Delete-group Jackknife Estimate in
Partially Linear Regression Models with Heteroscedasticity |
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Authors: | Email author" target="_blank">Jin-hong?YouEmail author Gemai?Chen |
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Institution: | (1) Department of Biostatistics, University of North Carolina, Chapel Hill, NC, 27599-7420, U.S.A.;(2) Department of Mathematics & Statistics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4 |
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Abstract: | Abstract
Consider a partially linear regression model with an
unknown vector parameter ,
an unknown function g(·), and
unknown heteroscedastic error variances. Chen,
You23] proposed a semiparametric
generalized least squares estimator (SGLSE) for
, 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]. |
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Keywords: | Partially linear regression model asymptotic variance heteroscedasticity delete-group jackknife semiparametric generalized least squares estimator |
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