Yadolah Dodge

on Statistical data analysis based on the L1-norm and related methods

An Introduction to Statistical Data Analysis L 1 -Norm Based (Y. Dodge). The Place of the L 1 -Norm in Robust Estimation (P.J. Huber). I. Historical Development. The Historical Development of the L 1 and L # Estimation Procedures (R.W. Farebrother). Bounded Influence Inference in Regression: A Review (E. Ronchetti). II. Computational Algorithms and Computer Packages. Algorithms for Unconstrained L 1 Linear Regression (J.E. Gentle, S.C. Narula, V.A. Sposito). The Reduced Gradient Algorithm (M.R. Osborne). The L 1 -Estimate as Limiting Case of an L p - or Huber-Estimate (H. Ekblom). A Review of Computational Methods for Solving the Nonlinear L 1 -Norm Estimation Problem (R. Gonin, A.H. Money). Fitting Data Through Homotopy Methods (J.-P. Schellhorn). BLINWDR: A Fortran Program for Robust and Bounded Influence Regression (R. Dutter). Solving Bounded Influence Regression Problems with ROBSYS (A. Marazzi). XploRe - A Computing Environment for eXploratory Regression (W. Hardle). III. Estimation, Characterization, Properties and Selection of Variables. L 1 -Distances in Statistical Inference: Comparison of Topological, Functional and Statistical Properties (I. Vajda). The Role Played by L 1 in Data Analysis (B. Fichet). L 1 -Embeddings of a Data Structure (I,D) (G. Le Calve). Assessing the Accuracy of the Sample Median: Estimated Standard Errors vs. Interpolated Confidence Intervals (S.J. Sheather). The Median of a Finite Measure on a Banach Space (J.H.B. Kemperman). Variable Selection in Linear Model Based on Trimmed Least Squares Estimator (J. Antoch). Numerical Techniques for Finding Estimates which Minimize the Upper Bound of the Absolute Deviation (A. Gaivoronski). Asymptotic Properties of Restricted L 1 -Estimates of Regression (J. Dupacova). Adaptive Combination of Least Squares and Least Absolute Deviations Estimators (Y. Dodge, J. Jureckova). IV. Statistical Inference Procedures. A Comparison of Asymptotic Testing Methods for L 1 -Regression (R. Koenker). Least Absolute Errors Analysis of Variance (J.W. McKean, R.M. Schrader). Small Sample Properties of Least Absolute Errors Analysis of Variance (R.M. Schrader, J.W. McKean). Bootstrap and Inference Procedures for L 1 -Regression (G. Stangenhaus). Invariant Tests in Bivariate Models and the L 1 -Criterion (B.M. Brown, T.P. Hettmansperger). Using Regression Fractiles to Identify Outliers (S. Portnoy). Various Discrepancy Measures in Model Testing (Two Competing Regression Models) (V.V. Fedorov). V. Nonparametric Analysis. Kernel Estimates of the Sparsity Function (A.H. Welsh). What Does Optimal Bandwidth Selection Mean for Nonparametric Regression Estimation? (J.S. Marron). Density Estimation from Dependent Sample (L. Gyorfi). VI. Cluster Analysis. Clustering by Means of Medoids (L. Kaufman, P.J. Rousseeuw). L 1 in Fuzzy Clustering (E. Trauwaert). Using the L 1 -Norm Within Cluster Analysis (H. Spath). VII. Applications. An Application of L 1 to Astronomy (P.J. Rousseeuw).

Application and comparison of classification algorithms for recognition of Alzheimer's disease in electrical brain activity (EEG)

The early detection of subjects with probable Alzheimers disease (AD) is crucial for effective appliance of treatment strategies. Here we explored the ability of a multitude of linear and non-linear classification algorithms to discriminate between the electroencephalograms (EEGs) of patients with varying degree of AD and their age-matched control subjects. Absolute and relative spectral power, distribution of spectral power, and measures of spatial synchronization were calculated from recordings of resting eyes-closed continuous EEGs of 45 healthy controls, 116 patients with mild AD and 81 patients with moderate AD, recruited in two different centers (Stockholm, New York). The applied classification algorithms were: principal component linear discriminant analysis (PC LDA), partial least squares LDA (PLS LDA), principal component logistic regression (PC LR), partial least squares logistic regression (PLS LR), bagging, random forest, support vector machines (SVM) and feed-forward neural network. Based on 10-fold cross-validation runs it could be demonstrated that even tough modern computer-intensive classification algorithms such as random forests, SVM and neural networks show a slight superiority, more classical classification algorithms performed nearly equally well. Using random forests classification a considerable sensitivity of up to 85% and a specificity of 78%, respectively for the test of even only mild AD patients has been reached, whereas for the comparison of moderate AD vs. controls, using SVM and neural networks, values of 89% and 88% for sensitivity and specificity were achieved. Such a remarkable performance proves the value of these classification algorithms for clinical diagnostics.

