Projection estimation in multiple regression with application to functional ANOVA models

By Jianhua Z. Huang. 1998

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Citations in the corpus

Additive models with trend filtering (2017, background): “, Lemma 10 in Huang (1998), give the result as stated the lemma.”
Chapter 76 Large Sample Sieve Estimation of Semi-Nonparametric Models (2007, background): “…to compute the estimators, but also make it convenient to discuss orthogonal projections and functional analysis of variance (ANOVA) decompositions (such as additivity) in the nonparametric multivariate regression framework; see e.g., Stone (1985, 1986), Andrews and Whang (1990), Huang (1998a).”
Testing in mixed-effects FANOVA models (2006, background): “There is a wide list of publications on fitting various FANOVA models and estimating their components (e.g., Wahba et al., 1995; Stone et al., 1997; Huang, 1998; Lin, 2000; Gu, 2002; Angelini et al., 2003).”
Regression Discontinuity Design with Continuous Measurement Error in the Running Variable (2017, unknown): “Assumption 6.4 is necessary to control the rate of uniform convergence of Qn,na to Q. Burman & Chen (1989), Newey (1997), Huang (1998), Blundell et al. (2007), or Chen & Pouzo (2012) use a stronger assumption, assuming that fZ is bounded below on its support.”
Conditional quantile processes based on series or many regressors (2011, result): “These findings on optimality of series estimators in the quantile regression setting complement results in the literature on optimality of series estimators in the mean regression setting; see [67, 49, 15, 9, 22].”
Estimation of nonparametric conditional moment models with possibly nonsmooth moments (2008, background): “See Newey (1997) and Huang (1998) for more details about tensor-product B-splines and other linear sieves.”
Gaussian approximation of suprema of empirical processes (2012, methodology): “For many commonly used basis functions such as Fourier series, splines and CDV wavelet bases, ξn = O(√Kn) as n → ∞; see, for example, [30] and [45].”
Hyperparameter Importance Across Datasets (2017, methodology): “predictions yˆ of a tree-based model, the average over these terms can be computed exactly by a procedure that is linear in the number of leaves in the model [22]. Functional ANOVA.. Functional ANOVA [18, 19, 25, 36] decomposes a functionyˆ : Θ1 ×···×Θn →R into additive components that only depend o”
Some new asymptotic theory for least squares series: Pointwise and uniform results (2012, background): “Excellent reviews of approximating properties of different series can also be found in Huang (1998) and Chen (2007), where additional references are provided.”
Identification of non‐linear additive autoregressive models (2004, methodology): “By letting the number of knots or, equivalently, the number of terms in expression (3) increase with the sample size, the spline estimate is consistent (Stone, 1985; Huang, 1998, 2001) in estimating any additive function with smooth components.”
Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions (2014, background): “(18) By Remark 2.5, under the same set of mild conditions imposed in Newey (1997) (except allowing for weakly dependent regressors), the bound (18) can be slightly improved to ‖ĥ− h0‖∞ ≤ Op ( ζK,n √ K/n + ‖PK,w,n‖∞,wK−p/d ) .”
Polynomial Spline Estimation and Inference for Varying Coefficient Models with Longitudinal Data (2003, background): “data (Huang (1998) and (2001)). By condition (C5), the approximation rate ρn can be determined in terms of Kn under commonly used smoothness conditions on the βl. When the βl have bounded second derivatives, we have ρn = O(K−2 n ) (Schumaker (1981, Theorem 6.27)), and the rates of convergence in The”
An Efficient Approach for Assessing Hyperparameter Importance (2014, methodology): “Functional Analysis of Variance (ANOVA) Functional analysis of variance (functional ANOVA) is a prominent data analysis method from the statistics literature (Sobol, 1993; Huang, 1998; Jones et al., 1998; Hooker, 2007).”
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.”
SPARSE VARYING COEFFICIENT MODELS FOR LONGITUDINAL DATA (2010, methodology): “The observation time points tij were generated by the same scheme as in Huang, Wu and Zhou (2002), where each subject had a set of “scheduled”time points {1, .”
Spline-backfitted kernel smoothing of nonlinear additive autoregression model (2006, background): “For the spline estimators, see [13, 23, 24] and [28].”