Specifying Statistical Models: From Parametric to Non-Parametric, Using Bayesian or Non-Bayesian Approaches

✍ Scribed by Léopold Simar (auth.), J. P. Florens, M. Mouchart, J. P. Raoult, L. Simar, A. F. M. Smith (eds.)

• Publisher: Springer-Verlag New York
• Year: 1983
• Tongue: English
• Leaves: 215
• Series: Lecture Notes in Statistics 16
• Edition: 1
• Category: Library

✦ Synopsis

During the last decades. the evolution of theoretical statistics has been marked by a considerable expansion of the number of mathematically and computationaly trac­ table models. Faced with this inflation. applied statisticians feel more and more un­ comfortable: they are often hesitant about their traditional (typically parametric) assumptions. such as normal and i. i. d . • ARMA forms for time-series. etc . • but are at the same time afraid of venturing into the jungle of less familiar models. The prob­ lem of the justification for taking up one model rather than another one is thus a crucial one. and can take different forms. (a) ~~~£ifi~~~iQ~ : Do observations suggest the use of a different model from the one initially proposed (e. g. one which takes account of outliers). or do they render plau­ sible a choice from among different proposed models (e. g. fixing or not the value of a certai n parameter) ? (b) tlQ~~L~~l!rQ1!iIMHQ~ : How is it possible to compute a "distance" between a given model and a less (or more) sophisticated one. and what is the technical meaning of such a "distance" ? (c) BQe~~~~~~ : To what extent do the qualities of a procedure. well adapted to a "small" model. deteriorate when this model is replaced by a more general one? This question can be considered not only. as usual. in a parametric framework (contamina­ tion) or in the extension from parametriC to non parametric models but also.

✦ Table of Contents

Front Matter....Pages i-xii
Protecting Against Gross Errors: The Aid of Bayesian Methods....Pages 1-12
Bayesian Approaches to Outliers and Robustness....Pages 13-35
The Probability Integral Transformation for Non Necessarily Absolutely Continuous Distribution Functions, and its Application to Goodness-of-Fit Tests....Pages 36-49
Simulation in the General First Order Autoregressive Process (Unidimensional Normal Case)....Pages 50-68
Non Parametric Prediction in Stationary Processes....Pages 69-84
Approximate Reductions of Bayesian Experiments....Pages 85-92
Theory and Applications of Least Squares Approximation in Bayesian Analysis....Pages 93-107
Non Parametric Bayesian Statistics: A Stochastic Process Approach....Pages 108-133
Robust Testing for Independent Non Identically Distributed Variables and Markov Chains....Pages 134-162
“On the Use of Some Variation Distance Inequalities to Estimate the Difference between Sample and Perturbed Sample”....Pages 163-175
A Contribution to Robust Principal Component Analysis....Pages 176-181
From Non Parametric Regression to Non Parametric Prediction: Survey of the Mean Square Error and Original Results on the Predictogram....Pages 182-204

✦ Subjects

Statistics, general