Showing papers on "Mathematical statistics published in 2011"

Statistics for High-Dimensional Data: Methods, Theory and Applications

Abstract: Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches, including the Lasso and versions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections.A special characteristic of the book is that it contains comprehensive mathematical theory on high-dimensional statistics combined with methodology, algorithms and illustrations with real data examples. This in-depth approach highlights the methods great potential and practical applicability in a variety of settings. As such, it is a valuable resource for researchers, graduate students and experts in statistics, applied mathematics and computer science.

Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions

Abstract: A unified introduction to a variety of computational algorithms for likelihood and Bayesian inference. This third edition expands the discussion of many of the techniques presented, and includes additional examples as well as exercise sets at the end of each chapter.

Basic Business Statistics: Concepts and Applications

Abstract: From the Publisher: Reflecting the latest trends and methodologies, this comprehensive and innovative study on business statistics uses a practical, data-analytic approach. Based on the development of a survey which integrates the various topics and provides a cohesive study of descriptive statistics, probability, statistical inference, and regression analysis, it now focuses on data analysis and interpretation of computer output with a reduced focus on hand calculations. Creates an Employee Satisfaction Survey yielding 400 sample responses which readers can use to integrate such topics as descriptive statistics, probability, statistical inference, and regression analysis. Offers over 1200 realistic applications problems, 170 Survey/Database Projects, and relevant case studies. Contains two distinct types of summary sections to facilitate understanding - Exploratory and Confirmatory Data Analysis sections (looking at the four components of good data analysis - plotting, observing, computing and describing), and Ethical Issue sections (helps readers learn to think critically about the ramifications of the ethical issues involved in data analysis). Provides thorough coverage of regression and multiple regression, and considers many popular methodologies, including exploratory data analysis (EDA) techniques and dot charts, Pareto diagrams and supertables. Now opens each chapter with a "Using Statistics" example that shows how statistics can be applied to accounting, finance, management or marketing - plus includes appendices on using Microsoft Excel 97 and Minitab; an additional chapter on multiple regression that focuses on model building; a new chapter on decision making; arunning case study, and more.

Statistics of Random Processes

Abstract: The phenomenon of self-organized criticality (SOC) can be identified from many observations in the universe, by sampling statistical distributions of physical parameters, such as the distributions of time scales, spatial scales, or energies, for a set of events. SOC manifests itself in the statistics of nonlinear processes.

Strong Approximations in Probability and Statistics.

Abstract: Inevitably, reading is one of the requirements to be undergone. To improve the performance and quality, someone needs to have something new every day. It will suggest you to have more inspirations, then. However, the needs of inspirations will make you searching for some sources. Even from the other people experience, internet, and many books. Books and internet are the recommended media to help you improving your quality and performance.

Applied Statistics: Principles and Examples

Abstract: This book should be of interest to senior undergraduate and postgraduate students of applied statistics.

Applied Data Analysis and Modeling for Energy Engineers and Scientists

Abstract: Models, data analysis and decision making.- Probability concepts and probability distributions.- Data collection and preliminary data analysis.- Making statistical inferences from samples.- Estimation of linear model parameters using least squares.- Designed experiments and analysis of non-intrusive data.- Time series models.- Topics in optimization, parameter estimation and clustering methods.- Inverse problems and illustrative examples.- Decision analysis and risk modeling.

Statistics and econometrics

Abstract: 1. Introduction 2. Descriptive Statistics 3. Probability and Probability Distributions 4. Statistical Inference: Estimation 5. Statistical Inference: Testing Hypotheses 6. Simple Regression Analysis 7. Multiple Regression Analysis 8. Further Techniques and Applications in Regression Analysis 9. Problems in Regression Analysis 10. Simultaneous-Equations Methods 11. Time-Series Methods 12. Computer Applications in Econometrics

