Statistical Inference: Theory and Practice.

Abstract

One. Formalization of statistical problems.- 1 Statistical description of empirical phenomena.- 1.1. Statistical spaces.- 1.2. Parameters and indices of probability distributions.- 1.3. Random variables and statistics.- 1.4. Observable events.- 1.5. Final remarks.- 2. A scheme of statistical problems.- 2.1. Formalization of the goal of research.- 2.2. Decision rules.- 2.3. Standard classes of statistical problems.- 2.4. Sufficient and prediction sufficient statistics.- 2.5. Reduction of a statistical problem.- 2.6. Final remarks.- Two. Selected theoretical topics.- 3. Discriminant analysis.- 3.1. Introduction.- 3.2. Probabilistic problems.- 3.3. Statistical problems.- 3.4. Class separability measures.- 3.5. Final remarks.- 4. Screening problems.- 4.1. Introduction.- 4.2.Probabilistic screening problems.- 4.3.Statistical screening problems in a normal model.- 4.4. Screening in a nonparametric model.- 4.5. Final remarks.- 5. Evaluation of stochastic dependence.- 5.1. Introduction.- 5.2. Dependence between two binary random variables.- 5.3. Dependence in case of bivariate distributions.- 5.4. Monotone dependence function.- 5.5. Codependence in a pair of random variables.- 5.6. Final remarks.- Three. Selected practical problems.- 6. Statistical problems of population genetics.- 6.1. Introduction.- 6.2. The genetic structure of man and its relations with the phenotype.- 6.3. Genetic parameters of the human population.- 6.4. Estimation of gene probabilities for a single locus.- 6.5. Testing the Hardy-Weinberg hypothesis.- 6.6. Final remarks.- 7. Paternity proving.- 7.1. Introduction.- 7.2. Schemes of paternity recognition.- 7.3. A study of blood group traits.- 7.4. Anthropological evidence.- 7.5. Final remarks.- 8. Studies on sister cells.- 8.1. Introduction.- 8.2. Study of a population of pairs of objects.- 8.3. Sister cells as an experimental system.- 8.4. Investigation of Chilodonella steini (Ciliata, Kinetophragminophora)sister cells.- 8.5. Sister systems in investigations of the cell cycle.- 8.6. Final remarks.- 9. Survival analysis for censored data.- 9.1. Introduction.- 9.2. A model of random censorship.- 9.3. The Kaplan-Meier estimator.- 9.4. Main asymptotic properties of the K-M estimator.- 9.5. A two-sample problem for censored data.- 9.6. Final remarks.- 10. Latent variables in experimental psychology.- 10.1. Introduction.- 10.2. Typical experimental schemes.- 10.3. Inference in parametric models.- 10.4. Inference in nonparametric models.- 10.5. Final remarks.- 11. Queueing models of computer systems.- 11.1. Introduction.- 11.2. A queueing model.- 11.3. Analysis of the model.- 11.4. System parameter estimation.- 11.5. Final remarks.- Closing remarks.- Appendix. Algorithms for evaluating monotone dependence function and screening threshold.- A.1. Introduction.- A.2. Algorithm for evaluating monotone dependence function for a bivariate discrete distribution /J. ?wik, A. Kowalski.- A.3. Algorithm for evaluating monotone dependence function for an empiricaldistribution based on a raw sample /J. ?wik, A. Kowalski.- A.4. Algorithm for evaluating screening threshold /J. ?wik.- References.