Mathematical Sciences: Topics in Statistical Theory

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The research project involves statistical resampling methods, analysis of directional data, survival analysis and semiparametric models. The development of a unified theory of resampling procedures that covers both the bootstrap and the jackknife methods will be supported. The resulting elements from k sampled blocks from a sequence of stationary m-dependent random variables will be used to provide bootstrap estimators of parameters and the properties of the estimators will be examined. Questions of robustness of these resampling procedures will be investigated. Notions of data depth for directional data will be developed along with nonparametric tests for them and corresponding classifications of data. Semiparametric models for survival analysis will be be studied for both censored and non- censored data.