Mathematical Statistics: An Introduction

摘要: Probability theory: probability spaces stochastic variables product measures and statistical independence functions of vectors expectation, variance covariance distribution distributions moments, moment generating characteristic function the central limit theorem exercises. Statistics their distributions, estimation introduction Gamma Chi-2-distribution t-distribution statistics to measure differences in mean F-distribution Beta populations which are not normally distributed Bayesian theory a more general framework maximum likelihood estimation, sufficiency Hypothesis testing: Neyman-Pearson hypothesis tests concerning Chi-2 test on goodness fit Simple regression analysis: method least squares construction an unbiased estimator Sigma-2 normal analysis Pearson's product-moment correlation coefficient sum errors as amount linear structure Normal variance: one-way two-way Non-parametric methods: sign Wilcoxon's signed-rank rank-sum runs rank Kruskal-Wallis Friedman's Stochastic its applications statistics: empirical associated with sample convergence Glivenko-Cantelli Kolmogorov-Smirnov statistic metrics set smoothing techniques robustness trimmed means, median, functionals von Mises derivative influence Bootstrap methods densities by kernel means histograms Vectorial algebra expectation vector operator vectorial samples conditional that emanate from Gaussian ones multiple exercise. Appendices: Lebesgue's theorems probabilities Cauchy metric spaces, equicontinuity Fourier transform existence stoutly tailed functions. List elementary frequently used symbols tables references.