Abstract: Preface.Statistical methods. Introduction to S Plus. Experimental design Central tendency. Probability. Variance. The Normal Distribution. Power calculations. Understanding data: graphical analysis. Understanding data: tabular analysis. Classical tests. Bootstrap and jackknife. Statistical models in S Plus. Regression. Analysis of variance. Analysis of covariance. Model criticism. Contrasts. Split plot Anova. Nested designs and variance components analysis. Graphs, functions and transformations. Curve fitting and piecewise regression. Non linear regression. Multiple regression. Model simplification. Probability distributions. Generalised linear models. Proportion data: binomial errors. Count data: Poisson errors. Binary response variables. Tree models. Non parametric smoothing. Survival analysis. Time series analysis. Mixed effects models. Spatial statistics. Bibliography. Index.

Abstract: A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed in Fan and Li (2001a). It has been shown there that the resulting procedures perform as well as if the subset of significant variables were known in advance. Such a property is called an oracle property. The proposed procedures were illustrated in the context of linear regression, robust linear regression and generalized linear models. In this paper, the nonconcave penalized likelihood approach is extended further to the Cox proportional hazards model and the Cox proportional hazards frailty model, two commonly used semi-parametric models in survival analysis. As a result, new variable selection procedures for these two commonly-used models are proposed. It is demonstrated how the rates of convergence depend on the regularization parameter in the penalty function. Further, with a proper choice of the regularization parameter and the penalty function, the proposed estimators possess an oracle property. Standard error formulae are derived and their accuracies are empirically tested. Simulation studies show that the proposed procedures are more stable in prediction and more effective in computation than the best subset variable selection, and they reduce model complexity as effectively as the best subset variable selection. Compared with the LASSO, which is the penalized likelihood method with the $L_1$ -penalty, proposed by Tibshirani, the newly proposed approaches have better theoretic properties and finite sample performance.

Abstract: Preface 1. Introducing R and S-PLUS S Basics An Extended Illustration S Functions for Basic Statistics 2. Reading and Manipulating Data Data Input Working with Data Frames Matrices, Arrays, and Lists Data Attributes, Modes, and Classes 3. Exploring and Transforming Data Examining Distributions Examining Relationships Examining Multivariate Data Transforming Data 4. Fitting Linear Models Linear Least-Squares Regression Dummy-Variable Regression Analysis of Variance Models User-Specified Contrasts* General Linear Hypotheses* Data and Confidence Ellipses More on 1m and Model Formulas 5. Fitting Generalized Linear Models The Structure of GLMs Models for Categorical Responses Poisson GLMs for Count Data Odds and Ends Fitting GLMs by Iterated Weighted Least-Squares* 6. Diagnosing Problems Unusual Data Non-Normal Errors Non-Constant Error Variance Nonlinearity Collinearity and Variable Selection Diagnostics for Generalized Linear Models 7. Drawing Graphs A General Approach to S Graphics Putting it Together Effect Displays Graphics Devices 8. Writing Programs Defining Functions Working With Matrices* Program Control: Conditionals, Loops, and Recursion Apply and its Relatives Object-Oriented Programming in S* Writing S Programs

Abstract: We propose an algorithm for regression tree construction called GUIDE. It is specifically designed to eliminate variable selection bias, a problem that can undermine the reliability of inferences from a tree structure. GUIDE controls bias by employing chi-square analysis of residuals and bootstrap calibration of signif- icance probabilities. This approach allows fast computation speed, natural ex- tension to data sets with categorical variables, and direct detection of local two- variable interactions. Previous algorithms are not unbiased and are insensitive to local interactions during split selection. The speed of GUIDE enables two further enhancements—complex modeling at the terminal nodes, such as polynomial or best simple linear models, and bagging. In an experiment with real data sets, the prediction mean square error of the piecewise constant GUIDE model is within ±20% of that of CART r � . Piecewise linear GUIDE models are more accurate; with bagging they can outperform the spline-based MARS r � method.

Abstract: Several MCMC methods have been proposed for estimating probabilities of models and associated ‘model-averaged’ posterior distributions in the presence of model uncertainty. We discuss, compare, develop and illustrate several of these methods, focussing on connections between them.

Abstract: The results of Davies (1977, 1987) are extended to a linear model situation with unknown residual variance.

