Lack-of-Fit Tests for Generalized Linear Models via Splines

References

• Agresti , A. ( 2002 ). Categorical Data Analysis. , 2nd ed. New York : John Wiley and Sons .
   Google Scholar
• Aerts , M. , Claeskens , G. , Hart , J. D. ( 1999 ). Testing the fit of a parametric function . J. Amer. Statist. Assoc. 94 : 869 – 879 .
   Web of Science ®Google Scholar
• Brockmann , H. J. ( 1996 ). Satellite male groups in horseshoe crabs, Limulus polypbemus . Ethology 102 : 1 – 21 .
   Web of Science ®Google Scholar
• Buja , A. , Hastie , T. , Tibshirani , R. ( 1989 ). Linear smoother and additive models (with Discussion) . Ann. Statist. 17 : 453 – 555 .
   Web of Science ®Google Scholar
• Cantoni , E. , Hastie , T. ( 2002 ). Degrees-of-freedom tests for smoothing splines . Biometrika 289 : 251 – 263 .
   Web of Science ®Google Scholar
• Castaño-Martínez , A. , López-Blázquez , F. ( 2005 ). Distribution of a sum of weighted central chi-square variables . Commun. Statist. Theor. Meth. 34 : 515 – 524 .
   Web of Science ®Google Scholar
• Crainiceanu , C. M. , Ruppert , D. ( 2004 ). Likelihood ratio tests for goodness-of-fit of a nonlinear regression model . J. Multivariate Anal. 91 : 35 – 52 .
   Web of Science ®Google Scholar
• Crainiceanu , C. M. , Ruppert , D. , Claeskens , G. , Wand , M. P. ( 2005 ). Exact likelihood ratio tests for penalised splines . Biometrika 92 : 91 – 103 .
   Web of Science ®Google Scholar
• Curry , H. B. , Schoenberg , I. J. ( 1966 ). On Pólya frequency functions IV: The fundamental splines and their limits . J. Anal. Math. 17 : 71 – 107 .
   Web of Science ®Google Scholar
• Davies , R. B. ( 1973 ). Numerical inversion of a characteristic function . Biometrika 60 : 415 – 417 .
   Web of Science ®Google Scholar
• Davies , R. B. (1980). The distribution of a linear combination of χ2 random variables. Appl. Statist. 29:323–333.
   Google Scholar
• de Boor , C. ( 2001 ). A Practical Guide to Splines . Revised edition. Applied Mathematical Sciences . Vol. 27 . New York : Spring-Verlag .
   Google Scholar
• Eilers , P. H. C. , Marx , B. D. ( 1996 ). Flexible smoothing with B-splines and penalties . Statist. Sci. 11 : 89 – 121 .
   Web of Science ®Google Scholar
• Good , I. J. , Gaskins , R. A. ( 1971 ). Nonparametric roughness penalties for probability densities . Biometrika 58 : 255 – 277 .
   Web of Science ®Google Scholar
• Green , P. J. , Yandell , B. S. ( 1985 ). Semi-Parametric Generalized Linear Models . Lecture Notes in Statistics. Berlin : Springer, Vol. 32, pp. 44–55 .
   Google Scholar
• Green , P. J. ( 1987 ). Penalized likelihood for general semi-parametric regression models . Int. Statist. Rev. 55 : 245 – 259 .
   Web of Science ®Google Scholar
• Green , P. J. , Silverman , B. W. ( 1994 ). Nonparametric Regression and Generalized Linear Models . New York : Chapman & Hall .
   Google Scholar
• Hart , J. D. ( 1997 ). Nonparametric Smoothing and Lack-of-Fit Tests . New York : Springer Verlag .
   Google Scholar
• Hastie , T. J. , Tisbshirani , R. J. ( 1990 ). Generalized Additive Models . New York : Chapman & Hall .
   Google Scholar
• Imhof , J. P. ( 1961 ). Computing the distribution of quadratic forms in normal variables . Biometrika 48 : 419 – 426 .
   Web of Science ®Google Scholar
• Kauermann , G. , Tutz , G. ( 2001 ). Testing generalized linear and semiparametric models against smooth alternatives . J. Roy. Statist. Soc. Ser. B 63 : 147 – 166 .
   Google Scholar
• Liu , A. , Wang , Y. ( 2004 ). Hypothesis testing in smoothing spline models . J. Statist. Computat. Simul. 74 : 581 – 597 .
   Web of Science ®Google Scholar
• McCullagh , P. , Nelder , J. A. ( 1989 ). Generalized Linear Models. , 2nd ed. London : Chapman & Hall .
   Google Scholar
• Nelder , J. A. Wedderburn , R. W. M. ( 1972 ). Generalized linear models . J. Roy. Statist. Soc. Ser. A 135 : 370 – 384 .
   Google Scholar
• Ruppert , D. , Wand , M. P. , Carroll , R. J. ( 2003 ). Semiparametric Regression . Cambridge : Cambridge University Press .
   Google Scholar
• Scheffé , H. ( 1959 ). The Analysis of Variance . New York : John Wiley and Sons .
   Google Scholar
• Schoenberg , I. J. ( 1946 ). Contributions to the problem of approximation of equidistant data by analytic functions. Quart. Appli. Math. 4:45–99; 112–141 .
   Google Scholar
• Severini , T. A. , Staniswalis , J. G. ( 1994 ). Quasi-likelihood estimation in semiparametric models . J. Amer. Statist. Assoc. 89 : 501 – 511 .
   Web of Science ®Google Scholar
• Sheil , J. , O'Muircheartaigh , I. ( 1977 ). The distribution of non-negative quadratic forms in normal variables . Appl. Statist. 26 : 92 – 98 .
   Google Scholar
• Smith , P. L. ( 1979 ). Splines as a useful and convenient statistical tool . Amer. Statist. 33 : 57 – 62 .
   Web of Science ®Google Scholar