Extensions of Billingsley's theorems on weak convergence of empirical processes
β Scribed by Ken -ichi Yoshihara
- Publisher
- Springer
- Year
- 1974
- Tongue
- English
- Weight
- 204 KB
- Volume
- 29
- Category
- Article
- ISSN
- 1432-2064
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π SIMILAR VOLUMES
Let X 1 ; : : : ; X n be a sequence of i.i.d. random variables with common distribution P on the real line. Assuming that P has a smooth density, we construct a histogram based estimator P n; H and establish weak convergence of the empirical process β n(P n; H -P)(f) fβF under sharp conditions. If
The Brownian bridge is well known to have Hrlder continuous sample paths with exponent c~ < 1/2 with probability one and to be the weak limit in C[0, 1] of the smoothed empirical process based on the empirical frequencies polygon. We propose to extend this weak convergence to Hrlder spaces. A genera