Standardized log-likelihood ratio statistics for mixtures of discrete and continuous observations. (English) Zbl 0613.62014

Jensen, J. L.

Ann. Stat. 15, 314-324 (1987).

When the log-likelihood statistic is divided by its mean, or an approximation to its mean, the limiting chi-squared distribution is often correct to order \(n^{-3/2}\). Similarly, when the signed version of the likelihood ratio statistic is standardized with respect to its mean and variance the normal approximation is correct to order \(n^{-3/2}.\)
Proofs for these statements have been given in great generality in the literature for the case of continuous observations. In this paper we consider cases where the minimal sufficient statistic is partly discrete and partly continuous. In particular, we consider testing problems associated with censored exponential life times.

MSC:

62E20	Asymptotic distribution theory in statistics
62F05	Asymptotic properties of parametric tests

Keywords:

mixtures of discrete and continuous observations; Edgeworth expansion; conditional expansion; Bartlett adjustment; log-likelihood statistic; minimal sufficient statistic; censored exponential life times