Inference on Filtered and Smoothed Probabilities in Markov-Switching Autoregressive Models

ABSTRACT

We derive a statistical theory that provides useful asymptotic approximations to the distributions of the single inferences of filtered and smoothed probabilities, derived from time series characterized by Markov-switching dynamics. We show that the uncertainty in these probabilities diminishes when the states are separated, the variance of the shocks is low, and the time series or the regimes are persistent. As empirical illustrations of our approach, we analyze the U.S. GDP growth rates and the U.S. real interest rates. For both models, we illustrate the usefulness of the confidence intervals when identifying the business cycle phases and the interest rate regimes.     

Bayesian monitoring of local residual autocorrelations taking into account the run-length

This paper proposes new two-sided monitoring algorithms for detecting the presence of first order residual autocorrelations in Dynamic Normal Models. The methodology uses a Bayesian decision approach with loss function which takes into account the run-length of the process. The power and mean run-length of the proposed algorithms are analysed by Monte Carlo methods. The results obtained improve those corresponding to the monitoring algorithm for residual autocorrelations proposed in Gargallo and Salvador [2003. Monitoring residual autocorrelations in dynamic linear models. Comm. Statist. Simulation Comput. 32(4), 1079–1104.] with respect to the run-length, and also exhibit more homogeneous behaviour.     

A multivariate version of Gini's rank association coefficient

In this paper, we introduce a multivariate generalization of the population version of Gini's rank association coefficient, giving a response to this open question posed in [4]. We also study some properties of this version, present the corresponding results for the sample statistic, and provide several examples.     

Influence diagnostics in the capital asset pricing model under elliptical distributions

In this paper we consider the Capital Asset Pricing Model under Elliptical (symmetric) Distributions. This class of distributions, which contains the normal distribution, t, contaminated normal and power exponential, among others, offers a more flexible framework for modelling asset prices or returns. In order to analyze the sensibility to possible outliers and/or atypical returns of the maximum likelihood estimators, the local influence method was implemented. The results are illustrated by using a set of shares from companies who trade in the Chilean Stock Market. Our main conclusion is that symmetric distributions having heavier tails than those of the normal distribution, especially the t distribution with small degrees of freedom, show a better fit and allow the reduction of the influence of atypical returns in the maximum likelihood estimators.     

A Statistical Framework for Hypothesis Testing in Real Data Comparison Studies

In computational sciences, including computational statistics, machine learning, and bioinformatics, it is often claimed in articles presenting new supervised learning methods that the new method performs better than existing methods on real data, for instance in terms of error rate. However, these claims are often not based on proper statistical tests and, even if such tests are performed, the tested hypothesis is not clearly defined and poor attention is devoted to the Type I and Type II errors. In the present article, we aim to fill this gap by providing a proper statistical framework for hypothesis tests that compare the performances of supervised learning methods based on several real datasets with unknown underlying distributions. After giving a statistical interpretation of ad hoc tests commonly performed by computational researchers, we devote special attention to power issues and outline a simple method of determining the number of datasets to be included in a comparison study to reach an adequate power. These methods are illustrated through three comparison studies from the literature and an exemplary benchmarking study using gene expression microarray data. All our results can be reproduced using R codes and datasets available from the companion website http://www.ibe.med.uni-muenchen.de/organisation/mitarbeiter/020_professuren/boulesteix/compstud2013.     

Life Domain Satisfactions as Predictors of Overall Life Satisfaction Among Workers: Evidence from Chile

This article examines the subjective antecedents of life satisfaction of workers. Adopting a ‘bottom-up’ perspective, we assessed the unique influence that satisfaction with multiple life domains have on evaluative judgments of overall life satisfaction. Based on a nationwide sample of 530 Chilean workers, we simultaneously tested the effects of seven life domain satisfactions that have been consistently included in extant models of life satisfaction and subjective well-being. These were satisfaction with health, financial situation, social relationships, one’s self-worth, leisure-time, family, and work. Having controlled for age and gender, results showed that satisfaction with one’s financial situation was the dominant predictor of overall life satisfaction of workers, with a weight of .36. Satisfaction with family, work, and health had effects of .25, .14, and .14, respectively. Interestingly, satisfaction with one’s self-worth, leisure-time, and social relationships did not have statistically significant effects on life satisfaction, although the first two showed t values near the critical value.     

Estimating the number of clusters

Hartigan (1975) defines the number q of clusters in a d ‐variate statistical population as the number of connected components of the set {f > c}, where f denotes the underlying density function on R^d and c is a given constant. Some usual cluster algorithms treat q as an input which must be given in advance. The authors propose a method for estimating this parameter which is based on the computation of the number of connected components of an estimate of {f > c}. This set estimator is constructed as a union of balls with centres at an appropriate subsample which is selected via a nonparametric density estimator of f. The asymptotic behaviour of the proposed method is analyzed. A simulation study and an example with real data are also included.     

Integer-valued autoregressive processes with periodic structure

In this paper the periodic integer-valued autoregressive model of order one with period T, driven by a periodic sequence of independent Poisson-distributed random variables, is studied in some detail. Basic probabilistic and statistical properties of this model are discussed. Moreover, parameter estimation is also addressed. Specifically, the methods of estimation under analysis are the method of moments, least squares-type and likelihood-based ones. Their performance is compared through a simulation study.     

Methodology for the Calculation of Annualized Incremental Risks in Systems of Dams

In the past few years, the field of dam safety has approached risk informed methodologies throughout the world and several methodologies and programs are appearing to aid in the systematization of the calculations. The most common way of implementing these calculations is through the use of event trees, computing event probabilities, and incremental consequences. This methodology is flexible enough for several situations, but its generalization to the case of systems of several dams is complex and its implementation in a completely general calculation methodology presents some problems. Retaining the event tree framework, a new methodology is proposed to calculate incremental risks. The main advantage of this proposed methodology is the ease with which it can be applied to systems of several dams: with a single risk model that describes the complete system and with a single calculation the incremental risks of the system can be obtained, being able to allocate the risk of each dam and of each failure mode. The article shows how both methodologies are equivalent and also applies them to a case study.