Local Estimation of a Multivariate Density and its Derivatives
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We present methods for estimating the multivariate probability density (or the -density) and its first and second order derivatives simultaneously. Two methods, local log-likelihood and Hyvärinen score estimation, are in terms of weighted scoring rules with local polynomials. A third approach is matching of local moments. Consistency and asymptotic convergence results are shown and compared with corresponding results for kernel density estimators.
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