Abstract: This article provides an overview of recent results on lexicographic, linear, and Bayesian models for paired comparison from a cognitive psychology perspective. Within each class, we distinguish subclasses according to the computational complexity required for parameter setting. We identify the optimal model in each class, where optimality is defined with respect to performance when fitting known data. Although not optimal when fitting data, simple models can be astonishingly accurate when generalizing to new data. A simple heuristic belonging to the class of lexicographic models is Take The Best (Gigerenzer & Goldstein (1996) Psychol. Rev. 102: 684). It is more robust than other lexicographic strategies which use complex procedures to establish a cue hierarchy. In fact, it is robust due to its simplicity, not despite it. Similarly, Take The Best looks up only a fraction of the information that linear and Bayesian models require; yet it achieves performance comparable to that of models which integrate information. Due to its simplicity, frugality, and accuracy, Take The Best is a plausible candidate for a psychological model in the tradition of bounded rationality. We review empirical evidence showing the descriptive validity of fast and frugal heuristics.

Abstract: Dedication. Preface. Times Series Following Generalized Linear Models. Regression Models for Binary Time Series. Regression Models for Categorical Time Series. Regression Models for Count Time Series. Other Models and Alternative Approaches. State Space Models. Prediction and Interpolation. Appendix: Elements of Stationary Processes. References. Index.

Abstract: This paper considers an extension of M-estimators in semiparametric models for independent observations to the case of longitudinal data. We approximate the nonparametric function by a regression spline, and any M-estimation algorithm for the usual linear models can then be used to obtain consistent estimators of the model and valid largesample inferences about the regression parameters without any specification of the error distribution and the covariance structure. Included as special cases are the analysis of the conditional mean and median functions for longitudinal data.

Abstract: Among the parametric nonlinear time series model families, the smooth transition regression (STR) model has recently received attention in the literature. The considerations in this dissertation focus on the univariate special case of this model, the smooth transition autoregression (STAR) model, although large parts of the discussion can be easily generalised to the more general STR case. Many nonlinear univariate time series models can be described as consisting of a number of regimes, each one corresponding to a linear autoregressive parametrisation, between which the process switches. In the STAR models, as opposed to certain other popular models involving multiple regimes, the transition between the extreme regimes is smooth and assumed to be characterised by a bounded continuous function of a transition variable. The transition variable, in turn, may be a lagged value of the variable in the model, or another stochastic or deterministic observable variable. A number of other commonly discussed nonlinear autoregressive models can be viewed as special or limiting cases of the STAR model.The applications presented in the first two chapters of this dissertation,Chapter I: Another look at Swedish Business Cycles, 1861-1988Chapter II: Modelling asymmetries and moving equilibria in unemployment rates, make use of STAR models.In these two studies, STAR models are used to provide insight into dynamic properties of the time series which cannot be be properly characterised by linear time series models, and which thereby may be obscured by estimating only a linear model in cases where linearity would be rejected if tested. The applications being of interest in their own right, an important common objective of these two chapters is also to develop, suggest, and give examples of various methods that may be of use in discussing the dynamic properties of estimated STAR models in general.Chapter III, Testing linearity against smooth transition autoregression using a parametric bootstrap, reports the result of a small simulation study considering a new test of linearity against STAR based on bootstrap methodology.

Abstract: Thoroughly updated throughout, A First Course in Linear Model Theory, Second Edition is an intermediate-level statistics text that fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. With an innovative approach, the authors introduce to students the mathematical and statistical concepts and tools that form a foundation for studying the theory and applications of both univariate and multivariate linear models. In addition to adding R functionality, this second edition features three new chapters and several sections on new topics that are extremely relevant to the current research in statistical methodology. Revised or expanded topics include linear fixed, random and mixed effects models, generalized linear models, Bayesian and hierarchical linear models, model selection, multiple comparisons, and regularized and robust regression. New to the Second Edition: Coverage of inference for linear models has been expanded into two chapters. Expanded coverage of multiple comparisons, random and mixed effects models, model selection, and missing data. A new chapter on generalized linear models (Chapter 12). A new section on multivariate linear models in Chapter 13, and expanded coverage of the Bayesian linear models and longitudinal models. A new section on regularized regression in Chapter 14. Detailed data illustrations using R. The authors' fresh approach, methodical presentation, wealth of examples, use of R, and introduction to topics beyond the classical theory set this book apart from other texts on linear models. It forms a refreshing and invaluable first step in students' study of advanced linear models, generalized linear models, nonlinear models, and dynamic models.

