Publication details
Optimal Choice of Nonparametric Estimates of a Density and of its Derivatives
| Authors | |
|---|---|
| Year of publication | 2002 |
| Type | Article in Periodical |
| Magazine / Source | Statistics & Decisions |
| MU Faculty or unit | |
| Citation | |
| Web | |
| Field | General mathematics |
| Keywords | asymptotic optimal estimate; bandwidth choice; canonical kernel; density estimates; derivatives estimation; kernel order choice; polynomial kernels |
| Description | Kernel smoothers are one of the most popular nonparametric functional estimates. These smoothers depend on three parameters: the bandwidth which controls the smoothness of the estimate, the form of the kernel weight function and the order of the kernel which is related to the number of derivatives assumed to exist in the nonparametric model. Because these three problems are closely related one to each other it is necessary to address them all together. In this paper we concentrate on the estimation of a density function and of its derivatives. We propose to use polynomial kernels and we construct data-driven choices for the bandwidth and the order of the kernel. We show a~theorem stating that this method for solving simultaneously the three selection problems mentioned before is asymptotically optimal in terms of Mean Integrated Squared Errors. As a by-product of our result we show an asymptotic optimality property for a~new bandwidth selector for density derivative which is quite appealing because of the simplicity of its implementation. |
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