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On the speed of convergence of log-likelihood ratio processes to standard mixtures of normal distributions. (English) Zbl 0827.62016
Summary: Under a very general dependence set-up, we obtain results on the rate of convergence of log-likelihood ratio processes to standard mixtures of normal distributions. Martingale techniques and the principle of contiguity have been exploited throughout. Examples of an explosive autoregressive process of first order and a super-critical Galton-Watson branching process have also been discussed in this context.
MSC:
62E20 Asymptotic distribution theory in statistics
62M99 Inference from stochastic processes
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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