ON DERIVATIVE ESTIMATION IN SPLINE REGRESSION

By S. Zhou, Douglas A. Wolfe. 2000

91 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/621521606c14c81655990e8e1aa2615aef059be5

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Citations in the corpus

Smoothing Parameter and Model Selection for General Smooth Models (2015, background): “9) for g(x) and O(n−4/9) for g′′. See ﬁgure S1b. Agarwal and Studden (1980) shows that the result for g(x) holds when the observations are spread out instead of being concentrated at the knots, while Zhou and Wolfe (2000) conﬁrms the equivalent for derivatives. In summary, cubic regression splines a”
Parameter estimation of ODE’s via nonparametric estimators (2007, methodology): “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 derivative can be obtained from local polynomial regression or wavelet estimator (e.”
Local Inference in Additive Models with Decorrelated Local Linear Estimator (2019, methodology): “Inference for function derivative has been actively studied in the nonparametric modeling, including local linear estimator [15], regression spline [45], kernel methods [17], empirical likelihood based methods [28] and others cited therein.”
Wild Variational Approximations (2016, background): “[38, 39, 40, 41, 42]; however, many of them require at least a noisy version of log q at the sampled locations, which is intractable in our case.”
Optimal convergence rates, Bahadur representation, and asymptotic normality of partitioning estimators☆ (2013, methodology): “Under similar conditions, analogous results restricted to d > 1 with [m] = 0 or d = 1 with [m] = m ≥ 0 are given by Ruppert and Wand (1994) for conventional local polynomial estimators and for d = 1 with [m] = m ≥ 0 by Huang (2003) and Zhou and Wolfe (2000) for regression splines.”
Estimating Derivatives for Samples of Sparsely Observed Functions, With Application to Online Auction Dynamics (2009, methodology): “These methods include various types of spline estimates, based on B-splines (de Boor 1972), smoothing splines (Chambers 1991; Zhou and Wolfe 2000), and P-splines (Ramsay and Silverman 2005), or kernel-based estimators, such as convolution-type kernel (Gasser and Müller 1984) or local polynomial…”