A high-dimensional Wilks phenomenon

Abstract: A theorem by Wilks asserts that in smooth parametric density estimation the difference between the maximum likelihood and the likelihood of the sampling distribution converges toward a Chi-square distribution where the number of degrees of freedom coincides with the model dimension. This observation is at the core of some goodness-of-fit testing procedures and of some classical model selection methods. This paper describes a non-asymptotic version of the Wilks phenomenon in bounded contrast optimization procedures. Using concentration inequalities for general functions of independent random variables, it proves that in bounded contrast minimization (as for example in Statistical Learning Theory), the difference between the empirical risk of the minimizer of the true risk in the model and the minimum of the empirical risk (the excess empirical risk) satisfies a Bernstein-like inequality where the variance term reflects the dimension of the model and the scale term reflects the noise conditions. From a mathematical statistics viewpoint, the significance of this result comes from the recent observation that when using model selection via penalization, the excess empirical risk represents a minimum penalty if non-asymptotic guarantees concerning prediction error are to be provided. From the perspective of empirical process theory, this paper describes a concentration inequality for the supremum of a bounded non-centered (actually non-positive) empirical process. Combining the now classical analysis of M-estimation (building on Talagrand’s inequality for suprema of empirical processes) and versatile moment inequalities for functions of independent random variables, this paper develops a genuine Bernstein-like inequality that seems beyond the reach of traditional tools.

Quantitative Methods: An Introduction for Business Management

Abstract: Preface. Part I. Motivations and Foundations. 1 Quantitative Methods: Should we Bother?. 1.1 A decision problem without uncertainty: product mix. 1.2 The role of uncertainty. 1.3 Endogenous vs. exogenous uncertainty: Are we alone?. 1.4 Quantitative models and methods. 1.5 Quantitative analysis and problem solving. Problems. For further reading. References. 2 Calculus. 2.1 A motivating example: economic order quantity. 2.2 A little background. 2.3 Functions. 2.4 Continuous functions. 2.5 Composite functions. 2.6 Inverse functions. 2.7 Derivatives. 2.8 Rules for calculating derivatives. 2.9 Using derivatives for graphing functions. 2.10 Higher-order derivatives and Taylor expansions. 2.11 Convexity and optimization. 2.12 Sequences and series. Problems. For further reading. References. 3 Linear Algebra. 3.1 A motivating example: binomial option pricing. 3.2 Solving systems of linear equations. 3.3 Vector algebra. 3.4 Matrix algebra. 3.5 Linear spaces. 3.6 Determinant. 3.7 Eigenvalues and eigenvectors. 3.8 Quadratic forms. 3.9 Calculus in multiple dimensions. Problems. For further reading. References. Part II Elementary Probability and Statistics. 4 Descriptive Statistics: On the Way to Elementary Probability. 4.1 What is Statistics?. 4.2 Organizing and representing raw data. 4.3 Summary measures. 4.4 Cumulative frequencies and percentiles. 4.5 Multidimensional data. Problems. For further reading. References. 5 Probability Theories. 5.1 Different concepts of probability. 5.2 The axiomatic approach. 5.3 Conditional probability and independence. 5.4 Total probability and Bayes theorems. Problems. For further reading. References. 6 Discrete Random Variables. 6.1 Random variables. 6.2 Characterizing discrete distributions. 6.3 Expected value. 6.4 Variance and standard deviation. Problems. For further reading. References. 7 Continuous Random Variables. 7.1 Building intuition: from discrete to continuous random variables. 7.2 Cumulative distribution and probability density functions. 7.3 Expected value and variance. 7.4 Mode, median, and quantiles. 7.5 Higher-order moments, skewness, and kurtosis. 7.6 A few useful continuous probability distributions. 7.7 Sums of independent random variables. 7.8 Miscellaneous applications. 7.9 Stochastic processes. 7.10 Probability spaces, measurability, and information. Problems. For further reading. References. 8 Dependence, Correlation, and Conditional Expectation. 8.1 Joint and marginal distributions. 8.2 Independent random variables. 8.3 Covariance and correlation. 8.4 Jointly normal variables. 8.5 Conditional expectation. Problems. For further reading. References. 9 Inferential Statistics. 9.1 Random samples and sample statistics. 9.2 Confidence intervals. 9.3 Hypothesis testing. 9.4 Beyond the mean of one population. 9.5 Checking the fit of hypothetical distributions: the chi-square test. 9.6 Analysis of variance. 9.7 Monte Carlo simulation. 9.8 Stochastic convergence and the law of large numbers. 9.9 Parameter estimation. 9.10 Some more hypothesis testing theory. Problems. For further reading. References. 10 Simple Linear Regression. 10.1 Least squares method. 10.2 The need for a statistical framework. 10.3 The case of a non-stochastic regressor. 10.4 Using regression models. 10.5 A glimpse of stochastic regressors and heteroskedastic errors. 10.6 A vector space look at linear regression. Problems. For further reading. References. 11 Time Series Models. 11.1 Before we start: Framing the forecasting process. 11.2 Measuring forecasting errors. 11.3 Time series decomposition. 11.4 Moving average. 11.5 Heuristic exponential smoothing. 11.6 A glance at advanced time series modeling. Problems. For further reading. References. Part III Models for Decision Making. 12 Deterministic Decision Models. 12.1 A taxonomy of optimization models. 12.2 Building linear programming models. 12.3 A repertoire of model formulation tricks. 12.4 Building integer programming models. 12.5 Nonlinear programming concepts. 12.6 A glance at solution methods. Problems. For further reading. References. 13 Decision Making under Risk. 13.1 Decision trees. 13.2 Risk aversion and risk measures. 13.3 Two-stage stochastic programming models. 13.4 Multi-stage stochastic linear programming with recourse. 13.5 Robustness, regret, and disappointment. Problems. For further reading. References. 14 Multiple Decision Makers, Subjective Probability, and Other Wild Beasts. 14.1 What is uncertainty?. 14.2 Decision problems with multiple decision makers. 14.3 Incentive misalignment in supply chain management. 14.4 Game theory. 14.5 Braess' paradox for traffic networks. 14.6 Dynamic feedback effects and herding behavior. 14.7 Subjective probability: the Bayesian view. Problems. For further reading. References. Part IV Advanced Statistical Modeling. 15 Introduction to Multivariate Analysis. 15.1 Issues in multivariate analysis. 15.2 An overview of multivariate methods. 15.3 Matrix algebra and multivariate analysis. For further reading. References. 16 Advanced Regression Models. 16.1 Multiple linear regression by least squares. 16.2 Building, testing, and using multiple linear regression models. 16.3 Logistic regression. 16.4 A glance at nonlinear regression. Problems. For further reading. References. 17 Dealing with Complexity: Data Reduction and Clustering. 17.1 The need for data reduction. 17.2 Principal component analysis (PCA). 17.3 Factor analysis. 17.4 Cluster analysis. For further reading. References. Index.

