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¿Cuántos clusters hay en una población?

Juan José Prieto Martínez (1998)

Qüestiió

Sea una población cerrada formada por un número desconocido K y finito de clusters. El método bootstrap es utilizado para estimar el número de clusters que constituyen una población. Se propone un estimador para K, el cual es ajustado y corregido por su sesgo estimado mediante el método bootstrap de Efron (1979). La varianza del "estimador bootstrap" se calcula por el método jackknife agrupado. Mediante simulación, el estimador es comparado con el de Bickel y Yavah (1985).

ε-Entropy and moduli of smoothness in L p -spaces

A. Kamont (1992)

Studia Mathematica

The asymptotic behaviour of ε-entropy of classes of Lipschitz functions in L p ( d ) is obtained. Moreover, the asymptotics of ε-entropy of classes of Lipschitz functions in L p ( ℝ d ) whose tail function decreases as O ( λ - γ ) is obtained. In case p = 1 the relation between the ε-entropy of a given class of probability densities on ℝ d and the minimax risk for that class is discussed.

φ PHI-divergences, sufficiency, Bayes sufficiency, and deficiency

Friedrich Liese (2012)

Kybernetika

The paper studies the relations between φ -divergences and fundamental concepts of decision theory such as sufficiency, Bayes sufficiency, and LeCam’s deficiency. A new and considerably simplified approach is given to the spectral representation of φ -divergences already established in Österreicher and Feldman [28] under restrictive conditions and in Liese and Vajda [22], [23] in the general form. The simplification is achieved by a new integral representation of convex functions in terms of elementary...

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