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By
Ferrer, Ernesto Veres
Resumen
En este trabajo se acomete una generalización de la definición de ShannonLindley para la información esperada proporcionada por un experimento que presupone la existencia de estratificación en el espacio muestral. Ante la evidente dificultad de cálculo de la información esperada en la situación planteada—dificultad que se deriva de la existencia de un vector como parámetro de interés y de un resultado muestral que es un conjunto de muestras obtenidas de poblaciones distintas—en este artículo se presentan dos procedimientos que reducen la situación planteada por la existencia de un experimento asociado a cierto diseño de estratificación a la situación de varias dimensiones de la ya estudiada por Lindley (1956). Finalmente, la coherencia de ambos procedimientos queda manifestada en su aplicación al modelo normal.
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By
Novak, Sergei Y.
2 Citations
Financial data (logreturns of exchange rates, stock indices, share prices) are often modeled by heavytailed distributions, i.e., distributions which admit the representation
(14.1)
$$P(X > x) = L(x){x^{  1/a}}(a > 0)$$
where the function L slowly varies:
$$\mathop {\lim }\limits_{x \to \infty } L(xt)/L(x) = 1(\forall t > 0)$$
.
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By
Arnold, Taylor; Tilton, Lauren
In this chapter, methods for loading, manipulating, and saving image files in R are presented. Dimension reduction and clustering analysis are developed in order to visually represent a corpus of images in standard scatter plots.
By
Bravo, M. Carmen; GarcíaSantesmases, José M.
2 Citations
Summary
Based in a generalised recursive treebuilding algorithm for populations partitioned into strata a method to obtain simple descriptions of strata is presented. Also strata with a common rule are obtained. Common predictors and criterion variable describe population in all strata or classes of individuals. Algorithm considers strata structure in treebuilding algorithm and combines in each step maximisation of an information content measure for the criterion variable in a new binary partition of the population and selection of decisional nodes, based in quality of prediction for subsets of strata. Each decisional tree node is composed of a set of strata and a rule for individuals in these strata that will jointly explain the criterion variable.
Symbolic data analysis fits the method. Input of the algorithm is composed of classes of individuals. Algorithm is extended to individuals described by probabilistic symbolic objects. As output, symbolic objects describe tree, decisional nodes and strata.
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By
Sun, Yiping; Ozturk, Omer
This paper develops a new nonparametric test for the location shift between two populations based on order restricted randomized design (ORRD). The ORRD exploits the use of subjective, imprecise or rough information among experimental units to create a blocking factor. The blocking factor, in a given set of H experimental units, is constructed by ranking the units from smallest to largest and then assigning them into H ranking classes (judgment blocks). The design then uses a restricted randomization to assign the treatment regimes to experimental units across these judgment blocks. This randomization scheme induces a positive correlation structure among withinset response measurements. The positive correlation structure then acts as a variance reduction technique in the inference of a contrast parameter in an ORRD. The paper develops a ranksum test to test the difference between two treatment medians. It is shown that the test performs better than its competitors regardless of the accuracy of the ranking information of withinset units. The paper also constructs point and interval estimators for the contrast parameter. For set sizes H > 2, there are more than one ORRDs. The paper constructs an optimal design that maximizes the asymptotic Pitman efficacy of the proposed test among all possible ORRDs. The proposed test is applied to ACTG 320 clinical trial data.
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By
Ringrose, T. J.; Krzanowski, W. J.
2 Citations
Canonical variate analysis often involves the construction of confidence regions round points representing group means in a 2dimensional plot. Traditionally circles have always been constructed, but some authors have recently advocated ellipses as being more appropriate. This paper describes a Monte Carlo study investigating the effect of a range of factors on the inclusion rates of true population means within both types of region for normal data. The traditional circles do not perform too badly within a restricted range, but they are nearly always underincluded. The ellipses usually have higher inclusion rates, and so are often closer to the nominal rate, but are sometimes overincluded.
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By
Korostelev, A. P.; Tsybakov, A. B.
Let f(x) be an unknown smooth image function defined on a domain G ⊂ R^{N} . Assume that some transform Rf(z) of the image f is available at given points z_{1},…,z_{n}, i.e. that the observations are of the form (9.1) Y_{i}=Rf(z_{i})+ξ_{i}, i=1,…,n. The random errors are supposed to be i.i.d. (0,σ^{2} )Gaussian random variables. We do not specify now the nature of the transform Rf. In the examples below Rf(z) is a realvalued function defined on a domain Z in the space R^{N} of the same dimension as G.
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