An Introduction to Probability and Statistical Inference

Abstract: Probability models, statistical methods, and the information to be gained from them is vital for work in business, engineering, sciences (including social and behavioral), and other fields. Data must be properly collected, analyzed and interpreted in order for the results to be used with confidence. Award-winning author George Roussas introduces readers with no prior knowledge in probability or statistics to a thinking process to guide them toward the best solution to a posed question or situation. An Introduction to Probability and Statistical Inference provides a plethora of examples for each topic discussed, giving the reader more experience in applying statistical methods to different situations. * Content, examples, an enhanced number of exercises, and graphical illustrations where appropriate to motivate the reader and demonstrate the applicability of probability and statistical inference in a great variety of human activities* Reorganized material in the statistical portion of the book to ensure continuity and enhance understanding* A relatively rigorous, yet accessible and always within the prescribed prerequisites, mathematical discussion of probability theory and statistical inference important to students in a broad variety of disciplines* Relevant proofs where appropriate in each section, followed by exercises with useful clues to their solutions* Brief answers to even-numbered exercises at the back of the book and detailed solutions to all exercises available to instructors in an Answers Manual

Comparison of sums of independent identically distributed random variables

Abstract: The final version of this paper appears in: "Probability and Mathematical Statistics" 14 (1993): 281-285. Print.

Sequential Quantile Prediction of Time Series

Abstract: Motivated by a broad range of potential applications, we address the quantile prediction problem of real-valued time series. We present a sequential quantile forecasting model based on the combination of a set of elementary nearest neighbor-type predictors called “experts” and show its consistency under a minimum of conditions. Our approach builds on the methodology developed in recent years for prediction of individual sequences and exploits the quantile structure as a minimizer of the so-called pinball loss function. We perform an in-depth analysis of real-world data sets and show that this nonparametric strategy generally outperforms standard quantile prediction methods.

