Estimation of finite population parameters with several realizations

Consider a finite population of size N with T possible realizations for each population unit. In reality the realizations may represent temporal, geographic or physical variations of the population unit. The paper provides design-based unbiased estimates for several population parameters of interest. Both simple random sampling and stratified sampling are considered. Some comparisons are given. An empirical study is also included with natural population data.     

Kshirsagar-Type Lower Bounds for Mean Squared Error of Prediction

Let Y be an observable random vector and Z be an unobserved random variable with joint density f(y, z | θ), where θ is an unknown parameter vector. Considering the problem of predicting Z based on Y, we derive Kshirsagar type lower bounds for the mean squared error of any predictor of Z. These bounds do not require the regularity conditions of Bhattacharyya bounds and hence are more widely applicable. Moreover, the new bounds are shown to be sharper than the corresponding Bhattacharyya bounds. The conditions for attaining the new lower bounds are useful for easy derivation of best unbiased predictors, which we illustrate with some examples.     

On the natural restrictions in the singular Gauss–Markov model

A Gauss–Markov model is said to be singular if the covariance matrix of the observable random vector in the model is singular. In such a case, there exist some natural restrictions associated with the observable random vector and the unknown parameter vector in the model. In this paper, we derive through the matrix rank method a necessary and sufficient condition for a vector of parametric functions to be estimable, and necessary and sufficient conditions for a linear estimator to be unbiased in the singular Gauss–Markov model. In addition, we give some necessary and sufficient conditions for the ordinary least-square estimator (OLSE) and the best linear unbiased estimator (BLUE) under the model to satisfy the natural restrictions.      

Sequential maximum likelihood estimation for reflected Ornstein-Uhlenbeck processes

The paper studies the properties of a sequential maximum likelihood estimator of the drift parameter in a one dimensional reflected Ornstein-Uhlenbeck process. We observe the process until the observed Fisher information reaches a specified precision level. We derive the explicit formulas for the sequential estimator and its mean squared error. The estimator is shown to be unbiased and uniformly normally distributed. A simulation study is conducted to assess the performance of the estimator compared with the ordinary maximum likelihood estimator.