Improving Upon Standard Estimators in Discrete Exponential Families with Applications to Poisson and Negative Binomial Cases
Improving Upon Standard Estimators in Discrete Exponential Families with Applications to Poisson and Negative Binomial Cases
Assume that $X_1, \cdots, X_p$ are independent random observations having discrete exponential densities $\rho_i(\theta_i)t_i(x_i)\theta^{xi}_i, i = 1, \cdots, p$ respectively. A general technique of improving upon the uniform minimum variance unbiased estimator (UMVUE) of $(\theta_1, \cdots, \theta_p)$ is developed under possibly weighted squared error loss functions. It is shown that …