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非正则估计（一）：位置参数估计量的方差界AI 解读

Maximum likelihood and other BAN estimators have been shown to possess certain optimal asymptotic properties in estimating the parameters of probability distributions satisfying specific regularity conditions. The subject of non-regular estimation is concerned with problems in which these conditions do not hold. In many such problems, classical lower bounds on the variance of unbiased estimators, such as the Cramér-Rao bound, lead to the trivial result V(t) ≧0, where t is…

若干圆形误差分位数估计量的渐近性质AI 解读

Quantiles of circular error, of which the CPE (circular probable error) is a special case, are of importance in the evaluation of ballistic missile systems. In these applications, a quantile of circular error is the radius, R, of a circle centered at (0, 0) above which lies a specified proportion, P, of the bivariate normal probability distribution. For this distribution, R may be estimated by substituting estimates for parameters in the integral equation defining R and…

若干圆形误差分位数估计量的渐近性质AI 解读

Quantiles of circular error, of which the CPE (circular probable error) is a special case, are of importance in the evaluation of ballistic missile systems. In these applications, a quantile of circular error is the radius, R, of a circle centered at (0, 0) above which lies a specified proportion, P, of the bivariate normal probability distribution. For this distribution, R may be estimated by substituting estimates for parameters in the integral equation defining R and…

二项分布混合模型的参数估计AI 解读

Let Y 1, ···, Y m be independent, each having distribution where 0 < p 1 < ··· < p r < 1, 0 < α j , < 1, Σα j = 1, and n ≧ 2r − 1. This distribution is a mixture of r binomials. It is shown to be an identifiable mixture under the given restrictions on the parameters. Moment estimators for the 2r − 1 parameters p 1, ···, P r , α1, ···, α r − 1 are constructed and the covariance matrix of the joint asymptotic normal distribution of the estimators is obtained. It is found by…