Introductory business statistics

Abstract: PART I: BUSINESS STATISTICS: INTRODUCTION AND BACKGROUND. 1. A Preview of Business Statistics. 2. Visual Description of Data. 3. Statistical Description of Data. 4. Data Collection and Sampling Methods. PART II: PROBABILITY. 5. Probability: Review of Basic Concepts. 6. Discrete Probability Distributions. 7. Continuous Probability Distributions. Part III: SAMPLING DISTRIBUTIONS AND ESTIMATION. 8. Sampling Distributions. 9. Estimation from Sample Data. PART IV: HYPOTHESIS TESTING. 10. Hypothesis Tests Involving a Sample Mean or Proportion. 11. Hypothesis Tests Involving Two Sample Means or Proportions. 12. Analysis of Variance Tests. 13. Chi-Square Applications. 14. Nonparametric Methods. Part V: REGRESSION, MODEL BUILDING, AND TIME SERIES. 15. Simple Linear Regression and Correlation. 16. Multiple Regression and Correlation. 17. Model Building. 18. Models for Time Series and Forecasting. PART VI: SPECIAL TOPICS. 19. Decision Theory. 20. Total Quality Management. 21. Ethics in Statistical Analysis and Reporting (online chapter). Appendix A: Statistical Tables. Appendix B: Selected Answers. Index. Glossary.

Frequentist Approach: Modelling and Simulation in Statistics and Probability Teaching

Abstract: In this chapter, a question is posed about the link between two traditional approaches to the notion of probability, classical (or Laplacian) and frequentist, in secondary teaching. Different conceptions of probability, objective and subjective, are considered, some didactical difficulties of the frequentist option are underlined, and the modelling view point is presented. A critical description of a modelling process of a random situation for teachers’ training in secondary teaching is proposed and it is developed for the example of a queue. Finally, the status of simulations on computers in classrooms is clarified and their didactical relevance is highlighted.

Fitting Straight Lines with Replicated Observations by Linear Regression. IV. Transforming Data

Abstract: By transforming variables it is possible to introduce non-linear terms to the mathematical framework of linear regression. The purpose of this article is to stress the importance of transforming data in the context of linear regression analysis. However, often problems arise when people unfamiliar with mathematical statistics attempt to put this theory into practice for a certain application. Reasons for making transformations, probability plots and normality, transformations to simplify relationships, and weighting transformation data are covered in this paper. Special attention has also been paid to the Box-Cox method, i.e., transformation based on sample data observations, which is very easy to apply in practice despite its mathematical background. Statistical measurements are also re-expressed after data transformation, and a number of applications concerning the use of transformation and variance stabilization in analytical chemistry are given in tabular form. The analytical, pharmaceutical, biochemi...

Mathematical Statistics: Asymptotic Minimax Theory

Abstract: Parametric models: The Fisher efficiency The Bayes and minimax estimators Asymptotic minimaxity Some irregular statistical experiments Change-point problem Sequential estimators Linear parametric regression Nonparametric regression: Estimation in nonparametric regression Local polynomial approximation of regression function Estimation of regression in global norms Estimation by splines Asymptotic optimality in global norms Estimation in nonparametric models: Estimation of functionals Dimension and structure in nonparametric regression Adaptive estimation Testing of nonparametric hypotheses Bibliography Index of notation Index

