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Studies in Nonlinear Dynamics & Econometrics Volume 16, Issue 3 2012 Article 1 Maximally Autocorrelated Power Transformations: A Closer Look at the Properties of Stochastic Volatility Models Esther Ruiz∗ Ana Pérez† ∗Universidad Carlos III de Madrid, ortega@est-econ.uc3m.es †Universidad de Valladolid, perezesp@eaee.uva.es DOI: 10.1515/1558-3708.1880 Copyright c©2012 De Gruyter. All rights reserved. Maximally Autocorrelated Power Transformations: A Closer Look at the Properties of Stochastic Volatility Models∗ Esther Ruiz and Ana Pérez Abstract There has

Abstract

This paper addresses the problem of estimating the population mean at the current occasion in two occasion successive sampling when non-response occurs on the current (second) occasions. Using the power transformation we have suggested classes of estimators of current population mean and their properties are studied. Optimum replacement strategies for the proposed estimators have been given and empirical studies are carried out to assess the performance of estimators. We have made suitable recommendation to the practitioners on the basis of the empirical study.

Martin Bollacher238 Françoise Kenk, Elias Canetti. Un Auteur Énigmatique dans L’Histoire Intellectuelle. Enquête. L’Harmattan, Paris 2003. 281 S., € 24,Ð. Johann P. Arnason / David Roberts, Elias Canetti’s Counter-Image of Society. Crowds, Power, Transformation. Camden House, Rochester Ð Woodbridge 2004. 166 S., $ 65,Ð. Dagmar C. G. Lorenz (Hg.), A Companion to the Works of Elias Canetti. Camden House, Rochester Ð Woodbridge 2004. XIV/350 S., $ 90,Ð. Elias Canetti, der als Spaniole, „deutscher Dichter“1 und „Dichter im Exil“2 im Schatten einer barbarischen

these factors. Of the various approaches proposed for judging the necessity of partitioning reference values, nested analysis of variance (ANOVA) is the likely method of choice owing to its ability to handle multiple groups and being able to adjust for mul- tiple factors. Box-Cox power transformation often has been used to transform data to a Gaussian distribution for para- metric computation of RIs. However, this transformation occasionally fails. Therefore, the non-parametric method based on determination of the 2.5 and 97.5 percentiles fol- lowing sorting of the

transformation, i.e. removing outliers and estimation reference limits. Nevertheless, we apply simple methods for reference interval estimation to generally demonstrate the usefulness of our approach but without the intention to discuss and evaluate different methods for reference interval estimation once the data have been transformed properly. Unknown proportion of abnormal results [ 3 ], [ 4 ], [ 7 ]. To overcome the problem of the unknown proportion of abnormal results, a common suggestion is to apply a power transformation of the form x ′= k · x λ (with x ′=log( x

has overcome both problems by the normalization of the distributions through power transformation and by a weighted summation of deltas based on biological variability. It also features exclusion of influential data points in deriving biological variability using an iterative procedure [9] and uniform expression of all test results by z-score. This method was designated as the weighted cumulative delta-check (wCDC) method. In this report, we describe the theoretical formulation and demonstrate the performance of the wCDC method with a simulation generating

not in the same manner. For Sweden we find a negative impact in accordance with the Holland hypothesis, whereas for Germany and the Netherlands we find the opposite in support of the Cukierman–Meltzer hypothesis. In a sensitivity analysis we show that an arbitrary choice of the heteroscedasticity parameter influences this relationship significantly. JEL classification: C22, E31. Keywords: GARCH-in-mean; inflation; level effect; nominal uncertainty; power transformation. 1. INTRODUCTION The issue of the welfare costs of inflation has been one of the most researched

Abstract

In the present paper, we introduce a new form of generalized Rayleigh distribution called the Alpha Power generalized Rayleigh (APGR) distribution by following the idea of extension of the distribution families with the Alpha Power transformation. The introduced distribution has the more general form than both the Rayleigh and generalized Rayleigh distributions and provides a better fit than the Rayleigh and generalized Rayleigh distributions for more various forms of the data sets. In the paper, we also obtain explicit forms of some important statistical characteristics of the APGR distribution such as hazard function, survival function, mode, moments, characteristic function, Shannon and Rényi entropies, stress-strength probability, Lorenz and Bonferroni curves and order statistics. The statistical inference problem for the APGR distribution is investigated by using the maximum likelihood and least-square methods. The estimation performances of the obtained estimators are compared based on the bias and mean square error criteria by a conducted Monte-Carlo simulation on small, moderate and large sample sizes. Finally, a real data analysis is given to show how the proposed model works in practice.

evidence that indicates it is too severe for data at large values; see Speed (2003). Other authors, such as van den Berg et al. (2006), have emphasized the need of using power transformations other than the logarithmic transformation. One of the most widely known power transformations is the Box-Cox transformation; see Box and Cox (1964). Thus, it is possible to introduce a family of transformations that considers the glog and power functions, in short gpower, in an analogous manner as the family of Box-Cox power transformations works. Probes, in a microarray solid

-Cox power transformations on the original data to yield an approximate normal distribution, increasing the size of the samples drawn from the process until the distribution of the sample means is considered normal, and modifying the x̄-chart to employ asymmetric control limits instead of limits that are equidistant from the process target mean. Since none of the remedies for handling nonnormal processes is completely satisfactory, we build on previous neural network research by developing a neural network to control nonnormal processes. Comparison of the performance of