L[1]-statistical analysis and related methods

Prologue. Thoughts on Real Data and Statistics (Y. Dodge). Some Statistical Tools for the Analysis of Complex Molecular Spectra (A.F. Ruckstuhl). Estimation, Testing and Property Characterization. The Gauss Markov Property for the Median (G.W. Basset, Jr.,). A Class of Estimators Based on Adaptative Convex Combinations of Two Estimation Procedures (Y. Dodge, J. Jureckova). Robustness of L1 Regression in the Light of Linear Programming (J. Dupacova). A Linear Model with a Pseudoisotropic Distribution of Errors (S. Kotz, Y.G. Kuritsyn). L1-Estimation and Testing in Conditionally Contaminated Linear Models (C.H. Muller). Explicit Scale Estimators with High Breakdown Point (P.J. Rousseeuw, C. Croux). M-Type Tests in Linear Models: Some Comments on Studentizing, and a Small Simulation (W.A. Stahel, P. Hartmann). High Breakdown Estimators in Nonlinear Regression (A. Stromberg). Graphical Analysis. Regression Plotting Based on Quadratic Predictors (R.D. Cook). The Notion of Sphericity for Finite L1-Figures of Data Analysis (B. Fichet). The Interpretation of Residuals Based on L1 Estimation (S.J. Sheather, J.W. McKean). Graphical Methods for Model Comparison (S. Weisberg). Nonparametric Estimation in Linear Models. Generalized Regression Quantiles: Forming a Useful Toolkit for Robust Linear Regression (P. Chaudhuri). Efficient L-Estimators in Semiparametric Linear Heteroscedastic Models (C. Gutenbrunner). Bounded Influence and High Breakdown Point Regression with Linear Combinations of Order Statistics and Rank Statistics (S. Heiler). Nonparametric Estimation of Conditional Quantile Functions (R. Koenker, S. Portnoy, P. Ng). Time Series Analysis. Recursive Time Series Methods in L1-Norm (T. Cipra, M.R. Romera). Asymptotics of Boscovich-Type Parameter Estimates for Infinite Variance Autoregressive Processes (K. Knight). L1-Norm Estimation of Regression Models with Serially Dependent Error Terms (H. Nyquist). Multivariate Analysis. On Multivariate Notions of Sign and Rank (T.P. Hettmansperger, J. Nyblom, H. Oja). Data Depth and Multivariate Rank Tests (R.Y. Liu). A Two Sample Extension of the Multivariate Interdirection Sign Test (R.H. Randles). Computational Procedures. Generating Median Graphs from Boolean Matrices (H.-J. Bandelt). Computational Algorithms for Least Absolute Value Regression (T.E. Dielman). Algorithms for Non-Linear Lp Estimation (H. Ekblom, K. Madsen). The Geometrical Foundations of a Class of Estimation Procedures which Minimise Sums of Euclidean Distances and Related Quantities (R.W. Farebrother). Computing P-Values in Robust Inference: Location/Scale (C. Field). Testing Software for Robust Regression (J.E. Gentle, S.C. Narula, V.A. Sposito). A Continuation Method for Linear L1 Estimation (K. Madsen, H.B. Nielsen). The Calculation of the Oja Multivariate Median (A.O. Niinimaa). Distributions and Density Estimation.

