Linear models in statistics

Preface. 1. Introduction. 2. Matrix Algebra. 3. Random Vectors and Matrices. 4. Multivariate Normal Distribution. 5. Distribution of Quadratic Forms in y. 6. Simple Linear Regression. 7. Multiple Regression: Estimation. 8. Multiple Regression: tests of Hypotheses and Confidence Intervals. 9. Multiple Regression: Model Validation and Diagnostics. 10. Multiple Regression: random x's. 11. Multiple Regression: Bayesian Inference. 12. Analysis-of-Variance Models. 13. One-Way Analysis-of-Variance: balanced Case. 14. Two-Way Analysis-of Variance: Balanced Case. 15. Analysis-of-Variance: The Cell Means Model for Unbalanced Data. 16. Analysis-of-Covariance. 17. Linear Mixed Models. 18. Additional Models. Appendix A. Answers and Hits to the Problems. References. Index.

[1]  W. H. Laverty,et al.  Answer to Query , 1908, Mathematical Gazette.

[2]  R. Fisher.  014: On the "Probable Error" of a Coefficient of Correlation Deduced from a Small Sample. , 1921 .

[3]  H. Hotelling.  Applications of the Theory of Error to the Interpretation of Trends , 1929 .

[4]  Mordecai Ezekiel,et al.  Methods of Correlation Analysis. , 1931 .

[5]  The Use of the Method of Partial Regression in the Analysis of Comparative Feeding Trial Data , 1933 .

[6]  Frank Yates,et al.  The Analysis of Multiple Classifications with Unequal Numbers in the Different Classes , 1934 .

[7]  W. G. Cochran,et al.  The distribution of quadratic forms in a normal system, with applications to the analysis of covariance , 1934, Mathematical Proceedings of the Cambridge Philosophical Society.

[8]  C. Bonferroni.  Il calcolo delle assicurazioni su gruppi di teste , 1935 .

[9]  P. Mahalanobis.  On the generalized distance in statistics , 1936 .

[10]  A. Wald.  Tests of statistical hypotheses concerning several parameters when the number of observations is large , 1943 .

[11]  S. Marcuse.  Optimum Allocation and Variance Components in Nested Sampling with an Application to Chemical Analysis , 1949 .

[12]  J. S. Gutsell.  The effect of sulfamerazine on the erythrocyte and hemoglobin content of trout blood. , 1951, Biometrics.

[13]  Anders Hald,et al.  Statistical Theory with Engineering Applications , 1952 .

[14]  H. Scheffé.  A METHOD FOR JUDGING ALL CONTRASTS IN THE ANALYSIS OF VARIANCE , 1953 .

[15]  F. Graybill.  On Quadratic Estimates of Variance Components , 1954 .

[16]  G. Box,et al.  The Exploration and Exploitation of Response Surfaces: An Example of the Link between the Fitted Surface and the Basic Mechanism of the System , 1955 .

[17]  F. Graybill,et al.  A Note on Uniformly Best Unbiased Estimators for Variance Components , 1956 .

[18]  Bernard Ostle,et al.  Statistics in Research: Basic Concepts and Techniques for Research Workers , 1990 .

[19]  H. O. Hartley,et al.  A Plan for Programming Analysis of Variance for General Purpose Computers , 1956 .

[20]  M. Healy,et al.  Missing Values in Experiments Analysed on Automatic Computers , 1956 .

[21]  P. Mahalanobis.  Professor Ronald Aylmer Fisher , 1964 .

[22]  N. L. Johnson,et al.  Linear Statistical Inference and Its Applications , 1966 .

[23]  M. Tiku.  Tables of the Power of the F-Test , 1967 .

[24]  F. M. Speed.  A new approach to the analysis of linear models , 1969 .

[25]  G. Zyskind.  Introduction to Matrices with Applications in Statistics , 1970 .

[26]  H. D. Patterson,et al.  Recovery of inter-block information when block sizes are unequal , 1971 .

[27]  Joseph R. Sligo,et al.  EMPIRICAL COMPARISON OF UNIVARIATE AND MULTIVARIATE ANALYSIS OF VARIANCE PROCEDURES , 1971 .

[28]  D. Lindley,et al.  Bayes Estimates for the Linear Model , 1972 .

[29]  W. Fuller,et al.  Transformations for Estimation of Linear Models with Nested-Error Structure , 1973 .

[30]  P. J. Huber.  Robust Regression: Asymptotics, Conjectures and Monte Carlo , 1973 .

[31]  B. J. Winer,et al.  Statistical Principles in Experimental Design, 2nd Edition. , 1973 .

[32]  N. S. Urquhart,et al.  Estimation associated with linear models: a revisitation , 1973 .

[33]  D. F. Andrews,et al.  A Robust Method for Multiple Linear Regression , 1974 .

[34]  F. Hampel.  The Influence Curve and Its Role in Robust Estimation , 1974 .

[35]  Solomon Kullback,et al.  Loglinear Models in Contingency Table Analysis , 1974 .

[36]  R. Welsch.  Confidence Regions for Robust Regression , 1975 .

