Description
Statistics Seminar.
Speaker: Raj Kamal Maurya.
Affiliation: IIT Patna.
Date and Time: Thursday, 16 May, 3:30 pm - 4:30 pm.
Venue: Room 216, Department of Mathematics.
Title: Some Problems of Estimation and Prediction under Progressive
Censoring.
Abstract: We have considered the problem of making statistical inferences for different lifetime
models on the basis of progressive type-II censored samples. In particular, we have
derived various estimates of parameters using both classical and Bayes methods. The
associated MLEs are computed using the EM algorithm. We also compute the ob-
served Fisher information matrices and based on these computations, the asymptotic
confidence intervals of parameters are constructed. Bootstrap intervals are also dis-
cussed. We also derive Bayesian estimates of parameters against different loss func-
tions. Most of these estimates appear in analytically intractable forms and so we
have used different approximation methods like importance sampling, Lindley, Tier-
ney and Kadane procedures to compute the Bayes estimates. In sequel, we have also
constructed highest posterior density intervals of parameters. We have also derived
predictive inference for censored observations under frequentist and Bayesian frame-
works. In particular, we obtain best unbiased predictor, conditional median predictor
from frequentist perspective. Among prediction intervals, we construct pivotal in-
terval, highest conditional density interval, equal tail interval and HPD interval for
future observations. Determination of optimal plans is one of the primary objective
in many life test studies. We have obtained such plans again using both frequentist
and Bayesian approaches under progressive censoring. We also consider estimation
of multicomponent stress-strength reliability under progressive censoring. We have
numerically compared the proposed methods using simulations for each problem. We
have also discussed real life examples in support of studied methods. We have provided
relevant information in each chapter of the thesis.