaeyypa0JabmiEayaafaWaaSba % aSqaaiaadMgaaeqaaOGaeqOSdiMaey4kaSIaam4zamaabmaabaGaam % iDamaaBaaaleaacaWGPbaabeaaaOGaayjkaiaawMcaaiabgUcaRiab % ew7aLnaaBaaaleaacaWGPbaabeaakiaacYcacaaMe8UaaGjbVlaayI % W7caaIXaGaeyizImQaamyAaiabgsMiJkaad6gaaaa!53DA! $$ y_{i} = {x}''_{i} \beta + g{\left( {t_{i} } \right)} + \varepsilon _{i} ,\;\;{\kern 1pt} 1 \leqslant i \leqslant n $$ , where y i?s are responses, % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca % WG4bWaaSbaaSqaaiaadMgaaeqaaOGaeyypa0ZaaeWaaeaacaWG4bWa % aSbaaSqaaiaadMgacaaIXaaabeaakiaacYcacaWG4bWaaSbaaSqaai % aadMgacaaIYaaabeaakiaacYcacqWIVlctcaGGSaGaamiEamaaBaaa % leaacaWGPbGaamiCaaqabaaakiaawIcacaGLPaaadaahaaWcbeqaaO % Gamai4gkdiIcaacaaMe8UaaGjbVlaaysW7caqGHbGaaeOBaiaabsga % caaMe8UaaGjbVlaaysW7caWG0bWaaSbaaSqaaiaadMgaaeqaaOGaey % icI4Saamivaaaa!5D82! $$ x_{i} = {\left( {x_{{i1}} ,x_{{i2}} , \cdots ,x_{{ip}} } \right)}^{\prime } \;\;\;{\text{and}}\;\;\;t_{i} \in {\cal T} $$ are known and nonrandom design points, % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca % WGubaaaa!393B! $$ {\cal T} $$ is a compact set in the real line % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaca % WGsbaaaa!3939! $$ {\cal R} $$ , ß = ( ß 1, ··· , ß p)? is an unknown parameter vector, g(·) is an unknown function and { e i} is a linear process, i.e., % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacq % aH1oqzdaWgaaWcbaGaamyAaaqabaGccaaMi8Uaeyypa0JaaGjcVpaa % qahabaGaeqiYdK3aaSbaaSqaaiaadQgaaeqaaOGaamyzamaaBaaale % aacaWGPbGaeyOeI0IaamOAaaqabaGccaGGSaGaaGjcVlaaysW7cqaH % ipqEdaWgaaWcbaGaaGimaaqabaGccaaMi8Uaeyypa0JaaGjcVlaaig % dacaGGSaGaaGjbVlaayIW7daaeWbqaamaaemaabaGaeqiYdK3aaSba % aSqaaiaadQgaaeqaaaGccaGLhWUaayjcSdGaeyipaWJaeyOhIukale % aacaWGQbGaeyypa0JaaGimaaqaaiabg6HiLcqdcqGHris5aaWcbaGa % amOAaiabg2da9iaaicdaaeaacqGHEisPa0GaeyyeIuoaaaa!6ABD! $$ \varepsilon _{i} {\kern 1pt} = {\kern 1pt} {\sum\limits_{j = 0}^\infty {\psi _{j} e_{{i - j}} ,{\kern 1pt} \;\psi _{0} {\kern 1pt} = {\kern 1pt} 1,\;{\kern 1pt} {\sum\limits_{j = 0}^\infty {{\left| {\psi _{j} } \right|} < \infty } }} } $$ , where e j are i.i.d. random variables with zero mean and variance % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacq % aHdpWCdaqhaaWcbaGaamyzaaqaaiaaikdaaaaaaa!3BF8! $$ \sigma ^{2}_{e} $$ . Drawing upon B-spline estimation of g(·) and least squares estimation of ß, we construct estimators of the autocovariances of { e i}. The uniform strong convergence rate of these estimators to their true values is then established. These results not only are a compensation for those of [23], but also have some application in modeling error structure. When the errors { e i} are an ARMA process, our result can be used to develop a consistent procedure for determining the order of the ARMA process and identifying the non-zero coeffcients of the process. Moreover, our result can be used to construct the asymptotically effcient estimators for parameters in the ARMA error process. [ABSTRACT FROM AUTHOR]

The empirical upper percentage points of the null distribution of a Kolmogorov-Smirnov type test for checking linearity in autoregressive models are tabulated in this paper, and the good power property of the test is demonstrated. [ABSTRACT FROM AUTHOR]