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An intrinsic approach to nonparametric density estimation. (Une approche intrinsèque de l’estimation non paramétrique de la densité.) (French) Zbl 0919.62028

Summary: We consider samples \(X_1,\dots,X_n\) partially observed through the indicators of the events \(\{X_i\in ((M-1+r)h\), \((M+r)h)\}\), \(1\leq i\leq n\), \(1\leq r\leq N\). We estimate the underlying density \(f\) by averaging a class of histograms based upon intervals with endpoints in \(\{kh:k \in\mathbb{N}\}\). We show that the resulting estimators are easy to use and have limiting properties which are bound to justify their use in statistical analysis.

MSC:

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference

Keywords:

histograms
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