Bootstrap Bandwidth and Kernel Order Selection for Density Weighted Averages
نویسنده
چکیده
Abstract: Density weighted average is a nonparametric quantity expressed by expectation of a function of random variables with density weight. It is associated with parametric components of some semiparametric models, and we are concerned with an estimator of this quantity. Asymptotic properties of semiparametric estimators have been studied in econometrics since the end of 1980’s and it is now widely recognized that they are n consistent in many cases. Many of them involve nonparametric estimates of unknown density or regression function but they are biased estimators for the true functions. Because of this, we typically need to use some bias reduction technique in the nonparametric estimates for n consistency of the semiparametric estimators. When we use a kernel estimator, a standard way is to take a higher order kernel function. For density estimation, the higher the kernel order is, the less becomes the bias without changing the order of variance in theory. However, it is also known that higher order kernels can inflate the variance which may cause the result that the mean squared error with very high order kernel becomes larger than that with low order kernel in small sample. This paper propose to select the bandwidth and kernel order by minimizing bootstrap mean squared error for a plug-in estimator of density weighted averages. We show standard bootstrap does not work at all for bias approximation as in density estimation, but smoothed bootstrap is useful in our problem if suitably transformed.
منابع مشابه
Bootstrap Bandwidth Selection
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