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## Details

Document Type: | Book |
---|---|

All Authors / Contributors: |
Tom Leonard; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER. |

OCLC Number: | 227533351 |

Description: | 17 p. |

### Abstract:

The problem addressed concerns the estimation of a p-dimensional multivariate density, given only a set of n observation vectors, together with information that the density function is likely to be reasonably smooth. A solution is proposed which employs up to n + 1/2 p(p+1) smoothing parameters, all of which may be estimated by their posterior means. This avoids the well-known difficulties, associated with even one-dimensional kernel estimators, of estimating the bandwidth or smoothing parameter by a mathematical procedure. The posterior mean value function, unconditional upon the smoothing parameters, turns out to be a data-based mixture of multivariate t-distributions. The corresponding estimate of the sampling covariance matrix may be viewed as a shrinkage estimator of the Bayes-Stein type. The results involve some finite series which may be evaluated by straightforward simulation procedure. (Author).

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## Similar Items

### Related Subjects:(18)

- Statistics and Probability.
- Estimates.
- Bayes theorem.
- Functions.
- Density.
- Mean.
- Value.
- Analysis of variance.
- Data bases.
- Mathematical analysis.
- Multivariate analysis.
- Shrinkage.
- Mixtures.
- Density functions
- Smoothing parameters
- Mean value function
- Kernel estimators
- Bayes estimation