The purpose of this book is to postulate some theories and test them numerically. Estimation is often a difficult task and it has wide application in social sciences and financial market. In order to obtain the optimum efficienty for some classes of estimators, the authors devoted this book into three specialized sections:
Part 1. In this section we have studied a class of shrinkage estimators for shape parameter beta in failure censored samples from two-parameter Weibull distribution when some 'apriori' or guessed interval containing the parameter beta is available in addition to sample information and analyses their properties. Some estimators are generated from the proposed class and compared with the minimum mean squared error (MMSE) estimator. Numerical computations in terms of percent relative efficiency and absolute relative bias indicate that certain of these estimators substantially improve the MMSE estimator in some guessed interval of the parameter space of beta, especially for censored samples with small sizes. Subsequently, a modified class of shrinkage estimators is proposed with its properties.
Part2. In this section we have analyzed the two classes of estimators for population median M_y of the study character Y using information on two auxiliary characters X and Z in double sampling. In this section we have shown that the suggested classes of estimators are more efficient than the one suggested by Singh et al (2001). Estimators based on estimated optimum values have been also considered with their properties. The optimum values of the first phase and second phase sample sizes are also obtained for the fixed cost of survey.
Part3. In this section, we have investigated the impact of measurement errors on a family of estimators of population mean using multiauxiliary information. This error minimization is vital in financial modeling whereby the objective function lies upon minimizing over-shooting and undershooting.
This book has been designed for graduate students and researchers who are active in the area of estimation and data sampling applied in financial survey modeling and applied statistics. In our future research, we will address the computational aspects of the algorithms developed in this book.