APPROXIMATION OF DENSITY FUNCTIONS BY SEQUENCES OF EXPONENTIAL FAMILIES

By Andrew R. Barron, Chyong-Hwa Sheu. 1991

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Citations in the corpus

Density Estimation in Infinite Dimensional Exponential Families (2013, methodology): “A related work was carried out by Barron and Sheu [2] (see also references therein) where the goal is to estimate a density, p 0 by approximating its logarithm as an expansion in terms of basis functions, such as polynomials, splines or trigonometric series.”
Adaptive estimation of the intensity of inhomogeneous Poisson processes via concentration inequalities (2003, background): “to A.R. Barron and C.-H. Sheu [ 4 ], W.-C. Kim and J.-Y.”
Efficient Estimation of Semiparametric Multivariate Copula Models (2006, unknown): “There are also many results on particular sieve density estimates (see, e.g., Stone 1990 for spline sieve; Barron and Sheu 1991 for polynomial, trigonometric, and spline sieves; and the Fisher norm v on the perturbation space V, it is often easier to verify these assumptions in terms of transformed…”
Learning deep kernels for exponential family densities (2018, background): “Moreover, the maximum likelihood solution may not even be well-deﬁned when θ is inﬁnite-dimensional, and other approximations to this solution can be challenging to implement in practice (Barron and Sheu 1991; Fukumizu 2009).”
Nonparametric likelihood ratio model selection tests between parametric likelihood and moment condition models (2007, methodology): “For example, Stone (1985) applied spline sieves, Barron and Sheu (1991) used orthogonal polynomials, splines and trigonometric sieves, and Chen and White (1999) considered neural network sieves for approximating log-densities; Chen and Shen”
Projection estimation in multiple regression with application to functional ANOVA models (1998, methodology): “Condition 1 was used by Barron and Sheu 1991 to obtain rates of convergence in univariate density estimation.”
GMM estimation of a maximum entropy distribution with interval data (2007, background): “Barron and Sheu (1991) characterized the maxent density alternatively as an approximation of the log density by some basis functions, such as polynomials, trigonometric series, or splines.”
Cross-validation for selecting a model selection procedure (2015, methodology): “For each δ ∈ Λ, model selection and parameter estimation are performed by δ on the training part, It, and we obtain CV (δ; Iv) = 1 nv ∑ i∈Iv ( Yi − It,M̂It,δi )2 , (5)”
A Practical Asymptotic Variance Estimator for Two-Step Semiparametric Estimators (2012, background): “After all, he will solve the same problem (8).”
Goodness of Fit via Non‐parametric Likelihood Ratios (2004, methodology): “Further results on the closeness of logKnðf̂ Þ to log Kn(f) can be reached via a careful study of approximation precision of the best finite-parametric Kullback–Leibler approximation fm to f; see Crain (1977), Barron & Sheu (1991) and Inglot & Ledwina (1996) for results of relevance.”
Convergence rates for posterior distributions and adaptive estimation (2004, unknown): “The proof of the fact is a straightforward application of an equation in Lemma 1 by Barron and Sheu (1991), which gives D ( fo‖fθ,jn )≤ 12e‖ logfo−logfθ,jn‖∞V (fo‖fθ,jn)(35) for all θ ∈ Rmjn .”
Improved Rates and Asymptotic Normality for Nonparametric Neural Network Estimators (1999, methodology): “a)The above log-density parameterization has been previously utilized by [20] and [19] using splines, by [ 3 ] using splines, polynomials, and trigonometric series, and by [14] using neural networks, among others.”