Waltraut Kahle, Friedrich Liese
Consistency and Asymptotic Normality of Minimum Contrast Estimation in Renewal Processes
The paper is published: Rostocker Mathematische Kolloquium
62F12 Asymptotic properties of estimators
62N05 Reliability and life testing, See also {90B25}
Abstract: The consistency and asymptotic normality of minimum contrast
estimation (which includes the maximum likelihood estimation
as a special case) is established if the sample is from a
renewal process and the observation time tends to infinity.
It is shown, that the conditions for consistency and asymptoti
normality for maximum likelihood estimation are fullfilled
if the distribution of the time between two renewals is
Weibull or Maxwell. This fact is used to construct simultaneous
confidence regions for the parameters of the Weibull
distribution and a confidence intervall for the parameter
of the Maxwell distribution.