On estimation and influence diagnostics for log-Birnbaum-Saunders Student-t regression models: Full Bayesian analysis

The purpose of this paper is to develop a Bayesian approach for log-Birnbaum-Saunders Student-t regression models under right-censored survival data. Markov chain Monte Carlo (MCMC) methods are used to develop a Bayesian procedure for the considered model. In order to attenuate the influence of the outlying observations on the parameter estimates, we present in this paper Birnbaum-Saunders models in which a Student-t distribution is assumed to explain the cumulative damage. Also, some discussions on the model selection to compare the fitted models are given and case deletion influence diagnostics are developed for the joint posterior distribution based on the Kullback-Leibler divergence. The developed procedures are illustrated with a real data set. (C) 2010 Elsevier B.V. All rights reserved.

Local influence for Student-t partially linear models

In this paper we extend partial linear models with normal errors to Student-t errors Penalized likelihood equations are applied to derive the maximum likelihood estimates which appear to be robust against outlying observations in the sense of the Mahalanobis distance In order to study the sensitivity of the penalized estimates under some usual perturbation schemes in the model or data the local influence curvatures are derived and some diagnostic graphics are proposed A motivating example preliminary analyzed under normal errors is reanalyzed under Student-t errors The local influence approach is used to compare the sensitivity of the model estimates (C) 2010 Elsevier B V All rights reserved

Robust modeling using the generalized epsilon-skew-t distribution

In this paper, an alternative skew Student-t family of distributions is studied. It is obtained as an extension of the generalized Student-t (GS-t) family introduced by McDonald and Newey [10]. The extension that is obtained can be seen as a reparametrization of the skewed GS-t distribution considered by Theodossiou [14]. A key element in the construction of such an extension is that it can be stochastically represented as a mixture of an epsilon-skew-power-exponential distribution [1] and a generalized-gamma distribution. From this representation, we can readily derive theoretical properties and easy-to-implement simulation schemes. Furthermore, we study some of its main properties including stochastic representation, moments and asymmetry and kurtosis coefficients. We also derive the Fisher information matrix, which is shown to be nonsingular for some special cases such as when the asymmetry parameter is null, that is, at the vicinity of symmetry, and discuss maximum-likelihood estimation. Simulation studies for some particular cases and real data analysis are also reported, illustrating the usefulness of the extension considered.

Robust statistical modeling using the Birnbaum-Saunders-t distribution applied to insurance

In this paper, we carry out robust modeling and influence diagnostics in Birnbaum-Saunders (BS) regression models. Specifically, we present some aspects related to BS and log-BS distributions and their generalizations from the Student-t distribution, and develop BS-t regression models, including maximum likelihood estimation based on the EM algorithm and diagnostic tools. In addition, we apply the obtained results to real data from insurance, which shows the uses of the proposed model. Copyright (c) 2011 John Wiley & Sons, Ltd.

Variational inference for Student-t MLP models

This paper presents a novel methodology to infer parameters of probabilistic models whose output noise is a Student-t distribution. The method is an extension of earlier work for models that are linear in parameters to nonlinear multi-layer perceptrons (MLPs). We used an EM algorithm combined with variational approximation, the evidence procedure, and an optimisation algorithm. The technique was tested on two regression applications. The first one is a synthetic dataset and the second is gas forward contract prices data from the UK energy market. The results showed that forecasting accuracy is significantly improved by using Student-t noise models.

Cramer-Rao-Type Bounds for Sparse Bayesian Learning

In this paper, we derive Hybrid, Bayesian and Marginalized Cramer-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their prior distribution parameters. We assume the unknown vector to be drawn from a compressible Student-prior distribution. We derive CRBs that encompass the deterministic or random nature of the unknown parameters of the prior distribution and the regression noise variance. We extend the MCRB to the case where the compressible vector is distributed according to a general compressible prior distribution, of which the generalized Pareto distribution is a special case. We use the derived bounds to uncover the relationship between the compressibility and Mean Square Error (MSE) in the estimates. Further, we illustrate the tightness and utility of the bounds through simulations, by comparing them with the MSE performance of two popular SBL-based estimators. We find that the MCRB is generally the tightest among the bounds derived and that the MSE performance of the Expectation-Maximization (EM) algorithm coincides with the MCRB for the compressible vector. We also illustrate the dependence of the MSE performance of SBL based estimators on the compressibility of the vector for several values of the number of observations and at different signal powers.

