Heuristic estimation of probability densities
| Autor: | William H. Fellner |
|---|---|
| Rok vydání: | 1974 |
| Předmět: |
Statistics and Probability
Location parameter Applied Mathematics General Mathematics Density estimation Conditional probability distribution Empirical probability Agricultural and Biological Sciences (miscellaneous) Joint probability distribution Prior probability Probability distribution Applied mathematics Statistics Probability and Uncertainty General Agricultural and Biological Sciences Random variable Mathematics |
| Zdroj: | Biometrika. 61:485-492 |
| ISSN: | 1464-3510 0006-3444 |
| DOI: | 10.1093/biomet/61.3.485 |
| Popis: | Most methods for the estimation of probability densities that have appeared in the literature involve a largely uniform treatment of the data. These include the common histogram, as well as the window method (Rosenblatt, 1956; Parzen, 1962; Bartlett, 1963; Watson & Leadbetter, 1963), the method of Fourier expansion (Tarter and Kronmal, 1968, 1970; Watson, 1969), and the fitting by splines (Boneva, Kendall & Stefanov, 1971). The use of such methods commonly requires the acceptance of a certain amount of roughness in the tails in order to avoid excessive smoothing of the central portion of the estimate. Nonuniform approaches to the estimation of density have been proposed by Whittle (1958) and by Good & Gaskins (1971). Whittle's method requires specification of the firstand second-order moments of the prior distribution of densities. The likelihood approach of Good & Gaskins produces a more general form of estimate, and the authors reduce the problem by constructing a plausible two-parameter family of prior distributions. In this paper, it is assumed that only the first-order moments of the prior distribution of densities are known. The convention of hypothesis testing is used to compensate for the lack of information about the higher-order moments. The method synthesizes the work of Whittle and of Tarter and Kronmal. In ? 2, it is shown that an estimate of the Tarter-Kronmal type is appropriate when the data have been transformed so that the first-order moments of the prior distribution are the uniform (0, 1) density. In ? 3, a heuristic approach related to hypothesis testing is used for the construction of the estimate. Application of the procedure is described in ? 4. |
| Databáze: | OpenAIRE |
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