[37]  Stephen E. Fienberg,et al.  Discrete Multivariate Analysis: Theory and Practice , 1976 .

[38]  R. R. Hocking,et al.  A Full Rank Analysis of Some Linear Model Problems , 1975 .

[39]  S. J. Devlin,et al.  Robust estimation and outlier detection with correlation coefficients , 1975 .

[40]  Franklin A. Graybill,et al.  Theory and Application of the Linear Model , 1976 .

[41]  R. R. Hocking.  The analysis and selection of variables in linear regression , 1976 .

[42]  Ronald D. Snee,et al.  Validation of Regression Models: Methods and Examples , 1977 .

[43]  Frederick Mosteller,et al.  Data Analysis and Regression , 1978 .

[44]  Shayle R. Searle.  Analyses of Variance of Unbalanced Data from 3-Way and Higher-Order Classifications , 1977 .

[45]  B. Bailey.  Tables of the Bonferroni t Statistic , 1977 .

[46]  C. Chatfield,et al.  Fourier Analysis of Time Series: An Introduction , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[47]  R. R. Hocking,et al.  Methods of Analysis of Linear Models with Unbalanced Data , 1978 .

[48]  Melvin W. Carter,et al.  A Comparison of Five Statistical Methods for Analyzing Pretest-Posttest Designs , 1978 .

[49]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[50]  C. R. Henderson,et al.  The Missing Subclass Problem in Two-Way Fixed Models , 1978 .

[51]  R. Welsch,et al.  The Hat Matrix in Regression and ANOVA , 1978 .

[52]  R. M. Loynes,et al.  Regression Methods: A Tool for Data Analysis , 1979 .

[53]  S. Holm.  A Simple Sequentially Rejective Multiple Test Procedure , 1979 .

[54]  Birch B. Jeffrey.  Some convergence properties of iterated reweighted least squares in the location model , 1980 .

[55]  G. Reinsel,et al.  Introduction to Mathematical Statistics (4th ed.). , 1980 .

[56]  S. R. Searle,et al.  Some Computational and Model Equivalences in Analyses of Variance of Unequal-Subclass-Numbers Data , 1981 .

[57]  S. Weisberg,et al.  Residuals and Influence in Regression , 1982 .

[58]  S. Fienberg,et al.  Textbook Analysis of Covariance -- Is It Correct? , 1982 .

[59]  R. Welsch,et al.  Efficient Bounded-Influence Regression Estimation , 1982 .

[60]  D. Scott,et al.  Covariance analyses with heterogeneity of slopes in fixed models. , 1982, Biometrics.

[61]  I. Guttman.  Linear models : an introduction , 1982 .

[62]  Clifford C. Clogg,et al.  The Analysis of Categorical Data (2nd Ed.). , 1983 .

[63]  J. Royston.  Some Techniques for Assessing Multivarate Normality Based on the Shapiro‐Wilk W , 1983 .

[64]  D. J. Pike,et al.  A course in linear models , 1983 .

[65]  R. N. Kackar,et al.  Approximations for Standard Errors of Estimators of Fixed and Random Effects in Mixed Linear Models , 1984 .

[66]  Robert M. Judish,et al.  Applied Linear Statistical Methods , 1984 .

[67]  F. G. Giesbrecht,et al.  Two-stage analysis based on a mixed model: large-sample asymptotic theory and small-sample simulation results , 1985 .

[68]  P. McCullagh.  Analysis of Ordinal Categorical Data , 1985 .

[69]  Eric R. Zieyel.  The Analysis of Linear Models , 1986 .

[70]  A. Rossier.  Letter to the Editor , 1986, Paraplegia.

[71]  J. Shaffer.  Modified Sequentially Rejective Multiple Test Procedures , 1986 .

[72]  R. Simes,et al.  An improved Bonferroni procedure for multiple tests of significance , 1986 .

[73]  B. Holland,et al.  An Improved Sequentially Rejective Bonferroni Test Procedure , 1987 .

[74]  Daniel R. Jeske,et al.  Prediction-interval procedures and (fixed-effects) confidence-interval procedures for mixed linear models , 1988 .

[75]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[76]  Y. Hochberg.  A sharper Bonferroni procedure for multiple tests of significance , 1988 .

[77]  Henri Theil,et al.  Information-Theoretic Measures of Fit for Univariate and Multivariate Linear Regressions , 1988 .

[78]  G. Hommel.  A stagewise rejective multiple test procedure based on a modified Bonferroni test , 1988 .

[79]  David W. Hosmer,et al.  Best subsets logistic regression , 1989 .

[80]  Ronald Christensen,et al.  Plane Answers to Complex Questions: The Theory of Linear Models , 1989 .

[81]  Bernhard W. Flury.  Understanding Partial Statistics and Redundancy of Variables in Regression and Discriminant Analysis , 1989 .

[82]  David W. Hosmer,et al.  Applied Logistic Regression , 1991 .

[83]  D. G. Simpson,et al.  The Statistical Analysis of Discrete Data , 1989 .

[84]  D. Rom.  A sequentially rejective test procedure based on a modified Bonferroni inequality , 1990 .

