Local asymptotics for polynomial spline regression

By Jianhua Z. Huang. 2003

248 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/0bc84d7d2f4d92c33c45a1a6a2536c139f82d226

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In Computational Mechanics

In Computer Vision and Pattern Recognition

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Citations in the corpus

SPLINE ESTIMATION OF SINGLE-INDEX MODELS (2009, methodology): “The greatest advantages of spline smoothing, as pointed out in Huang and Yang (2004) and Xue and Yang (2006b), are its simplicity and fast computation.”
Bivariate Penalized Splines for Regression (2013, background): “(2.1) This corresponds to Condition A.2 in Huang (2003b).”
Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling (2014, background): “Assumption B1 is required for the nonparametric smoothing approaches (Huang 2003; Xue, Miao, and Wu 2010).”
Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions (2014, methodology): “Corollary 3.1 part (a) extends the weakest known result on pointwise asymptotic normality of spline LS estimators in Huang (2003b) to general sup-norm bounded linear functionals of spline or wavelet series LS estimators.9 Corollary 3.2 Let f be an irregular but sup-norm bounded nonlinear…”
Efficient and fast spline-backfitted kernel smoothing of additive models (2009, background): “of convergence. These were later called polynomial spline estimators in Stone (1994), Huang (1998, 2003) .”
Semi-nonparametric estimation of the call-option price surface under strike and time-to-expiry no-arbitrage constraints☆ (2015, unknown): “, Jackson et al. (1998), Coleman et al.”
Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations (2013, unknown): “or D is traceable to the nonlinear model. 19This is standard in xed-dimension models, and has been used for diverging-dimensions parametric models (He and Shao 2000) and nonparametrics (Newey 1997, Huang 2003, Cattaneo and Farrell 2013, Belloni, Chernozhukov, Chetverikov, and Kato 2015, Chen and Ch”
Spline Regression in the Presence of Categorical Predictors (2015, methodology): “Assumption A1 provides a smoothness condition of the regression function g. /, which is also given in Section 5.2 of Huang (2003).”
Estimation of nonparametric conditional moment models with possibly nonsmooth moments (2008, background): “Thus, by assumption 3.9(iii), the result follows from Lemma 4 of Huang (1998) for general linear sieves {pk}Jnk=1 and Corollary 3 of Huang (2003) for polynomial spline sieves.”
Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines (2007, methodology): “Some useful lemmas We shall employ the machinery developed in Huang (1998, 2003) and Huang et al. (2004) to prove our asymptotic results.”
Consistent Model Selection for Marginal Generalized Additive Model for Correlated Data (2010, background): “Assumptions similar to (C1)–(C4) were also considered by Huang (1998), Huang (2003), and Xue (2009).”
Estimation of Nonparametric Conditional Moment Models with Possibly Nonsmooth Generalized Residuals (2011, background): “An ≍ ξn . Thus, by assumption 2.2(iii), the result follows from Lemma 4 of Huang (1998) for general linear sieves {pk} Jn k=1 and Corollary 3 of Huang (2003) for polynomial spline sieves.”
Varying Coefficient Regression Models: A Review and New Developments (2015, methodology): “X/, this was discussed in Zhou, Shen & Wolfe (1998) and Huang (2003).”
Polynomial Spline Estimation and Inference for Varying Coefficient Models with Longitudinal Data (2003, result): “If lim n K n log K n /n = 0 and lim n K n max i n i /n = 0, then {var( ˆ The above result extends similar result of Huang (2003) for i.i.d. data.”
Efficient estimation of a semiparametric partially linear varying coefficient model (2005, background): “Huang (2003) has obtained the asymptotic distribution of spline estimators under quite general conditions (provided the data are slightly undersmoothed).”