References
- Sacks , J. and Ylvisaker , D. 1970 . Designs for regression problems with correlated errors III . Ann. Math. Stat. , 41 : 2057 – 2074 .
- von Neumann , J. 1941 . Distribution of the ratio of mean squared successive difference to variance . Ann. Math. Stat. , 12 : 367 – 395 .
- Raz , J. 1990 . Testing for no effect when estimating a smooth function by nonparametric regression: a randomization approach . J. Am. Stat. Assoc. , 85 : 132 – 138 .
- Barry , D. and Hartigan , J. A. 1990 . An omnibus test for departures from constant mean . Ann. Stat. , 18 : 1340 – 1357 .
- Eubank , R. L. and Hart , J. D. 1992 . Testing goodness-of-fit in regression via order selection criteria . Ann. Stat. , 20 : 1412 – 1425 .
- Eubank , R. L. 2000 . Testing for no effect by cosine series methods . Scand. J. Stat. , 27 : 747 – 763 .
- Azzalini , A. and Bowman , A. 1993 . On the use of nonparametric regression for checking linear relationships . J. R. Stat. Soc. B , 55 : 549 – 559 .
- González Manteiga , W. and Cao , R. 1993 . Testing the hypothesis of a general linear model using nonparametric regression estimation . 2 : 161 – 188 . Test
- Härdle , W. and Mammen , E. 1993 . Comparing nonparametric versus parametric regression fits . Ann. Stat. , 21 : 1926 – 1947 .
- Fan , Y. and Li , Q. 1996 . Consistent model specification tests: omitted variables and semiparametric functional forms . Econometrica , 64 : 865 – 890 .
- Stute , W. 1997 . Nonparametric model checks for regression . Ann. Stat. , 25 : 613 – 641 .
- Hart , J. 1997 . “ Nonparametric Smoothing and Lack-of-fit Test ” . New York : Springer-Verlag .
- Dette , H. and Munk , A. 1998 . Validation of linear regression models . Ann. Stat. , 26 : 778 – 800 .
- Dette , H. and Munk , A. 1998 . Testing heteroscedasticity in nonparametric regression . J. R. Stat. Soc. B , 60 : 693 – 708 .
- Ai¨t-Sahalia , Y. , Bickel , P. J. and Stoker , T. M. 2001 . Goodness-of-fit tests for kernel regression with an application to option implied volatilities . J. Econ. , 105 : 363 – 412 .
- Fan , J. Q. and Huang , L. S. 2001 . Goodness-of-fit tests for parametric regression models . J. Am. Stat. Assoc. , 96 : 640 – 652 .
- Fan , J. , Zhang , C. M. and Zhang , J. 2001 . Generalized likelihood ratio statistics and Wilks phenomenon . Ann. Stat. , 29 : 153 – 193 .
- Horowitz , J. L. and Spokoiny , V. G. 2001 . An adaptive, rate-optimal test of a parametric mean-regression model against a nonparametric alternative . Econometrica , 69 : 599 – 631 .
- Munk , A. 2002 . Testing the goodness of fit of parametric regression models with random Toeplitz forms . Scand. J. Stat. , 29 ( 3 ) : 501 – 535 .
- Akritas , M. G. and Papadatos , N. 2004 . Heteroscedastic one-way ANOVA and lack-of-fit test . J. Am. Stat. Assoc. , 99 : 368 – 382 .
- Boos , D. D. and Brownie , C. 1995 . ANOVA and rank tests when the number of treatments is large . Stat. Probab. Lett. , 23 : 183 – 191 .
- Akritas , M. G. and Arnold , S. 2000 . Asymptotics for analysis of variance when the number of levels is large . J. Am. Stat. Assoc. , 95 : 212 – 226 .
- Akritas , M. G. 2000 . Nonparametric regression and lack-of-fit tests . Unpublished lecture notes
- Schott , J. R. 2005 . “ Matrix Analysis for Statistics ” . In , 2nd , New York : Wiley .
- Rice , J. 1984 . Bandwidth choice for nonparametric regression . Ann. Stat. , 12 : 1215 – 1230 .
- Geyer , C. J. 1991 . Constrained maximum likelihood exemplified by isotonic convex logistic regression . J. Am. Stat. Assoc. , 86 : 717 – 724 .
- Billingsley , P. 1986 . “ Probability and Measures ” . New York : Wiley .