Statistical Theory and Applications: Papers in Honor of Herbert A. David

Abstract: I General Distribution Theory and Inference.- 1 PIC: Power Divergence Information Criterion.- 1.1 Introduction.- 1.2 The Power Divergence Measures.- 1.3 Power-divergence Information Criterion (PIC).- 1.4 Count Data from the Framingham Study.- 1.5 Conclusions.- 1.6 References.- 2 Multivariate Student's t and Its Applications.- 2.1 Introduction.- 2.2 A Multivariate Student t Distribution.- 2.2.1 Definition and Probability Integral.- 2.2.2 Computing the Probability Integral for p > 2.- 2.2.3 An Approximation for the Unequal pij Case.- 2.3 Applications of Multivariate t.- 2.3.1 Two-stage Indifference Zone Selection.- 2.3.2 Subset Selection.- 2.3.3 Treatments Versus Control Multiple Comparisons.- 2.3.4 Testing Multiple Contrasts.- 2.3.5 Multiple Comparisons with the "Best".- 2.3.6 Additional Applications.- 2.4 References.- 3 Two Sets of Multivariate Bonferroni-type Inequalities.- 3.1 Introduction.- 3.2 The Results.- 3.3 Proofs.- 3.4 References.- 4 On the Proportion above Sample Mean for Symmetric Stable Laws.- 4.1 Introduction.- 4.2 The Result.- 4.3 A Partial Converse.- 4.4 Remarks and Extensions.- 4.5 References.- 5 The Relative Efficiency of Several Statistics Measuring Skewness.- 5.1 Introduction.- 5.2 Skewness Functional for X with Finite Support.- 5.3 Relative Efficiency of Skewness Estimators when X has Finite Support.- 5.4 Relative Efficiency of Skewness Estimators when X has Infinite Support.- 5.5 Summary.- 5.6 References.- 6 On a Class of Symmetric Nonnormal Distributions with a Kurtosis of Three.- 6.1 Introduction.- 6.2 Symmetric Mixtures with ?2 = 3.- 6.3 Examples.- 6.4 Limiting Distributions of the Extremes.- 6.5 Comments.- 6.6 References.- II Order Statistics - Distribution Theory.- 7 Moments of the Selection Differential from Exponential and Uniform Parents.- 7.1 Introduction.- 7.2 Moments of D from an Exponential Parent.- 7.3 Moments of D from a Uniform Parent.- 7.4 Asymptotes for the Moments of D.- 7.5 Convergence of the Moments: Exponential Parent.- 7.6 Convergence of the Moments: Uniform Parent.- 7.7 Tabular Analysis.- 7.7.1 Mean.- 7.7.2 Variance.- 7.7.3 Skewness.- 7.7.4 Kurtosis.- 7.8 Practical Implications.- 7.9 References.- 8 The Tallest Man in the World.- 8.1 Introduction.- 8.2 Some Useful Results on Branching Processes.- 8.3 The Tallest Man in the World.- 8.4 The Tallest Man in History.- 8.5 What Kind of Limit Laws can be Encountered?.- 8.6 References.- 9 Characterizing Distributions by Properties of Order Statistics - A Partial Review.- 9.1 Introduction.- 9.2 Independence of Linear Functions.- 9.3 Identical Distributions of Functions of Order Statistics.- 9.4 Moment Properties.- 9.5 Statistical Properties.- 9.6 Asymptotic Properties.- 9.7 References.- 10 Stochastic Ordering of the Number of Records.- 10.1 Introduction.- 10.2 The Results.- 10.2.1 Stochastic Ordering.- 10.2.2 Expectation of the Number of k-th Records.- 10.2.3 Integrated Likelihood Ratio Ordering.- 10.3 Proofs and an Example.- 10.4 References.- 11 Moments of Cauchy Order Statistics via Riemann Zeta Functions.- 11.1 Introduction.- 11.2 An Expression for the Mean.- 11.3 Expressions for Product Moments.- 11.4 References.- 12 Order Statistics of Bivariate Exponential Random Variables.- 12.1 Introduction.- 12.2 Freund, Marshall-Olkin, ?nd Raftery's BVE Distributions.- 12.3 Joint Distributions.- 12.4 Marginal Distributions.- 12.4.1 Properties of T1.- 12.4.2 Properties of T2.- 12.5 Copula Functions.- 12.6 References.- III Order Statistics in Inference and Applications.- 13 Maximum Likelihood Estimation of the Laplace Parameters Based on Type-II Censored Samples.- 13.1 Introduction.- 13.2 Maximum Likelihood Estimators.- 13.3 Efficiency Relative to BLUE's.- 13.4 References.- 14 The Impact of Order Statistics on Signal Processing.- 14.1 Introduction.- 14.2 Order Statistic Filters.- 14.2.1 Median and Rank-Order Filters.- 14.2.2 RO Filters.- 14.2.3 OS Filters.- 14.3 Generalizations.- 14.3.1 ? and Ll Filters.- 14.3.2 Permutation Filters.- 14.3.3 WMMR Filters.- 14.3.4 Stack Filters.- 14.3.5 Morphological Filters.- 14.4 Related Applications of Order Statistics.- 14.4.1 Edge Detection.- 14.4.2 Signal Enhancement and Restoration.- 14.5 Conclusions.- 14.6 References.- 15 A Nonlinear Ordered Rank Test to Detect Stochastic Ordering Between Two Distributions.- 15.1 Introduction.- 15.2 The Proposed Test.- 15.3 Simulation Study.- 15.4 Discussion.- 15.5 Asymptotic Properties.- 15.6 References.- 16 Estimation of Location and Scale Parameters of a Logistic Distribution Using a Ranked Set Sample.- 16.1 Introduction.- 16.2 Estimation of the Location Parameter.- 16.2.1 Best Linear Unbiased Estimator.- 16.2.2 Which Order Statistic?.- 16.3 Estimation of the Scale Parameter.- 16.4 Estimation of Quantiles.- 16.5 Proofs.- 16.6 References.- 17 Probability Models for an Employment Problem.- 17.1 Introduction.- 17.2 Definition of the Problem.- 17.2.1 Hiring Criteria.- 17.2.2 Notation.- 17.3 The Case of Couples and Single Applicants.- 17.3.1 Small Sample Results.- 17.3.2 Asymptotic Results.- 17.4 A Strategy for Couples.- 17.5 Conclusions.- 17.6 References.- IV Analysis of Variance and Experimental Design.- 18 On the Robustness of Bayes Estimators of the Variance Ratio in Balanced One-Way ANOVA Models with Covariates.- 18.1 Introduction.- 18.2 The Bayes Estimator and its Asymptotic Properties.- 18.3 Jackknifed Estimator of the Asymptotic Variance and Asymptotic Confidence Intervals.- 18.4 Simulation Results.- 18.5 References.- 19 Interchange Algorithms for Constructing Designs with Complex Blocking Structures.- 19.1 Historical Perspective.- 19.2 Optimality Criteria.- 19.3 Interchange Algorithms.- 19.4 Objective Functions.- 19.5 Discussion.- 19.6 References.- 20 Paired Comparisons for Multiple Characteristics: An ANOCOVA Approach.- 20.1 Introduction.- 20.2 ANOCOVAPC for Paired Characteristics.- 20.3 Probability Laws for Multiple Dichotomous Attributes.- 20.4 MANOCOVAPC Paired Comparisons Models and Analyses.- 20.5 Concluding Remarks.- 20.6 References.- V Biometry and Applications.- 21 On Assessing Multiple Equivalences with Reference to Bioequivalence.- 21.1 Introduction.- 21.2 Many-to-One Comparisons.- 21.3 Assessing Equivalence of k Formulations.- 21.4 Multiple Partial Equivalences.- 21.5 Example.- 21.6 References.- 22 Competing Risks.- 22.1 Introduction.- 22.2 Some Independent Competing Risk Results (After 1978).- 22.3 Non-identifiability Issues.- 22.4 Methods Assuming Informative Censoring (Dependent Competing Risks).- 22.5 Inference Using Estimable Quantities.- 22.6 Summary.- 22.7 References.- 23 Statistical Aspects of the Detection of Activation Effects in Cerebral Blood Flow and Metabolism by Positron Emission Tomography.- 23.1 Introduction: The Analysis of PET Data.- 23.2 The Activation Experiment and the Data.- 23.3 Activation Effects and a Simple Whole Brain Adjustment.- 23.4 Adjustment by the Analysis of Covariance.- 23.5 References.- 24 On Optimality of Q-Charts for Outliers in Statistical Process Control.- 24.1 Introduction.- 24.2 The Normal Mean Q-Chart.- 24.3 The Binomial Q-Chart.- 24.4 The Poisson Q-Chart.- 24.5 References.- VI Postscript.- 25 Herbert A. David.- 26 Conference Abstracts, Anecdotes, and Appreciation.