Abstract: We introduce a new computer-intensive method to estimate the distribution of robust regression estimates. The basic idea behind our method is to bootstrap a reweighted representation of the estimates. To obtain a bootstrap method that is asymptotically correct, we include the auxiliary scale estimate in our reweighted representation of the estimates. Our method is computationally simple because for each bootstrap sample we only have to solve a linear system of equations. The weights we use are decreasing functions of the absolute value of the residuals and hence outlying observations receive small weights. This results in a bootstrap method that is resistant to the presence of outliers in the data. The breakdown points of the quantile estimates derived with this method are higher than those obtained with the bootstrap. We illustrate our method on two datasets and we report the results of a Monte Carlo experiment on confidence intervals for the parameters of the linear model.

Abstract: The paper presents a unified jackknife theory for a fairly general class of mixed models which includes some of the widely used mixed linear models and generalized linear mixed models as special cases. The paper develops jackknife theory for the important, but so far neglected, prediction problem for the general mixed model. For estimation of fixed parameters, a jackknife method is considered for a general class of M-estimators which includes the maximum likelihood, residual maximum likelihood and ANOVA estimators for mixed linear models and the recently developed method of simulated moments estimators for generalized linear mixed models. For both the prediction and estimation problems, a jackknife method is used to obtain estimators of the mean squared errors (MSE). Asymptotic unbiasedness of the MSE estimators is shown to hold essentially under certain moment conditions. Simulation studies undertaken support our theoretical results.

Abstract: Future end game interception scenarios of autonomous uncrewed e ying vehicles are expected to be characterized by variable velocities and lateral acceleration limits. A time-varying linear pursuit ‐evasion game model with bounded controls is presented that can be used to analyze such scenarios. The usefulness of this model is demonstrated by simulations of a realistic ballistic missile defense scenario, as an example. It is shown that a differential game guidance law derived using this time-varying model provides a signie cant improvement in the homing accuracy compared to a guidance law based on a model with constant velocities and lateral acceleration limits. Moreover, the time-varying linear model provides a much more accurate prediction of the miss distance, cone rming its validity. Also a general review of possible structures of the game space decomposition is presented. Oneofthese structuresimpliesthateven ifthepursuerdoesnot havea maneuverability advantage overtheevader, but has an agility advantage, a zero miss distance can still be achieved for some initial conditions.

Abstract: Among the various forms of canonical analysis available in the statistical literature, RDA (redundancy analysis) and CCA (canonical correspondence analysis) have become instruments of choice for ecological research because they recognize different roles for the explanatory and response data tables. Data table Y contains the response variables (e.g., species data) while data table X contains the explanatory variables. RDA is an extension of multiple linear regression; it uses a linear model of relationship between the variables in X and Y. In CCA, the response variables are chi-square transformed as the initial step, but the relationship between the transformed response data and the explanatory variables in X is still assumed to be linear. There is no special reason why nature should linearly relate changes in species assemblages to changes in environmental variables. When modeling ecological processes, to assume linearity is unrealistic in most instances and is only done because more appropriate methods of analysis are not available. We propose two empirical methods of canonical analysis based on polynomial regression to do away with the assumption of linearity in modeling the relationships between the variables in X and Y. They are called polynomial RDA and polynomial CCA, respectively, and may be viewed as alternatives to classical linear RDA and CCA. Because the analysis uses nonlinear functions of the explanatory variables, new ways of representing these variables in biplot diagrams have been developed. The use of these methods is demonstrated on real data sets and using simulations. In the examples, the new techniques produced a noticeable increase in the amount of variation of Y accounted for by the model, compared to standard linear RDA and CCA. Freeware to carry out the new analyses is available in ESA's Electronic Data Archive, Ecological Archives.

