Literatur zum Statistischen Praktikum WS 97/98

Aus der klassischen Theorie der lineare Modelle brauchen wir als Bezugspunkte:
€ Definition des allgemeinen linearen Modells
€ Kleinster-Quadrate-Schätzer
€ Gauss-Markoff-Theorem
€ Güte von F- bzw. t-Test
Dies findet sich in fast allen klassischen Büchern über lineare Modelle (Christensen, John, Jørgensen, Rao, Searle, Seber, Serfling). Wird zu Anfang des Praktikums wiederholt.

Die lineare Covarianzanalyse ist z.B. in Christensen, Searle oder Seber diskutiert.

Fragen

Wie vergleicht man die Macht von Tests unter Berücksichtigung von Covariablen?
z.B. Asymptotische relative Effizienz (Lehmann, Serfling, Shervish).
Wie kann man Covariablen berücksichtigen, die nicht-linearen Einfluß haben ?
z.B. Ansätze aus der nicht-linearen Regression übernehmen (Birkes&Dodge, Eubank, Green & Silverman, Wand & Jones)
Wie kann man Covariable berücksichten, in denen sich ein zeitlicher Verlauf widerspiegelt ?
z.B. Ansätze aus der Longitudinaldaten-Analyse übernehmen (Diggle et al., Green & Silverman)


Literatur: Lehrbücher

Birkes, D. & Dodge, Y.: Alternative Methods of Regression. Wiley: NewYork 1993

Christensen, R.: Analysis of Variance, Design and Regression. Chapman & Hall: London 1996
Ch. 10: Analysis of Covariance
Ch. 18: Nonlinear Regression

Diggle, P.J.; Liang, K-Y. & Zeger, S.: Analysis of Longitudinal Data. Oxford Science Publications. Oxford 1994
Ch. 6 Analysis of Variance Methods
Ch. 7 Generalized Linear Models for Longitudinal Data

Eubank, R. L.: Spline Smoothing and Nonparametric Regression. Marcel Decker: NewYork 1988.
Ch. 6.2.4 Partial splines

Green, P.J. & Silverman, B.W.: Nonparametric Regression and Generalized Linear Models. Chapman & Hall: London 1994
Ch. 5: Generalized linear models

Hoaglin, D.C.; Mosteller, F. & Tukey, J.W.: Fundamentals of Exploratory Analysis of Variance. Wiley: London 1991

Ivanov, A.V.: Asymptotic Theory of Nonlinear Regression. Kluwer: Dordrecht 1997
Ch. 3.16: Asymptotic Expansions of Distributions of Quadratic Functionals of the Least Square Estimator
Ch. 3.17: Comparison of Powers ...

John, P.W.M: Statistical Design and Analysis of Experiments. Macmillan: NewYork 1971

Jørgensen, B. The Theory of Linear Models. Chapman & Hall 1993.

Lehmann, E.L.: Theory of Point Estimation. Wiley: London 1983
Ch. 3.4: Linear Models (Normal)
Ch. 6.1: Asymptotic efficiency

Rao, C.R.: Linear Statistical Inference and Its Applications. Wiley: London 1973

Searle, S.R.: Linear Models. Wiley: London 1971
Ch. 8.2 Covariance
Ch. 8.2b The 1-way classification

Seber, G. A. F.: Linear Regression. Wiley 1977
Ch. 10 Analysis of Covariance and Missing Observations

Serfling, R.J.: Approximation Theorems of Mathematical Statistics. Wiley: London 1980
Ch. 10 Asymptic Relative Efficiency

Shervish, M.: Theory of Statistics. Springer: Heidelberg 1995
Ch. 7.3 Large Sample Estimation, (incl. asymptotic relative efficiency)

Wand, M.P. & Jones, M.C.: Kernel Smoothing. Chapman & Hall: London 1995
Ch. 5 Kernel Regression


Literatur: Original-Literatur zur Covarianz-Analyse

(wird in Auszügen referiert und diskutiert)

Bhapkar, Vasant P.: Univariate and multivariate multisample location and scale tests. In: Nonparametric methods, Handb. Stat. 4, 31-62 (1984).

Bingham, C. & Fienberg, S.E.: Textbook Analysis of Covariance - Is it Correct ? Biometrics 38 (1982) 741-753

Birch, J. B. & Myers, R.H.: Robust Analysis of Covariance. Biometrics 38 (1982) 699-713.

Boehnke K. : The influence of several sample characteristics on the efficiency of parametric and nonparametric analysis of variance. Springer-Verlag (Berlin, New York) Springer:Berlin 1983, 173p. Siehe auch Enderlein 1985.

Breslow, N.: Covariance Adjustment of Relative-Risk Estimates in Matched Studies. Biometrics 38 (1982) 661-672.

Enderlein, G.: Review of ``The influence of several sample characteristics on the efficiency of parametric and nonparametric analysis of variance'' K. Boehnke, (Auth);. Biometrical J., Zeitschrift für Math. Meth. in den Biowissenschaften 27 (1985) 590.

Conover, W.J. & Iman, R.L.: Anylysis of Covariance Using the Rank Transformation. Biometrics 38 (1982) 715-724.

Cox, D.R. & McCullagh, P.: Some Aspects of Analysis of Covariance. Biometrics 38 (1982) 541-561.

Dugue, D.: A non parametric test in covariance analysis. Recent Dev. Stat., Proc. Eur. Meet. Stat. Grenoble 1976, 427-428 (1977).

Hall, P. & Hart, J.D.: Bootstrap test for difference between means in nonparametric regression. J. of the Amer. Stat'l. Assn. 85 (1990) 1039-1049.

Hemmerle, W.J.: Analysis of Covariance Algorithms. Biometrics 38 (1982) 725-736

Henderson, C.R.: Analysis of Covariance in the Mixed Model: Higher-Level, Nonhomogeneous, and Random Regressions. Biometrics 38 (1982) 623-640.

Lane, P.W. & Nelder, J.A.: Analysis of Covariance and Standardization as Instances of Prediction. Biometrics 38 (1982) 613-621.

Maxwell, S. E., Delaney, H. D. & Manheimer, J. M.: ANOVA of residuals and ANCOVA: Correcting an illusion by using model comparisons and graphs. Journal of Educational Statistics 10 (1985) 197-209.

Olejnik, S. F. & Algina, J.: Parametric ANCOVA and the rank transform ANCOVA when the data are conditionally non-normal and heteroscedastic. Journal of Educational Statistics 9 (1984) 129-149.

Olejnik, S. F. & Algina, J.: An analysis of statistical power for parametric ANCOVA and rank transform ANCOVA. Communications in Statistics, Part A--Theory and Methods 16 (1987) 1923-1949.

Quade, D.: Nonparametric analysis of covariance by matching. Biometrics 38 (1982) 597- 611.

Seaman, S. L., Algina, J. & Olejnik, S. F.: Type I error probabilities and power of the rank and parametric ANCOVA procedures. Journal of Educational Statistics 10 (1985) 345-367.

Shoemaker, L.H.: A nonparametric method for analysis of variance. Communications in Stat., Part B--Simulation and Comp. 15 (1986) 609-632.

Stephenson, W.R.;David Jacobson, J.: A comparison of nonparametric analysis of covariance techniques. Communications in Stat., Part B--Simulation and Comp. 17 (1988) 451-461.

Wilcox, R.R.: Non-parametric analysis of covariance based on predicted medians. British Journal of Mathematical and Statistical Psychology 44 (1991) 221-230.