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- W1985329097 abstract "Let f be a m-variate unknown density with respect to a σ-finite measure on Em, the m- dimensional Euclidean space, and let x=(x1,…,xm) and p=(p1,…,pm) be in Em, where p j≥0 are arbitrary integers. This paper exhibits kernel estimators of mixed partial derivatives f(p)(x)=(∂p1+…+pmf∂(x))/(∂xP11…∂xPmm) of f based on a random sample from f and investigates the speed of convergence for various asymptotic properties (of the estimators) including asymptotic unbiasedness, mean square consistency, strong consistency and asymptotic normality. Local bounds for the bias and mean square error as well as uniform convergence rate results for asymptotic unbiasedness, mean square consistency and strong consistency of the estimators are obtained. Rate result for covariance of the estimators evaluated at two distinct points in Em is also given." @default.
- W1985329097 created "2016-06-24" @default.
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- W1985329097 date "1981-01-01" @default.
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- W1985329097 title "Speed of convergence in nonparametric estimation of a multivariate μ-density and its mixed partial derivatives" @default.
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- W1985329097 doi "https://doi.org/10.1016/0378-3758(81)90009-4" @default.
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