On Local U-Statistic Processes and the Estimation of Densities of Functions of Several Sample Variables
A notion of local U-statistic process is introduced and central limit theorems in various norms are obtained for it. This involves the development of several inequalities for U-processes that may be useful in other contexts. This local U-statistic process is based on an estimator of the density of a...
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| Veröffentlicht in: | The Annals of statistics 2007-07, Vol.35 (3), p.1105-1145 |
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| container_title | The Annals of statistics |
| container_volume | 35 |
| creator | Giné, Evarist Mason, David M. |
| description | A notion of local U-statistic process is introduced and central limit theorems in various norms are obtained for it. This involves the development of several inequalities for U-processes that may be useful in other contexts. This local U-statistic process is based on an estimator of the density of a function of several sample variables proposed by Frees [J. Amer. Statist. Assoc. 89 (1994) 517-525] and, as a consequence, uniform in bandwidth central limit theorems in the sup and in the $L_{p}$ norms are obtained for these estimators. |
| doi_str_mv | 10.1214/009053607000000154 |
| format | Article |
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| source | Project Euclid_欧几里德项目期刊; JSTOR Mathematics and Statistics; Free E-Journal (出版社公開部分のみ）; JSTOR |
| subjects | 60F05 60F15 62E20 62G30 Banach space Central limit theorem central limit theorems Covariance Density Density estimation empirical process Estimating techniques Estimators Exact sciences and technology General topics kernel density estimation Limit theorems Mathematical constants Mathematical functions Mathematical models Mathematics Nonparametric inference Perceptron convergence procedure Probability and statistics Probability theory and stochastic processes Probability theory on algebraic and topological structures Random variables Sciences and techniques of general use Statistical methods Statistics Studies Topics in Nonparametric Statistics U-statistics |
| title | On Local U-Statistic Processes and the Estimation of Densities of Functions of Several Sample Variables |
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