%0 Journal Article
%A Amini, Morteza
%A Ahmadi, Jafar
%T Asymptotic Efficiencies of the MLE Based on Bivariate Record Values from Bivariate Normal Distribution
%J Journal of the Iranian Statistical Society
%V 12
%N 2
%U http://jirss.irstat.ir/article-1-231-en.html
%R
%D 2013
%K Additivity, bivariate distribution, Fisher information matrix, inverse sampling, Jensen’s inequality.,
%X Abstract. Maximum likelihood (ML) estimation based on bivariate record data is considered as the general inference problem. Assume that the process of observing k records is repeated m times, independently. The asymptotic properties including consistency and asymptotic normality of the Maximum Likelihood (ML) estimates of parameters of the underlying distribution is then established, when m is large enough. The bivariate normal distribution is considered as an highly applicable example in order to estimate the parameter θ = (μ1, σ1, μ2, σ2) by ML method of estimation based on mk bivariate record data. Asymptotic variances of the ML estimators are calculated by deriving the Fisher information matrix about θ contained in the vector of the first k bivariate record data. As another application, we concerned the problem of “breaking boards” of Glick (1978, Amer. Math. Monthly, 85, 2-26) by considering three different sampling schemes of breaking boards and we computed the relative asymptotic efficiencies of ML estimators based on these three types of data.
%> http://jirss.irstat.ir/article-1-231-en.pdf
%P 235-252
%& 235
%!
%9
%L A-11-1-106
%+
%G eng
%@ 1726-4057
%[ 2013