[85]  D. Turner.  An easy way to tell what you are esting in analysis of variance , 1990 .

[86]  A. C. Rencher,et al.  Assessing the contribution of individual variables following rejection of a multivariate hypothesis , 1990 .

[87]  F. Kianifard,et al.  A first course in the theory of linear statistical models , 1990 .

[88]  Sheldon M. Ross,et al.  Introduction to Probability Models (4th ed.). , 1990 .

[89]  D. Saville.  Multiple Comparison Procedures: The Practical Solution , 1990 .

[90]  G. A. Barnard,et al.  Student: A Statistical Biography of William Sealy Gosset , 1990 .

[91]  Eric R. Ziegel,et al.  Handbook of Nonlinear Regression Models , 1991 .

[92]  A. Hossain,et al.  A comparative study on detection of influential observations in linear regression , 1991 .

[93]  J. Neter,et al.  Applied Linear Statistical Models (3rd ed.). , 1992 .

[94]  G. Casella,et al.  Explaining the Gibbs Sampler , 1992 .

[95]  J. H. Schuenemeyer,et al.  Generalized Linear Models (2nd ed.) , 1992 .

[96]  Shein-Chung Chow,et al.  Advanced Linear Models: Theory and Applications , 1993 .

[97]  A. C. Rencher.  The contribution of individual variables to Hotelling's T2, Wilks' lambda, and R2. , 1993, Biometrics.

[98]  Franklin A. Graybill,et al.  Regression Analysis-Concepts and Applications , 1995 .

[99]  Gary G. Koch,et al.  Categorical Data Analysis Using The SAS1 System , 1995 .

[100]  Dale Borowiak,et al.  The Theory of Linear Models , 1995 .

[101]  P. Diggle.  Analysis of Longitudinal Data , 1995 .

[102]  James H. Stapleton,et al.  Linear Statistical Models , 1995 .

[103]  John A. Nelder,et al.  The Computer Analysis of Factorial Experiments: In Memoriam—Frank Yates , 1995 .

[104]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .

[105]  Geert Molenberghs,et al.  THE STATISTICAL ANALYSIS OF CATEGORICAL DATA (3rd edn). , 1996 .

[106]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[107]  P. Cornelius,et al.  Approximate F-tests of multiple degree of freedom hypotheses in generalized least squares analyses of unbalanced split-plot experiments , 1996 .

[108]  Thomas P. Ryan,et al.  Modern Regression Methods , 1996 .

[109]  Angela M. Dean.  Methods and Applications of Linear Models , 1996 .

[110]  W. Mendenhall,et al.  A Second Course in Statistics: Regression Analysis , 1996 .

[111]  Keith E Muller,et al.  THE DISTRIBUTION OF COOK'S D STATISTIC. , 1997, Communications in statistics: theory and methods.

[112]  E. Smith.  Methods of Multivariate Analysis , 1997 .

[113]  M. Kenward,et al.  Small sample inference for fixed effects from restricted maximum likelihood. , 1997, Biometrics.

[114]  David E. Booth,et al.  Multivariate statistical inference and applications , 1997 .

[115]  D. Harville.  Matrix Algebra From a Statistician's Perspective , 1998 .

[116]  E. Lehmann.  Elements of large-sample theory , 1998 .

[117]  Russell D. Wolfinger,et al.  The analysis of repeated measurements: a comparison of mixed-model satterthwaite f tests and a nonpooled adjusted degrees of freedom multivariate test , 1999 .

[118]  M. Driscoll,et al.  An Improved Result Relating Quadratic Forms and Chi-Square Distributions , 1999 .

[119]  Richard F. Gunst,et al.  Applied Regression Analysis , 1999, Technometrics.

[120]  Arthur E. Hoerl,et al.  Ridge Regression: Biased Estimation for Nonorthogonal Problems , 2000, Technometrics.

[121]  A. Winsor.  Sampling techniques. , 2000, Nursing times.

[122]  James K. Lindsey,et al.  Applying Generalized Linear Models , 2000 .

[123]  S M Stigler.  The problematic unity of biometrics. , 2000, Biometrics.

[124]  Helen Brown,et al.  Applied Mixed Models in Medicine , 2000, Technometrics.

[125]  Saad T. Bakir,et al.  Nonparametric Regression and Spline Smoothing , 2000, Technometrics.

[126]  Tim B. Swartz,et al.  Approximating Integrals Via Monte Carlo and Deterministic Methods , 2000 .

[127]  Y. Benjamini,et al.  THE CONTROL OF THE FALSE DISCOVERY RATE IN MULTIPLE TESTING UNDER DEPENDENCY , 2001 .

[128]  Sujit K. Ghosh,et al.  Essential Wavelets for Statistical Applications and Data Analysis , 2001, Technometrics.

[129]  Ana Ivelisse Avilés,et al.  Linear Mixed Models for Longitudinal Data , 2001, Technometrics.

[130]  J. A. Díaz-García,et al.  SENSITIVITY ANALYSIS IN LINEAR REGRESSION , 2022 .