Adaptive density estimation based on real and artificial data
| Autor: | Tina Felber, Michael Kohler, Adam Krzyżak |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
Independent and identically distributed random variables Variable kernel density estimation Kernel (statistics) Statistics Kernel density estimation Kernel regression Applied mathematics Convex combination Density estimation Statistics Probability and Uncertainty Multivariate kernel density estimation Mathematics |
| Zdroj: | Journal of Nonparametric Statistics. 27:1-18 |
| ISSN: | 1029-0311 1048-5252 |
| Popis: | Let X, X1, X2, … be independent and identically distributed ℝd-valued random variables and let m:ℝd→ℝ be a measurable function such that a density f of Y=m(X) exists. The problem of estimating f based on a sample of the distribution of (X,Y) and on additional independent observations of X is considered. Two kernel density estimates are compared: the standard kernel density estimate based on the y-values of the sample of (X,Y), and a kernel density estimate based on artificially generated y-values corresponding to the additional observations of X. It is shown that under suitable smoothness assumptions on f and m the rate of convergence of the L1 error of the latter estimate is better than that of the standard kernel density estimate. Furthermore, a density estimate defined as convex combination of these two estimates is considered and a data-driven choice of its parameters (bandwidths and weight of the convex combination) is proposed and analysed. |
| Databáze: | OpenAIRE |
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