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Weak convergence of smoothed empirical process in Hölder spaces

✍ Scribed by D. Hamadouche

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
411 KB
Volume
36
Category
Article
ISSN
0167-7152

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✦ Synopsis

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 general result for weak convergence in Hrlder spaces is proved. The weak convergence of the smoothed empirical process in each Hrlder space with exponent c~ < 1/4 follows from this result. The bound ~<1/4 is shown to be optimal. Convolution smoothing of the empirical process is also considered and leads to the bound ~< 1/2. (~) 1998 Elsevier Science B.V.

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