Second Order Approximation in the Partially Linear Regression Model
Copyright policy )Second Order Approximation in the Partially Linear Regression Model
Summary: We examine the second order properties of various quantities of interest in the partially linear regession model. We obtain a stochastic expansion with remainder \(o_P (n^{-2 \mu})\), where \(\mu < 1/2\), for the standardized semiparametric least squares estimator, a standard error estimator, and a studentized statistic. We use the second order expansions to correct the standard error estimates for second order effects, and to define a method of bandwidth choice. A Monte Carlo experiment provides favorable evidence on our method of bandwidth choice.
error estimator, Linear regression; mixed models, Asymptotic distribution theory in statistics, bandwidth choice, local polynomial, asymptotic expansions, studentized statistic, second order effects, Density estimation, second order properties, semiparameter least squares estimator, partially linear regession model, stochastic expansion, second order expansions, Monte Carlo
error estimator, Linear regression; mixed models, Asymptotic distribution theory in statistics, bandwidth choice, local polynomial, asymptotic expansions, studentized statistic, second order effects, Density estimation, second order properties, semiparameter least squares estimator, partially linear regession model, stochastic expansion, second order expansions, Monte Carlo
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