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• W2000318912 abstract "Abstract Smoothing splines have a penalized likelihood motivation (Good and Gaskins 1971) allowing direct application to nonparametric regression in likelihood-based models. The notion of a weighted likelihood for the nonparametric kernel estimation of a regression function is proposed, generalizing the local likelihood theory of Tibshirani and Hastie (1987). Let the data be of the form (xi, Yi ) (i = 1, …, n), where xi ∈ [0, 1] d are lattice points and the Yi are independent random variables from a family of distributions with parameter λi = g(xi ), with g having continuous partial derivatives of order k ≥ 2. The goal is to arrive at a nonparametric estimate λ o of λ o = g(xo ) for a fixed point xo ∈ [0, 1] d. We consider the estimator λ o that maximizes the weighted likelihood function W(λ) = Σ n i=1 W[(xo – xi )/b] log f(Yi :λ), with f the density of Yi, W a symmetric kernel with compact support, and b the bandwidth that controls the degree of smoothing. Sufficient conditions for consistency and asympt..." @default.
• W2000318912 created "2016-06-24" @default.
• W2000318912 creator A5014448524 @default.
• W2000318912 date "1989-03-01" @default.
• W2000318912 modified "2023-10-18" @default.
• W2000318912 title "The Kernel Estimate of a Regression Function in Likelihood-Based Models" @default.
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• W2000318912 doi "https://doi.org/10.1080/01621459.1989.10478766" @default.
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