Statistical data analysis and inference

Prologue. C. Radhakrishna Raos Contributions to Statistics (Y. Dodge). Nonlinear Estimation in Linear Models (F. Hampel). On the Maximum Number of Factors in Two Construction Methods for Orthogonal Arrays (A.S. Hedayat, J. Stufken). Some Geometrical Aspects of Data Analysis and Statistics (J.M. Oller). Inferences and Test of Hypotheses. On Bayes and Empirical Bayes Two-Stage Allocation Procedures for Selection Problems (S.S. Gupta, T.C. Liang). Multi-Sample Functional Statistical Data Analysis (E. Parzen). Discussing Truth or Falsity by Computing a Q-Value (W. Schaafsma, J. Tolboom, B. van der Meulen). Linear Pivotals and the Bayes-Non Bayes Compromise (G.A. Barnard). Bayes Modified Minimax Experimental Design (R.V. Canfield). A Simple Class of Tests Locally Better than the Score Test (T.K. Chandra). Comparison of Tests in the Presence of a Nuisance Parameter (R. Mukerjee). Tests for Redundancy of Some Variables in Multivariate Analysis (Y. Fujikoshi). Model Choice in the Context of Simultaneous Inference (T. Havranek, O. Soudsky). First Zeros of Empirical Characteristic Functions and Extreme Values of Gaussian Processes (J. Husler). Parameter and Variance Estimation. Comparison of Experiments with Weighted Distributions (M.J. Bayarri, M.H. De Groot). Optimal Estimation for Weighted Distributions: Semi-Parametric Models (V.P. Godambe, M.B. Rajarshi). On Efficiency for Quasi-Likelihood and Composite Quasi-Likelihood Methods (C.C. Heyde). Improved Estimators of Dispersion of an Inverse Gaussian Distribution (N.Pal, B.K. Sinha). Applications of Edgeworth Expansions to Bootstrap - A Review (G.J. Babu). Dual Poincare- Type Inequalities via the Cramer-Rao and the Cauchy-Schwarz Inequalities and Related Characterizations (Th. Cacoullos). Some Optimality Results on Steins Two-Stage Sampling (J.K. Ghosh, R. Mukerjee). The Cramer-Frechet-Rao Inequality for Sequential Estimation in Non-Regular Case (Z. Govindarajulu, I. Vincze). Whither Delete-K Jackknifing for Smooth Statistical Functionals? (P.K. Sen). Distributions, Weighted Distributions and Characterization. Three Useful Expressions for Expectations Involving a Wishart Matrix and its Inverse (G.P.H. Styan). Characterizations of Distributions via Moments of Order Statistics: A Survey and Comparison of Methods (G.D. Lin). Constancy of Regression of a Polynomial of Sample Average of Positive Random Variables on their Ratios Characterizes Gamma Distribution (A. Kagan). Probing Encountered Data, Meta Analysis and Weighted Distribution Methods (G.P. Patil, C. Taillie). Further Results on Identification when the Parameters are Partially Unknown (S. El Khattabi, F. Streit). Linear Models and Matrices . Weighted-Least-Squares Estimation in the General Gauss-Markov Model (J.K. Baksalary, S. Puntanen). Evaluating Pre-Test Predictors of Success in Linear Regression Models (A. Cohen, H.B. Sackrowitz). Optimum Invariant Tests in Mixed Linear Models with Two Variance Components (Th. Mathew).

Analysis of Experiments with Missing Data.

Prologue One Factor Experiments: Comparing Treatments Experiments Involving Two Factors Additive Two-Way Classification with Missing Observations: Estimability and Analysis Additive Three-Way Classification with Missing Observations: Estimability and Analysis Additive N-Way Classifications with Missing Observations: Estimability and Analysis Generalized Inverses for Classification Models Minimally Connected Factorial Experiments and the Problems of Selecting a Factorial Experiment Index.

Direction dependence in a regression line

In this paper, we derive some simple formulae to express the association between two random variables in the case of a linear relationship, One of these representations, the cube of the correlation coefficient, is given as the ratio of the skewness of the response variable to that of the explanatory variable. This result, along with other expressions of the correlation coefficient presented in this paper, has implications for choosing the response variable in a linear regression modelling.

The Complications of the Fourth Central Moment

Abstract This article illustrates the additional complications in the mathematical formulas involving the fourth central moment in comparison with those involving the first moment, the second central moment, and the third central moment.

An introduction to L 1 -norm based statistical data analysis

Abstract A brief introduction to statistical data analysis based on the minimization of L 1 - norm is given for those who are not familiar with the subject. A selected bibliography on the statistical data analysis L 1 - norm based is provided.

Estimation of quantile density function based on regression quantiles

We propose two estimators of quantile density function in linear regression model. The estimators, either of histogram or of kernel types, are based on regression quantiles and extend the Falk (1986) estimators based on order statistics from the location to the linear regression model. Unlike various other estimators proposed in the literature, our estimators are regression invariant and scale equivariant and hence applicable in estimation, testing, bounded-length confidence interval estimation and other inference based on L1-norm.

The Guinea Pig of Multiple Regression

The role played by a 21×4 data set in the development (progress and regress) of multiple regression is discussed. While this ‘famous’ data set has been (and is being) used as a guinea pig1 for almost every method of estimation introduced in the regression market, it appears that no one has questioned the origin and correctness in the last 30 years. An attempt is made to clarify some points in this regard. In particular, it is argued here that this data set is in fact a subset of a longer data set of which the rest is missing.