CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Eventssee all events
Events        
next up previous
Next: Lajos Horváth - Best Up: Probability Theory / Théorie Previous: Geneviéve Gauthier - Asymptotic

Edit Gombay - Correcting some limit theorems about the likelihood ratio



EDIT GOMBAY, Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta  T6G 2G1, Canada
Correcting some limit theorems about the likelihood ratio


To put the new results into perspective, first, we review some aspects of the history of the likelihood ratio since its definition by Neyman and Pearson in 1928.

Strong approximation of the maximum likelihood ratio statistic by a diffusion process under the null hypothesis is given. This allows one to develop statistics using different weight functions. Sequential tests will be defined and the precision of the approximation is examined.

The asymptotic distribution of the likelihood ratio under noncontiguous alternatives is shown to be normal for the exponential family of distributions. The rate of convergence of the parameters to the hypothetical value is specified where the asymptotic noncentral chi-square distribution no longer holds. It is only a little slower than O(n-1/2). The result provides compact power approximation formulae and is shown to work reasonably well even for moderate sample sizes.

In conclusion, we briefly consider the consequences of these theorems in sequential testing theory.


next up previous
Next: Lajos Horváth - Best Up: Probability Theory / Théorie Previous: Geneviéve Gauthier - Asymptotic
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/