Smoothing spline density estimation: theory

By Chong Gu, Chun-hang Qiu. 1993

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Citations in the corpus

Density Estimation in Infinite Dimensional Exponential Families (2013, neutral): “3 KL(p0kpfˆ m ) = Op0(n−2r/(2r+1)) with m= n1/(2r+1) for each of the approximating families, where KL(pkq) = R p(x)log(p(x)/q(x))dxis the KL divergence between pand q. Similar work was carried out by Gu and Qiu (1993), who assumed that logp0 lies in an RKHS, and proposed an estimator based on penali”
Posterior consistency of logistic Gaussian process priors in density estimation (2007, unknown): “See also Gu and Qiu (1993).”
Local and global asymptotic inference in smoothing spline models (2012, methodology): “Classical results on rates of convergence are obtained through either linearization techniques, for example, [7], or quadratic approximation devices, for example, [13, 14].”
Semiparametric Nonlinear Mixed-Effects Models and Their Applications (2001, background): “As long as this space is well chosen, the convergence rate may be retained (Gu and Qiu 1993; Gu 1993).”
PENALIZED LIKELIHOOD DENSITY ESTIMATION: DIRECT CROSS-VALIDATION AND SCALABLE APPROXIMATION (2003, methodology): “To make the logistic density transform one-to-one, Gu and Qiu (1993) ”
A note on margin-based loss functions in classification (2004, background): “See e.g., Silverman (1982), Wahba (1990), Cox and O’Sullivan (1990), Van de Geer (1990), Gu and Qiu (1993), Shen (1998) for references.”
DENSITY ESTIMATION BY DUAL ASCENT OF THE LOG-LIKELIHOOD ∗ (2010, background): “In a parametric approach, one considers a family of probability densities depending on a set of parameters, and maximizes the likelihood of the observations in the allowed parameter range; Gaussian mixtures [3] and smoothing splines [9] are popular choices.”
Kernel Exponential Family Estimation via Doubly Dual Embedding (2018, methodology): “The most signiﬁcant diﬀerence of the bound provided above, compared to Gu and Qiu (1993); Altun and Smola (2006), is the explicit consideration of the bias from the dual parametrization.”