| Título: | Concentration inequalities for order statistics |
| Autores: |
Boucheron, Stéphane Vincent; Université Paris-Diderot Thomas, Maud; Université Paris-Diderot |
| Fecha: | 2012-01-02 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: | Peer-reviewed Article |
| Tema: |
concentration inequalities;entropy method;order statistics 60E15;60F10;60G70;62G30;62G32 |
| Descripción: | This note describes non-asymptotic variance and tail bounds for order statistics of samples of independent identically distributed random variables. When the sampling distribution belongs to a maximum domain of attraction, these bounds are checked to be asymptotically tight. When the sampling distribution has a non decreasing hazard rate, we derive an exponential Efron-Stein inequality for order statistics, that is an inequality connecting the logarithmic moment generating function of order statistics with exponential moments of Efron-Stein (jackknife) estimates of variance. This connection is used to derive variance and tail bounds for order statistics of Gaussian samples that are not within the scope of the Gaussian concentration inequality. Proofs are elementary and combine Rényi's representation of order statistics with the entropy approach to concentration of measure popularized by M. Ledoux. |
| Idioma: | Inglés |
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