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Amini M, Ahmadi J. Asymptotic Efficiencies of the MLE Based on Bivariate Record Values from Bivariate Normal Distribution. JIRSS. 2013; 12 (2) :235-252
URL: http://jirss.irstat.ir/article-1-231-fa.html
Asymptotic Efficiencies of the MLE Based on Bivariate Record Values from Bivariate Normal Distribution. پژوهشنامه انجمن آمار ایران. 1392; 12 (2) :235-252

URL: http://jirss.irstat.ir/article-1-231-fa.html


چکیده:   (3833 مشاهده)
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.
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