TY - JOUR
T1 - Asymptotic Efficiencies of the MLE Based on Bivariate Record Values from Bivariate Normal Distribution
TT - Asymptotic Efficiencies of the MLE Based on Bivariate Record Values from Bivariate Normal Distribution
JF - JIRSS
JO - JIRSS
VL - 12
IS - 2
UR - http://jirss.irstat.ir/article-1-231-fa.html
Y1 - 2013
SP - 235
EP - 252
KW - Additivity
KW - bivariate distribution
KW - Fisher information matrix
KW - inverse sampling
KW - Jensen’s inequality.
N2 - 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.
M3
ER -