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Averaged shifted histograms: Effective nonparametric density estimators in several dimensions. (English) Zbl 0589.62022
Let \(X_ 1,X_ 2,..\). be i.i.d. from some unknown density f in \({\mathbb{R}}\). For a given bin-width \(h>0\) and an integer \(m\geq 1\) let, for \(0\leq i\leq m-1\), \(\hat a_ i\) be the histogram for the grid \(rh+ih/m\), \(r\in {\mathbb{Z}}.\)
The author proposes \(\hat f_ n\), the average of the \(\hat a_ i's\), as an estimator for f, and derives an expansion for the IMSE both as a function of h and m. It turns out that as \(m\to \infty\), \(\hat f_ n\) behaves like a kernel estimate with triangular kernel. Also the multivariate case is discussed.
Reviewer: W.Stute

MSC:
62G05 Nonparametric estimation
62E10 Characterization and structure theory of statistical distributions
62H12 Estimation in multivariate analysis
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