A note on the moments of the Riesz distribution

This paper derives the first two moments of the two versions of the Riesz distribution in the terms of their characteristic functions.     

Volatility-Related Exchange Traded Assets: An Econometric Investigation

We develop a theoretical framework for covariance stationary but persistent positively valued processes which combines a semi-nonparametric expansion of the Gamma distribution with a component version of the multiplicative error model. Our conditional mean assumption allows for slow, possibly nonmonotonic mean-reversion, while our distribution assumption provides more flexibility than a traditional Laguerre expansion while preserving positivity of the density. We apply our framework to a dynamic portfolio allocation for Exchange Traded Notes tracking short- and mid-term VIX futures indices, which are increasingly popular but risky financial instruments. We show the superior performance of the strategies based on our econometric model.     

Weights in Multidimensional Indices of Wellbeing: An Overview

Multidimensional indices are becoming increasingly important instruments to assess the wellbeing of societies. They move beyond the focus on a single indicator and yet they are easy to present and communicate. A crucial step in the construction of a multidimensional index of wellbeing is the selection of the relative weights for the different dimensions. The aim of this article is to study the role of these weights and to critically survey eight different approaches to set them. We categorize the approaches in three classes: data-driven, normative, and hybrid weighting, and compare their respective advantages and drawbacks.     

Step-Down diagnostic analysis for monitoring the covariance matrix of bivariate normal processes

ABSTRACT

A comparison among VMIX, VMAX and the adapted step-down Sullivan et al. (SE) tests for covariance matrix under bivariate normal assumption is presented. The type I error and power estimates were obtained by using Monte Carlo simulation under different scenarios with respect to covariance and correlation structures. In general, VMIX was more powerful than VMAX being SE more powerful than both, with few exceptions. SE test is more general since it can be used for normal and non-normal data, with no restriction with respect to the pattern of the covariance matrix shifts, and for larger dimension than the bivariate case.     

Influence Analysis in Principal Component Analysis Through Power-Series Expansions

ABSTRACT

In influence analysis several problems arise in the field of Principal Components when applying different sample versions. Among these are the difficulty of determining a certain correspondence between the eigenvalues before and after the deletion of observations, the choice of the sign of the eigenvectors and the computational problem derived from the resolution of a great number of eigenproblems. In this article, such problems are discussed from the joint influence point of view and a solution is proposed by using approximations. Furthermore, the influence on a new parameter of interest is introduced: the proportion of variance explained by a set of principal components.     

The Non Dominated Set in Bayesian Decision Problems with Convex Loss Functions

Bayesian decision problems require subjective elicitation of the inputs: beliefs and preferences. Sometimes, elicitation methods may not represent perfectly the judgements of the decision maker. Several foundations propose to overlay this problem using robust approaches. In these models, beliefs are modelled by a class of probability distributions and preferences by a class of loss functions. Then, we are in the conditions of a Pareto order. Hence the solution concept is the set of non dominated alternatives. In this article we focus on the computation of the efficient set when the preferences are modeled by a class of convex loss functions.     

Sensitivity Analysis in Gaussian Bayesian Networks Using a Divergence Measure

This article develops a method for computing the sensitivity analysis in a Gaussian Bayesian network. The measure presented is based on the Kullback–Leibler divergence and is useful to evaluate the impact of prior changes over the posterior marginal density of the target variable in the network. We find that some changes do not disturb the posterior marginal density of interest. Finally, we describe a method to compare different sensitivity measures obtained depending on where the inaccuracy was. An example is used to illustrate the concepts and methods presented.     

Mean Estimation Under Successive Sampling with Calibration Estimators

The estimation of the finite population mean in successive occasions is investigated with calibration estimators in this article. We propose several estimators based on calibration techniques with arbitrary sampling design in each of the occasions. Asymptotic variance formulaes are derived for the proposed estimators. The properties of these estimators are studied via a simulation study and using natural populations.     

Weighting Elementary Prices in Consumer Price Index Construction Using Spatial Autocorrelation

The Consumer Price Indexes (CPI) are used in current economic systems to measure inflation. When constructing CPIs, however, official institutions have systematically overlooked the spatial dimension of elementary prices. Ignoring the fact that prices are collected at geographical locations implicitly implies considering prices as spatially independent, when in fact they are not. To solve this problem, this article proposes to weight basic price data by taking into account the spatial correlation they display. The weighted geometric and arithmetic means suggested generalize and improve the simple geometric and arithmetic means currently in use.     

On the Strong Consistency of Ridge Estimates

In this article, we establish strong consistency of the ridge estimates using extended results for the strong consistency of the least squares estimates in multiple regression models which discard the usual assumption of null mean value for the errors and only requires them to be i.i.d. with absolute moment of order r (0 < r ? 1).