Estimating functionals of the error distribution in parametric and nonparametric regression

References

• Akritas , MG and Keilegom , Van I . (2001) . Non-parametric estimation of the residual distribution . Scand. J. Statist. , 28 : 549 – 567 .
   Web of Science ®Google Scholar
• Bickel PJ Klaassen CAJ Ritov Y Wellner JA (1998) Efficient and Adaptive Estimation for Semiparametric Models, Springer New York
   Google Scholar
• Carroll , RJ . (1982) . Adapting for heteroscedasticity in linear models . Ann. Statist. , 10 : 1224 – 1233 .
   Web of Science ®Google Scholar
• Chiou , J-M and Müller , H-G . (1999) . Nonparametric quasi-likelihood . Ann. Statist. , 27 : 36 – 64 .
   Web of Science ®Google Scholar
• Hájek , J . (1970) . A characterization of limiting distributions of regular estimates . Z. Wahrsch. Verw. Gebiete , 14 : 323 – 330 .
   Web of Science ®Google Scholar
• Hoeffding , W . (1963) . Probability inequalities for sums of bounded random variables . J. Amer. Statist. Assoc. , 58 : 13 – 30 .
   Web of Science ®Google Scholar
• Koul , HL . (1969) . Asymptotic behavior of Wilcoxon type confidence regions in multiple linear regression . Ann. Math. Statist. , 40 : 1950 – 1979 .
   Google Scholar
• Koul , HL . (1970) . Some convergence theorems for ranks and weighted empirical cumulatives . Ann. Math. Statist. , 41 : 1768 – 1773 .
   Google Scholar
• Koul HL (2002) Weighted Empirical Processes in Dynamic Nonlinear Models 2nd ed.,, Lecture Notes in Statistics 166 Springer New York
   Google Scholar
• Koul , HL and Schick , A . (2003) . Testing for superiority among two regression curves . J. Statist. Plann. Inference , 117 : 15 – 33 .
   Web of Science ®Google Scholar
• Cam Le L (1956) On the asymptotic theory of estimation and testing hypotheses In: Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability I University of California Press Berkeley pp. 129–156
   Google Scholar
• Li , B . (2000) . Nonparametric estimating equations based on a penalized information criterion . Canad. J. Statist. , 28 : 621 – 639 .
   Google Scholar
• Li , B . (2001) . On quasi likelihood equations with non-parametric weights . Scand. J. Statist. , 28 : 577 – 602 .
   Google Scholar
• Loynes , RM . (1980) . The empirical distribution function of residuals from generalised regression . Ann. Statist. , 8 : 285 – 299 .
   Web of Science ®Google Scholar
• Mammen , E . (1996) . Empirical process of residuals for high-dimensional linear models . Ann. Statist. , 24 : 307 – 335 .
   Web of Science ®Google Scholar
• Müller , UU , Schick , A and Wefelmeyer , W . (2004) . Estimating linear functionals of the error distribution in nonparametric regression . J. Statist. Plann. Inference , 119 : 75 – 93 .
   Web of Science ®Google Scholar
• Müller , H-G and Stadtmüller , U . (1987) . Estimation of heteroscedasticity in regression analysis . Ann. Statist. , 15 : 610 – 625 .
   Web of Science ®Google Scholar
• Portnoy , S . (1986) . Asymptotic behavior of the empiric distribution of M-estimated residuals from a regression model with many parameters . Ann. Statist. , 14 : 1152 – 1170 .
   Web of Science ®Google Scholar
• Robinson , PM . (1987) . Asymptotically efficient estimation in the presence of heteroskedasticity of unknown form . Econometrica , 55 : 875 – 891 .
   Web of Science ®Google Scholar
• Rudin W (1974) Real and Complex Analysis 2nd ed. McGraw-Hill New York
   Google Scholar
• Schick , A . (1987) . A note on the construction of asymptotically linear estimators . J. Statist. Plann. Inference , 16 : 89 – 105 .
   Web of Science ®Google Scholar
• Schick , A . (1993), (1995) . On efficient estimation in regression models, Correction and addendum . Ann. Statist. , 21, 23 : 1486, 1862 – 1521, 1863 .
   Google Scholar
• Schick , A . (1999) . Improving weighted least-squares estimates in heteroscedastic linear regression when the variance is a function of the mean response . J. Statist. Plann. Inference , 76 : 127 – 144 .
   Google Scholar
• Schick , A and Wefelmeyer , W . (2002) . Estimating the innovation distribution in nonlinear autoregressive models . Ann. Inst. Statist. Math. , 54 : 245 – 260 .
   Web of Science ®Google Scholar
• Wefelmeyer , W . (1996) . Quasi-likelihood models and optimal inference . Ann. Statist. , 24 : 405 – 422 .
   Web of Science ®Google Scholar