Probability Theory, Random Processes and Mathematical Statistics

Abstract: Preface. Annotation. 1. Introductory probability theory. 2. Random processes. 3. An introduction to mathematical statistics. 4. Basic elements of probability theory. 5. Elements of stochastic analysis and stochastic differential equations. Subject index.

Probability and Statistics in Particle Physics

Abstract: Notions of probability and statistics are of fundamental importance not only for those physicists who want to work in experimental physics, but also for those who want to perform comparison of models and/or theory with experimental results. In this course we will revise the general ideas of probability and statistics as well as some probability distributions which most frequently appear in physics, including sampling distributions like the χ2 one, which are important to decide about the quality of theoretical models fits to experimental data. We will also discuss error propagation and methods to compare theory with experimental results, including parameter estimators, Maximum Likelihood and Least Squares.

Application of Random Matrix Theory to Multivariate Statistics

Abstract: This is an expository account of the edge eigenvalue distributions in random matrix theory and their application in multivariate statistics. The emphasis is on the Painleve representations of these distribution functions.

Supervised Classification for a Family of Gaussian Functional Models

Abstract: This is the peer reviewed version of the following article: Scandinavian Journal of Statistics 38.3 (2011): 480-498, which has been published in final form at http://dx.doi.org/10.1111/j.1467-9469.2011.00734.x. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving