Maximal Smoothing
| Authors | |
|---|---|
| Year of publication | 2003 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Electrical Engineering |
| MU Faculty or unit | |
| Citation | |
| Field | Applied statistics, operation research |
| Keywords | Kernel; density; estimate; bandwidth; maximal smoothing principle |
| Description | Nonparametric density estimates attempt to reconstruct the probability density from which a random sample has come. A large part of the literature on density estimation is concerned with the issue of how to choose the degree of smoothness of the estimate. This paper describes the principle of maximal smoothing. The formula for asymptotically optimal bandwidth $h_f$ with respect to MISE is well-known. This formula depends on $\integral(f^{(k)}(x))^2dx$ reciprocally, where $f$ is an unknown probability density function. Our goal will be to make this integral as small as possible. Then we obtain the upper boundary for the bandwidth. The prsented paper is dealing with this procedure. |
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