Advanced Theory of Statistics I

3 Units

A systematic development of advanced statistical theory. Background concepts. Limits, order comparisons, convergence. Sample moments, quantiles and other statistics. Transformations. Characterization of distribution functions and characteristic functions. Normal and other approximations to distributions. Quadratic forms and other functions of asymptotically normal statistics. Asymptotic properties of statistics including asymptotic efficiency, consistency. Admissibility, sufficiency and ancillarity. Nuisance parameters, parameter orthogonality. Distribution theory in nuisance parameters. Prereq: STAT 446 .