Spline Smoothing and Optimal Rates of Convergence in Nonparametric Regression Models

By Paul L. Speckman. 1985

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Citations in the corpus

Fully Bayesian spline smoothing and intrinsic autoregressive priors (2003, methodology): “However, for large n, with the help of approximations given for example in Speckman (1985), it is possible to show that”
Minimax estimation via wavelet shrinkage (1998, background): “Theorem 8 inf sup 2Msp;q L( ; ) = sup 2Msp;q inf L( ; ) (38) We give the formalities of the proof, assuming that certain objects (e.”
A Distribution-Free Theory of Nonparametric Regression (2002, unknown): “For historical details we refer to Hald (1998), Farebrother (1999), and Stigler (1999). The principle of penalized modeling, in particular, smoothing splines, goes back to Whittaker (1923), Schoenberg (1964), and Reinsch (1967); see Wahba (1990) for additional references.”
Minimax Bayes, Asymptotic Minimax and Sparse Wavelet Priors (1994, background): “Then a least favorable prior for B = B ( p;q; ") = inf ̂ sup 2ME E jĵ jj2 (29) ( when 2 is restricted to a subsequence 2h = 2 h) may be constructed as |k = "hXj;k j = | h; (30) where (Xj) = (Xj;1; Xj;2j ) is a vector distributed i.”
CONSISTENCY OF CROSS VALIDATION FOR COMPARING REGRESSION PROCEDURES (2007, background): “, Speckman [22] and Burman [5] for spline estimation, Härdle, Hall and Marron [12], Hall and Johnstone [11] and references therein for kernel estimation).”
Nonparametric Independence Screening in Sparse Ultra-High Dimensional Additive Models (2009, methodology): “Substantial improvements are sometimes possible by using a more ﬂexible class of nonparametric models, such as the additive model Y = =1 m j ( X j ) + ε , introduced by Stone (1985).”
Semiparametric Regression Pursuit (2012, background): “Examples include the partial spline estimator (Wahba (1984), Engle et al. (1986), and Heckman (1986)), the partial residual estimator (Robinson (1988), Speckman (1985)), and polynomial spline estimator (Chen (1988)).”
Smoothing Parameter and Model Selection for General Smooth Models (2015, background): “ossible for a non-parametric estimator of a C4 function is O(n−8/9) (Cox, 1983), which a cubic smoothing spline can achieve under certain assumptions on the the rate of change of λwith n(Stone, 1982; Speckman, 1985). Hall and Opsomer (2005) obtain the same rate for penalized cubic regression splines”