Nonparametric Regression and Spline Smoothing

By Saad T. Bakir. Technometrics, 2000

478 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c3dc5711b4c7618c7e7f937f9b748c9c9ada43e6

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In Statistics and Probability

Citations in the corpus

Estimation of the density of regression errors (2005, background): “Following Fan and Gijbels [22], Hart [28] and Eubank [ 21 ], suppose that the statistician observes n independent and identically distributed (i.i.d.) realizations (X1,Y1),...,(Xn,Yn) of the pair (X,Y ) of random variables.”
Knot selection for least-squares and penalized splines (2013, methodology): “The following choices were used for the regression functions (shown in Figure 2), sample size, variance and number of knots for the fixed and free-knot estimators: • The ExpSum function from [36]: μ(x) = 26(exp(−3.”
STATISTICAL INFERENCES FOR LINEAR MODELS WITH FUNCTIONAL RESPONSES (2011, methodology): “For curve data from stationary Gaussian processes, Fan and Lin (1998) developed some adaptive Neyman tests.”
Statistical inferences for functional data (2007, methodology): “We expect that this is true not only for LPK but also for any other linear smoothers, for example, smoothing splines [14, 27], regression splines or orthogonal series [ 7 ], among others.”
Wavelet Estimators in Nonparametric Regression: A Comparative Simulation Study (2001, methodology): “Cross-validation is widely used as an automatic procedure to choose the smoothing parameter in many statistical settings – see, for example, Green & Silverman (1994) or Eubank (1999).”
Applications of functional data analysis: A systematic review (2013, background): “Although some authors believe that FDA can be considered as a smoothed version of multivariate data analysis, recent work has shown the advantage of direct application of smoothing techniques to reduce some of the inherent randomness in the observed data [1,25,113].”
Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models (2009, methodology): “Generally, λ is chosen by generalized cross validation (GCV) ([37]), m-fold CV ([38]), or related methods (pp. 239-243, [39], pp. 42- 52, [40]).”
Functional Data Analysis (2016, methodology): “…smoothing methods, notably kernel, local least squares and spline smoothing for which various excellent reference books exist (Wand & Jones 1995; Fan & Gijbels 1996; Eubank 1999; de Boor 2001), functional analysis (Conway 1994; Hsing & Eubank 2015) and stochastic processes (Ash & Gardner 1975).”
ON SEMIPARAMETRIC REGRESSION WITH O'SULLIVAN PENALIZED SPLINES (2008, background): “Recent synopses include Eubank (1999), Gu (2002), Ruppert, Wand & Carroll (2003) and Denison et al.”
Smoothing spline estimation in varying‐coefficient models (2004, methodology): “Under certain conditions (see, for example, Hastie and Tibshirani (1993) and comments below) the estimator that is obtained from expression (3) is unique.”
Nonparametric Multiplicative Regression for Habitat Modeling (2011, methodology): “Despite the profusion of books and papers in the statistical literature on smoothing techniques and nonparametric regression (Bowman & Azzalini 1997, Eubank 1999, Fan & Gijbels 1996, Green & Silverman 1994, Hastie et al. 2001, Scott 1992, Wand and Jones 1995), these techniques have largely been…”
A Note on Penalized Spline Smoothing With Correlated Errors (2007, methodology): “The toolbox for estimating μ(x) based on data pairs (xi, yi), i = 1, . . . , n, is large including, for instance, local approaches (see Fan and Gijbels 1996) or spline methods (see Wahba 1990; Eubank 1999).”
1 Trend Filtering (2009, unknown): “H-P filtering can be viewed as an approximate discretization of this continuous function estimation problem, when ti are regularly spaced: ti = t1 + (i− 1)h for some h > 0.”
A NEW PANEL DATA TREATMENT FOR HETEROGENEITY IN TIME TRENDS (2012, background): “Spline theory implies that any solution ν̂i , i = 1, . . . ,n, of (12) possess an expansion ν̂i (t) = ∑Tj=1 ζ̂j i z j (t) in terms of a natural spline basis z1, . . . , zT of order 2m (for a discussion of natural splines and definitions of possible basis functions see, for example, Eubank, 1988).”
Marginal Longitudinal Nonparametric Regression (2002, methodology): “4 and earlier), and choices of different kernel functions often have small effects on asymptotic ef ciency (Eubank 1999, p. 177), the results in this section suggest that for the longitudinal marginal model, spline methods may be preferable to the kernel methods studied in this article.”
Consistencies and rates of convergence of jump-penalized least squares estimators (2009, unknown): “Hence, this paper also answers the question how to choose the partition of the regressogram in an asymptotic optimal way [cf. Eubank (1999)] over a large scale of approximation spaces.”