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Local likelihood density estimation. (English) Zbl 0867.62034
Summary: Local likelihood was introduced by R. Tibshirani and T. Hastie [J. Am. Stat. Assoc. 82, 559-567 (1987; Zbl 0626.62041)] as a method of smoothing by local polynomials in non-Gaussian regression models. In this paper an extension of these methods to density estimation is discussed, and comparison with other methods of density estimation presented. The local likelihood method has particularly strong advantages over kernel methods when estimating tails of densities and in multivariate settings. Suppose constraints are incorporated in a simple manner. Asymptotic properties of the estimate are discussed. A method for computing the estimate is outlined.

62G07Density estimation
62G20Nonparametric asymptotic efficiency
62H12Multivariate estimation