The following is a brief review of three landmark papers of Peter Bickel on theoretical and methodological aspects of nonparametric density and regression estimation and the related topic of goodness-of-fit testing, including a class of semiparametric goodness-of-fit tests. We consider the context of these papers, their contribution and their impact. Bickel’s first work on density estimation was carried out when this area was still in its infancy and proved to be highly influential for the subsequent wide-spread development of density and curve estimation and goodness-of-fit testing.
KeywordsKernel Density Estimation Nonparametric Regression Optimal Bandwidth Kernel Density Estimator Mean Integrate Square Error
- Bickel P, Li B (2007). Local polynomial regression on unknown manifolds. In: Complex datasets and inverse problems: tomography, networks and beyond. IMS lecture notes-monograph series, vol 54. Institute of Mathematical Statistics, Beachwood, pp 177–186Google Scholar
- Čencov N (1962) Evaluation of an unknown density from observations. Sov Math 3:1559–1562Google Scholar
- Daniell P (1946) Discussion of paper by M.S. Bartlett. J R Stat Soc Suppl 8:88–90Google Scholar
- Einstein A (1914) Méthode pour la détermination de valeurs statistiques d’observations concernant des grandeurs soumises à des fluctuations irrégulières. Arch Sci Phys et Nat Ser 4 37:254–256Google Scholar