Teaching Principled negotiation skills to parents and their children : the impact of parental involvement /

This study explored the impact of training parents and children concurrently in principled negotiation skills for the purpose of developing negotiation skills and problem solving abilities in children. A second experimental group was utilized to determine the viability of negotiation skills training of junior elementary students for the purpose of improving problem solving and conflict resolving abilities. The student population in each experimental group was trained using The Program for Young Negotiators (Curhan, 1996). A control group was also established using the remaining grade four and five students attending the participating school. These students did not receive training as part of this study. Student group distribution was as follows: Experimental group 1 (students with parent participant) consisted of 10 (5 grade five and 5 grade 4 students), Experimental group 2 students without parent participant) consisted of 48 (20 grade 4 and 28 grade 5 students), and the Control group 3 (55 grade 4 and 5 students). The impact of training was measured using the Five Factor Negotiation Scale developed for use with the Program for Young Negotiators (Curhan, 1996). This measure was employed as a pre- and post-test questionnaire to the total student population, (113 students) to determine levels of ability in each of the key elements of negotiation, personal initiative, collaboration, communication, conflict based perspective taking, and conflict resolution approach (Nakkula & Nikitopoulos, unpublished). This measure has a coefficient alpha of .75 which is acceptable for this type of affective instrument. As well, open ended ability questions designed to measure ability, knowledge, and behaviour as they relate to negotiation skill application were given to the total student population, (113 students). Finally, journals were maintained by the students in both experimental groups, and informal feedback discussions were held with students and parents participating in the study.The intent of using both qualitative and quantitative measures was to provide an overall perspective of student abilities as they related to principled negotiation skills. While the quantitative measures were from the student perspective, more qualitative information was sought from parents and teachers through informal interviews, discussions, and use of confidential feedback cards. For analysis purposes, the ability questions were randomly selected for Experimental group 2 and Control group 3 in an effort to balance the groups more equitably with Experimental group 1. The findings of this study indicate that students of the junior elementary school age can be taught how to perceive conflict in a more constructive way. However, they are not as likely to use their skills when the conflict is with a sibling as they are with a peer, a teacher, or a parent. While no statistically significant differences between mean scores for Experimental groups 1 and 2 exist some subtle differences are noted. Overall, increases in mean scores for grade 4 students exceeded the increases for grade 5 students within Experimental group 1 . The implication being that younger students benefit more from having a parent trained in principled negoUation skills than older students. The skill level of a parent in principled negotiation can not be underesUmated. Without a consistent and effective role model the likelihood of developing student skill level to a point of automaticity is greatly reduced. Enough so that perhaps the emphasis should be placed on training parents more so than the students.

Finite-Sample Diagnostics for Multivariate Regressions with Applications to Linear Asset Pricing Models

In this paper, we propose several finite-sample specification tests for multivariate linear regressions (MLR) with applications to asset pricing models. We focus on departures from the assumption of i.i.d. errors assumption, at univariate and multivariate levels, with Gaussian and non-Gaussian (including Student t) errors. The univariate tests studied extend existing exact procedures by allowing for unspecified parameters in the error distributions (e.g., the degrees of freedom in the case of the Student t distribution). The multivariate tests are based on properly standardized multivariate residuals to ensure invariance to MLR coefficients and error covariances. We consider tests for serial correlation, tests for multivariate GARCH and sign-type tests against general dependencies and asymmetries. The procedures proposed provide exact versions of those applied in Shanken (1990) which consist in combining univariate specification tests. Specifically, we combine tests across equations using the MC test procedure to avoid Bonferroni-type bounds. Since non-Gaussian based tests are not pivotal, we apply the “maximized MC” (MMC) test method [Dufour (2002)], where the MC p-value for the tested hypothesis (which depends on nuisance parameters) is maximized (with respect to these nuisance parameters) to control the test’s significance level. The tests proposed are applied to an asset pricing model with observable risk-free rates, using monthly returns on New York Stock Exchange (NYSE) portfolios over five-year subperiods from 1926-1995. Our empirical results reveal the following. Whereas univariate exact tests indicate significant serial correlation, asymmetries and GARCH in some equations, such effects are much less prevalent once error cross-equation covariances are accounted for. In addition, significant departures from the i.i.d. hypothesis are less evident once we allow for non-Gaussian errors.

