Variance inequalities for covariance kernels and applications to central limit theorems
Ημερομηνία
1997Συγγραφέας
Cacoullos, TheophilosPapadatos, Nickos
Papathanasiou, Vassilis
ISSN
0040-585XSource
Theory of Probability and its ApplicationsVolume
42Issue
1Pages
149-162Google Scholar check
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Εμφάνιση πλήρους εγγραφήςΕπιτομή
A simple estimate for the error in the CLT, valid for a wide class of absolutely continuous r.v.'s, is derived without Fourier techniques. This is achieved by using a simple convolution inequality for the variance of covariance kernels or w-functions in conjunction with bounds for the total variation distance. The results are extended to the multivariate case. Finally, a simple proof of the classical Darmois-Skitovich characterization of normality is obtained.