Asymptotic equivalence for nonparametric regression with non-regular errors
- 271 Downloads
Asymptotic equivalence in Le Cam’s sense for nonparametric regression experiments is extended to the case of non-regular error densities, which have jump discontinuities at their endpoints. We prove asymptotic equivalence of such regression models and the observation of two independent Poisson point processes which contain the target curve as the support boundary of its intensity function. The intensity of the point processes is of order of the sample size n and involves the jump sizes as well as the design density. The statistical model significantly differs from regression problems with Gaussian or regular errors, which are known to be asymptotically equivalent to Gaussian white noise models.
KeywordsExtreme value statistics Frontier estimation Le Cam distance Le Cam equivalence Poisson point processes
Mathematics Subject Classification (2010)62B15 62G08 62M30
Unable to display preview. Download preview PDF.
- 7.Carter, A.: Asymptotically sufficient statistics in nonparametric regression experiments with correlated noise. J. Prob. Stat. 2009, 19 (2009) (ID 275308)Google Scholar
- 9.DeVore R.A., Lorentz G.G.: Constructive Approximation, Grundlehren Series vol. 303. Springer, Berlin (1993)Google Scholar
- 14.Ibragimov, I.A., Hasminskii, R.Z.: Statistical Estimation. Asymptotic Theory. Springer, New York (1981) (translated from the Russian by S. Kotz)Google Scholar
- 29.van de Geer S.A.: Empirical Processes in M-Estimation. Reprint, Cambridge University Press, New York (2006)Google Scholar