Probability Lrg Sample Theory

3 Credits · Level: Graduate

This is a course for Ph.D students with advanced knowledge of probability, statistics, and mathematics. The class covers both advanced probability theory and basic theory of stochastic processes to facilitate research of biostatistics and biomedical sciences. For probability theory, the following topics will be taught: measures, integration, probability, large sample theory of random variables. For stochastic processes, an introduction of martingales and point processes with applications to survival analysis will be taught. Text books • A course in Large Sample Theory, Ferguson, T. S., Chapman & Hall/CRC, 1996 • Weak Convergence and Empirical Processes with Applications to Statistics, van der Vaart, A. W. and Wellner, J. A., Springer, 1996 • Probability for Statisticians, Shorack, G. R., Springer, 2000