Robust inference in an heteroscedastic measurement error model

In this paper we deal with robust inference in heteroscedastic measurement error models Rather than the normal distribution we postulate a Student t distribution for the observed variables Maximum likelihood estimates are computed numerically Consistent estimation of the asymptotic covariance matrices of the maximum likelihood and generalized least squares estimators is also discussed Three test statistics are proposed for testing hypotheses of interest with the asymptotic chi-square distribution which guarantees correct asymptotic significance levels Results of simulations and an application to a real data set are also reported (C) 2009 The Korean Statistical Society Published by Elsevier B V All rights reserved

A new class of survival regression models with heavy-tailed errors: robustness and diagnostics

Birnbaum-Saunders models have largely been applied in material fatigue studies and reliability analyses to relate the total time until failure with some type of cumulative damage. In many problems related to the medical field, such as chronic cardiac diseases and different types of cancer, a cumulative damage caused by several risk factors might cause some degradation that leads to a fatigue process. In these cases, BS models can be suitable for describing the propagation lifetime. However, since the cumulative damage is assumed to be normally distributed in the BS distribution, the parameter estimates from this model can be sensitive to outlying observations. In order to attenuate this influence, we present in this paper BS models, in which a Student-t distribution is assumed to explain the cumulative damage. In particular, we show that the maximum likelihood estimates of the Student-t log-BS models attribute smaller weights to outlying observations, which produce robust parameter estimates. Also, some inferential results are presented. In addition, based on local influence and deviance component and martingale-type residuals, a diagnostics analysis is derived. Finally, a motivating example from the medical field is analyzed using log-BS regression models. Since the parameter estimates appear to be very sensitive to outlying and influential observations, the Student-t log-BS regression model should attenuate such influences. The model checking methodologies developed in this paper are used to compare the fitted models.

Bayesian longitudinal data analysis with mixed models and thick-tailed distributions using MCMC

Linear mixed effects models are frequently used to analyse longitudinal data, due to their flexibility in modelling the covariance structure between and within observations. Further, it is easy to deal with unbalanced data, either with respect to the number of observations per subject or per time period, and with varying time intervals between observations. In most applications of mixed models to biological sciences, a normal distribution is assumed both for the random effects and for the residuals. This, however, makes inferences vulnerable to the presence of outliers. Here, linear mixed models employing thick-tailed distributions for robust inferences in longitudinal data analysis are described. Specific distributions discussed include the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted, and the Gibbs sampler and the Metropolis-Hastings algorithms are used to carry out the posterior analyses. An example with data on orthodontic distance growth in children is discussed to illustrate the methodology. Analyses based on either the Student-t distribution or on the usual Gaussian assumption are contrasted. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process for modelling distributions of the random effects and of residuals in linear mixed models, and the MCMC implementation allows the computations to be performed in a flexible manner.

Minimum Description Length Principle in Discriminating Marginal Distributions

2010 Mathematics Subject Classification: 94A17, 62B10, 62F03.

A mixture model approach for formant tracking and the robustness of student's-t distribution

We address the problem of robust formant tracking in continuous speech in the presence of additive noise. We propose a new approach based on mixture modeling of the formant contours. Our approach consists of two main steps: (i) Computation of a pyknogram based on multiband amplitude-modulation/frequency-modulation (AM/FM) decomposition of the input speech; and (ii) Statistical modeling of the pyknogram using mixture models. We experiment with both Gaussian mixture model (GMM) and Student's-t mixture model (tMM) and show that the latter is robust with respect to handling outliers in the pyknogram data, parameter selection, accuracy, and smoothness of the estimated formant contours. Experimental results on simulated data as well as noisy speech data show that the proposed tMM-based approach is also robust to additive noise. We present performance comparisons with a recently developed adaptive filterbank technique proposed in the literature and the classical Burg's spectral estimator technique, which show that the proposed technique is more robust to noise.

What student attributes affect experience of PBL in Virtual Space?

Some Engineering Faculties are turning to the problem-based learning (PBL)paradigm to engender necessary skills and competence in their graduates. Since, at the same time, some Faculties are moving towards distance education, questions are being asked about the effectiveness of PBL for technical fields such as Engineering when delivered in virtual space. This paper outlines an investigation of how student attributes affect their learning experience in PBL courses offered in virtual space. A frequency distribution was superimposed on the outcome space of a phenomenographical study on a suitable PBL course to investigate the effect of different student attributes on the learning experience. It was discovered that the quality, quantity, and style of facilitator interaction had the greatest impact on the student learning experience. This highlights the need to establish consistent student interaction plans and to set, and ensure compliance with, minimum standards with respect to facilitation and student interactions.

Foldback current control for a DG to achieve Fast Arc Extinction in a distribution network

The distribution network reliability can be increased if distributed generators (DGs) are allowed to operate in both grid-connected and islanded operations when the network has a high DG penetration level. However, the current utility regulations do not allow for the islanded operation. The arc faults are the one of the major issues preventing the islanded operation, since the arc will not extinguish if the DGs are not disconnected. In this paper, the effect of a converter interfaced DG on an arc fault is investigated by considering different control strategies for the converter. The foldback current control characteristic is proposed to a converter interfaced DG to achieve quick arc extinction and self-restoration without disconnecting the DG in the event of an arc fault. The results are validated through PSCAD/EMTDC simulations.