Estimating regression functions and their derivatives by the kernel method

By Theo Gasser, H. Muller. 1984

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Citations in the corpus

Estimating Derivatives for Samples of Sparsely Observed Functions, With Application to Online Auction Dynamics (2009, background): “An area in which the problem of differentiation under noise is commonly encountered is the analysis of growth curves (Gasser et al. 1984).”
Piecewise polynomial regression trees (1994, background): “…arguments, include B-splines and smoothing splines (de Boor (1978); Eubank (1988); Ramsay (1988); Wahba (1990)), kernel smoothers (Gasser and Muller (1979); Gasser and Muller (1984); Nadarya (1964); Rosenblatt (1971); Watson (1964)), and locally weighted regression (Cleveland and Devlin (1988)).”
Applied Nonparametric Regression: The kernel method (1990, unknown): “From Gasser and Müller (1984) (figure 1) with the permission of the Scandinavian Journal of Statistics. sented in Engle, Granger, Rice and Weiss (1986).”
Functional linear regression with derivatives (2006, background): “Let us point out, however, that in pioneering works Gasser and Müller [9] and then Gasser and Härdle [10] studied kernel and robust estimates of regression functions through techniques which could be carried out in our framework to obtain the derivatives of the data from the original curves.”
Estimating Semiparametric Panel Data Models by Marginal Integration (2012, unknown): “The popular estimators are Nadaraya-Watson (Nadaraya (1964); Watson (1964)), Gasser-M¨uller (Gasser and M¨uller (1984)), and local linear (Stone (1977); Cleveland (1979); Fan (1992); Ruppert and Wand (1994)), among others.”
Parameter estimation of ODE’s via nonparametric estimators (2007, methodology): “of the derivative x˙∗ by diﬀerentiating directly the smoothed curved ˆxn so that we have ˆx˙n = xˆ˙n. This simple device provides consistent estimator of the derivative for Nadaraya-Watson estimators [17], spline regression [45], smoothing splines [43], but other consistent estimators of the derivat”
A general asymptotic scheme for inference under order restrictions (2006, background): “Compute the Gasser–Müller kernel estimate (see [19]), mn(t) = h−1 ∫ k ( t − u”
Local Likelihood Estimation in Generalized Additive Models (2003, background): “This holds if g tends more slowly to zero than h [see, e.g. Fan & Gijbels (1996) or Gasser & Müller (1984)].”
Local Polynomial Fitting with Long-Memory, Short-Memory and Antipersistent Errors (2002, methodology): “Hence, in local polynomial tting p is often taken to be odd in order that the MISE can be calculated over the whole support [0; 1] of g. Similar to the terminology in Gasser and M uller (1984), we call a ( + 1)-th local polynomial estimator ĝ( ) with k = + 2 a standard local polynomial estimator.”