Abstract: Investigators in clinical research are often interested in determining the association between patient characteristics and post-operative length of stay (LOS). We examined the relative performance of seven different statistical strategies for analyzing LOS in a cohort of patients undergoing CABG surgery. We compared linear regression; linear regression with log-transformed length of stay; generalized linear models with the following distributions: Poisson, negative binomial, normal, and gamma; and semi-parametric survival models. Nine of twenty patient characteristics were found to be significantly associated with increased LOS in all models. The models disagreed upon the statistical significance of the association between the remaining patient characteristics and increased LOS. Generalized linear models with Poisson, negative binomial, and gamma distributions, and the Cox regression model demonstrated the greatest consistency. With the exception of Cox regression, all models had similar ability to predict length of stay in the actual data. However, the generalized linear models tended to have marginally lower prediction error than the linear models. Using four measures of prediction error, Cox regression had substantially higher prediction error than the other models. Generalized linear models were best able to predict patient length of stay in Monte Carlo simulations that were performed. Researchers should consider generalized linear models with normal, Poisson, or negative binomial distributions for predicting length of stay following CABG surgery. Post-operative length of stay is a complex phenomenon that is difficult to incorporate into a simple parametric model due to a small proportion of patients having very long lengths of stay.

Abstract: In this paper we propose and study non-parametric tests for the validity of (composite) Generalized Linear Models with a given parametric link structure, which are based on certain empirical processes marked by the residuals. When properly transformed to their innovation part the resulting test statistics are distribution-free. The method perfectly adapts to a situation, when also the input vector follows a dimension reducing model.

Abstract: We consider estimation and statistical hypothesis testing on classification images obtained from the two-alternative forced-choice experimental paradigm. We begin with a probabilistic model of task performance for simple forced-choice detection and discrimination tasks. Particular attention is paid to general linear filter models because these models lead to a direct interpretation of the classification image as an estimate of the filter weights. We then describe an estimation procedure for obtaining classification images from observer data. A number of statistical tests are presented for testing various hypotheses from classification images based on some more compact set of features derived from them. As an example of how the methods we describe can be used, we present a case study investigating detection of a Gaussian bump profile.

Abstract: Author(s): Sun, Hongyu; Liu, Henry X.; Xiao, Heng; Ran, Bin | Abstract: Traffic data is highly nonlinear and also varies with time of day. It changes abruptly when entering or leaving a congestion hour. Therefore,the prediction of travel time requires accurate models. This leads to the problem of approximating nonlinear and time-variant functions. In this paper, we propose and apply local linear regression models to short-term traffic prediction. Local linear regression is one type of local weighted regression methods. It has been applied to many problems, including artificial intelligence, dynamic system identification and data mining. It can be used for nonlinear time series prediction under certain mixing conditions. The performance of the proposed model is compared with previous nonparametric approaches, such as nearest neighborhood and kernel methods using 32-day traffic speed data collected on the Houston, Texas, US-290 Northwest Freeway. We found that the local linear methods consistently outperform the nearest neighborhood and kernel smoothing methods.

Abstract: Logan's graphical model is a robust estimation of the total distribution volume (DVt) of reversibly bound radiopharmaceuticals, but the resulting DVt values decrease with increasing noise. The authors hypothesized that the noise dependence can be reduced by a linear regression model that minimizes the sum of squared perpendicular rather than vertical (y) distances between the data points and fitted straight line. To test the new method, 15 levels of simulated noise (repeated 2,000 times) were added to synthetic tissue activity curves, calculated from two different sets of kinetic parameters. Contrary to the traditional method, there was no ( P > 0.05) or dramatically decreased noise dependence with the perpendicular model. Real dynamic 11C (+) McN5652 serotonin transporter binding data were processed either by applying Logan analysis to average counts of large areas or by averaging the Logan slopes of individual-voxel data. There were no significant differences between the parameters when the perpendicular regression method was used with both approaches. The presented experiments show that the DVt calculated from the Logan plot is much less noise dependent if the linear regression model accounts for errors in both the x and y variables, allowing fast creation of unbiased parametric images from dynamic positron-emission tomography studies.

Abstract: The objective of a thermal error compensation system for CNC machine tools is improved machining accuracy through real time error compensation. The compensation capability depends on the accuracy of the thermal error model. A thermal error model can be obtained using an appropriate combination of temperature variables. In this study, the thermal error modeling is based on a correlation grouping and a successive linear regression analysis. During the successive regression analysis, the residual mean square is minimized using a judgement function, which, although simple, is effective in the selection of variables in the error model. When evaluating the proposed thermal error model, the multi-collinearity problem and computational time are both improved through the correlation grouping, and the linear model is more robust against measurement noises than the engineering judgement model, which includes variables with higher order terms. The modeling method used in this study can be effectively and practically applied to real-time error compensation because it includes the advantages of simple application, reduced computational time, sufficient model accuracy, and model robustnesss.