Nonparametric Bayes Estimation of Distribution Functions and the Study of Probability Density Estimates.
Final rept. 1 Jun 79-13 May 81,
SOUTH CAROLINA UNIV COLUMBIA DEPT OF MATHEMATICS AND STATISTICS
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In work under this contract, major results were obtained in the broad areas of survival analysis and life testing, probability density estimates and laws of large numbers, estimation after testing, robustness and distribution-free procedures, and stochastic systems. In particular, nonparametric estimators of the failure rate function and survival probability were developed under the assumption of increasing failure rate using both maximum likelihood and Bayesian approaches. These particular results have attracted wide attention due to their generality and applicability in survival analysis and reliability estimation from arbitrarily right-censored data. Also, consistency results for both univariate and multivariate kernel estimates for probability density functions and regression functions were obtained using techniques and results of function-space probability theory. Stochastic convergence results for weighted sums of random elements in various function spaces were also obtained. Sequential procedures were developed and analyzed which provided interval estimators of the parameter of interest after testing certain hypotheses. Various robustness and nonparametric methods for incomplete samples and broken samples were studied, as well as nonparametric repeated significance testing and randomized block designs. Thus, maintenance policies and development of new, more reliable, equipment may be formulated using the statistical procedures and theory from these results. Author
- Statistics and Probability