دانلود کتاب Data analysis and approximate models : model choice, location-scale, analysis of variance, nonparametic regression and image analysis

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Content: Introduction Introduction Approximate Models Notation Two Modes of Statistical Analysis Towards One Mode of Analysis Approximation, Randomness, Chaos, Determinism Approximation A Concept of Approximation Approximation Approximating a Data Set by a Model Approximation Regions Functionals and Equivariance Regularization and Optimality Metrics and Discrepancies Strong and Weak Topologies On Being (almost) Honest Simulations and Tables Degree of Approximation and p-values Scales Stability of Analysis The Choice of En(alpha, P) Independence Procedures, Approximation and Vagueness Discrete Models The Empirical Density Metrics and Discrepancies The Total Variation Metric The Kullback-Leibler and Chi-Squared Discrepancies The Po(lambda) Model The b(k, p) and nb(k, p) Models The Flying Bomb Data The Student Study Times Data Outliers Outliers, Data Analysis and Models Breakdown Points and Equivariance Identifying Outliers and Breakdown Outliers in Multivariate Data Outliers in Linear Regression Outliers in Structured Data The Location-Scale Problem Robustness Efficiency and Regularization M-functionals Approximation Intervals, Quantiles and Bootstrapping Stigler's Comparison of Eleven Location Functionals Based on Historical Data Sets An Attempt at an Automatic Procedure Multidimensional M-functionals The Analysis of Variance The One-Way Table The Two-Way Table The Three-Way and Higher Tables Interactions in the Presence of Noise Examples Nonparametric Regression: Location A Definition of Approximation Regularization Rates of Convergence and Approximation Bands Choosing Smoothing Parameters Joint Approximation of Two or More Samples Inverse Problems Heterogeneous Noise Nonparametric Regression: Scale The Standard Model and a Concept of Approximation Piecewise Constant Scale and Local Approximation GARCH Segmentation The Taut String and Scale Smooth Scale Functions Comparison of the Four Methods Location and Scale Image Analysis Two and Higher Dimensions The Approximation Region Linear Programming and Related Methods Choosing Smoothing Parameters Nonparametric Densities Introduction Approximation Regions and Regularization The Taut String Strategy for Densities Smoothing the Taut String Approximation A Critique of Statistics Likelihood Bayesian Statistics Sufficient Statistics Efficiency Asymptotics Model Choice What Can Actually Be Estimated? Bibliography Index
Abstract: "This book presents a philosophical study of statistics via the concept of data approximation. Developed by the well-regarded author, this approach discusses how analysis must take into account that models are, at best, an approximation of real data. It is, therefore, closely related to robust statistics and nonparametric statistics and can be used to study nearly any statistical technique. The book also includes an interesting discussion of the frequentist versus Bayesian debate in statistics. "--

"This book stems from a dissatisfaction with what is called formal statistical inference. The dissatisfaction started with my first contact with statistics in a course of lectures given by John Kingman in Cambridge in 1963. In spite of Kingman's excellent pedagogical capabilities it was the only course in the Mathematical Tripos I did not understand. Kingman later told me that the course was based on notes by Dennis Lindley, but the approach given was not a Bayesian one. From Cambridge I went to LSE where I did an M.Sc. course in statistics. Again, in spite of excellent teachers including David Brillinger, Jim Durbin and Alan Stuart I did not really understand what was going on. This did not prevent me from doing whatever I was doing with success and I was awarded a distinction in the final examinations. Later I found out that I was not the only person who had problems with statistics. Some years ago I asked a respected German colleague D.W. Müller of the University of Heidelberg why he had chosen statistics. He replied that it was the only subject he had not understood as a student. Frank Hampel has even written an article entitled 'Is statistics too difficult?'. I continued at LSE and wrote my Ph. D. thesis on random entire functions under the supervision of Cyril Offord. It involved no statistics whatsoever. From London I moved to Constance in Germany, from there to Sheffield, then back to Germany to the town of Münster. All the time I continued writing papers in probability theory including some on the continuity properties of Gaussian processes. At that time Jack Cuzick now of Queen Mary, University of London, and Cancer Research UK also worked on this somewhat esoteric subject."