Influence diagnostics in heteroscedastic and/or autoregressive nonlinear elliptical models for correlated data

In this paper, we propose nonlinear elliptical models for correlated data with heteroscedastic and/or autoregressive structures. Our aim is to extend the models proposed by Russo et al. [22] by considering a more sophisticated scale structure to deal with variations in data dispersion and/or a possible autocorrelation among measurements taken throughout the same experimental unit. Moreover, to avoid the possible influence of outlying observations or to take into account the non-normal symmetric tails of the data, we assume elliptical contours for the joint distribution of random effects and errors, which allows us to attribute different weights to the observations. We propose an iterative algorithm to obtain the maximum-likelihood estimates for the parameters and derive the local influence curvatures for some specific perturbation schemes. The motivation for this work comes from a pharmacokinetic indomethacin data set, which was analysed previously by Bocheng and Xuping [1] under normality.

Selecting from amongst non–nested conditional variance models: information criteria and portfolio determination

We consider the finite sample properties of model selection by information criteria in conditionally heteroscedastic models. Recent theoretical results show that certain popular criteria are consistent in that they will select the true model asymptotically with probability 1. To examine the empirical relevance of this property, Monte Carlo simulations are conducted for a set of non–nested data generating processes (DGPs) with the set of candidate models consisting of all types of model used as DGPs. In addition, not only is the best model considered but also those with similar values of the information criterion, called close competitors, thus forming a portfolio of eligible models. To supplement the simulations, the criteria are applied to a set of economic and financial series. In the simulations, the criteria are largely ineffective at identifying the correct model, either as best or a close competitor, the parsimonious GARCH(1, 1) model being preferred for most DGPs. In contrast, asymmetric models are generally selected to represent actual data. This leads to the conjecture that the properties of parameterizations of processes commonly used to model heteroscedastic data are more similar than may be imagined and that more attention needs to be paid to the behaviour of the standardized disturbances of such models, both in simulation exercises and in empirical modelling.

Can portmanteau nonlinearity tests serve as general mis-specification tests?

A number of recent papers have employed the BDS test as a general test for mis-specification for linear and nonlinear models. We show that for a particular class of conditionally heteroscedastic models, the BDS test is unable to detect a common mis-specification. Our results also demonstrate that specific rather than portmanteau diagnostics are required to detect neglected asymmetry in volatility. However for both classes of tests reasonable power is only obtained using very large sample sizes.

Optimal design for correlated processes with input-dependent noise

Optimal design for parameter estimation in Gaussian process regression models with input-dependent noise is examined. The motivation stems from the area of computer experiments, where computationally demanding simulators are approximated using Gaussian process emulators to act as statistical surrogates. In the case of stochastic simulators, which produce a random output for a given set of model inputs, repeated evaluations are useful, supporting the use of replicate observations in the experimental design. The findings are also applicable to the wider context of experimental design for Gaussian process regression and kriging. Designs are proposed with the aim of minimising the variance of the Gaussian process parameter estimates. A heteroscedastic Gaussian process model is presented which allows for an experimental design technique based on an extension of Fisher information to heteroscedastic models. It is empirically shown that the error of the approximation of the parameter variance by the inverse of the Fisher information is reduced as the number of replicated points is increased. Through a series of simulation experiments on both synthetic data and a systems biology stochastic simulator, optimal designs with replicate observations are shown to outperform space-filling designs both with and without replicate observations. Guidance is provided on best practice for optimal experimental design for stochastic response models. © 2013 Elsevier Inc. All rights reserved.

Heteroscedastic Nonlinear Regression Models

In this article, we present a generalization of the Bayesian methodology introduced by Cepeda and Gamerman (2001) for modeling variance heterogeneity in normal regression models where we have orthogonality between mean and variance parameters to the general case considering both linear and highly nonlinear regression models. Under the Bayesian paradigm, we use MCMC methods to simulate samples for the joint posterior distribution. We illustrate this algorithm considering a simulated data set and also considering a real data set related to school attendance rate for children in Colombia. Finally, we present some extensions of the proposed MCMC algorithm.

Estimation and diagnostics for heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions

An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. This novel class of models provides a useful generalization of the heteroscedastic symmetrical nonlinear regression models (Cysneiros et al., 2010), since the random term distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as skew-t, skew-slash, skew-contaminated normal, among others. A simple EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters is presented and the observed information matrix is derived analytically. In order to examine the performance of the proposed methods, some simulation studies are presented to show the robust aspect of this flexible class against outlying and influential observations and that the maximum likelihood estimates based on the EM-type algorithm do provide good asymptotic properties. Furthermore, local influence measures and the one-step approximations of the estimates in the case-deletion model are obtained. Finally, an illustration of the methodology is given considering a data set previously analyzed under the homoscedastic skew-t nonlinear regression model. (C) 2012 Elsevier B.V. All rights reserved.

Approximately optimal experimental design for heteroscedastic Gaussian process models

This paper presents a greedy Bayesian experimental design criterion for heteroscedastic Gaussian process models. The criterion is based on the Fisher information and is optimal in the sense of minimizing parameter uncertainty for likelihood based estimators. We demonstrate the validity of the criterion under different noise regimes and present experimental results from a rabies simulator to demonstrate the effectiveness of the resulting approximately optimal designs.

The cross-currency hedging performance of implied versus statistical forecasting models

This article examines the ability of several models to generate optimal hedge ratios. Statistical models employed include univariate and multivariate generalized autoregressive conditionally heteroscedastic (GARCH) models, and exponentially weighted and simple moving averages. The variances of the hedged portfolios derived using these hedge ratios are compared with those based on market expectations implied by the prices of traded options. One-month and three-month hedging horizons are considered for four currency pairs. Overall, it has been found that an exponentially weighted moving-average model leads to lower portfolio variances than any of the GARCH-based, implied or time-invariant approaches.

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

Hypothesis testing in an errors-in-variables model with heteroscedastic measurement errors

In many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors. The main goal of this paper is to consider inference on such models with error-prone observations and variances of the measurement errors changing across observations. We suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed. Aggregate data allow the estimation of the error variances. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed. Test statistics are proposed for testing hypotheses of interest. Further, we implement a simple graphical device that enables an assessment of the model`s goodness of fit. Results of simulations concerning the properties of the test statistics are reported. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease. Copyright (C) 2008 John Wiley & Sons, Ltd.

Fitting spatial models in the R package: hglm

We present a new version of the hglm package for fittinghierarchical generalized linear models (HGLM) with spatially correlated random effects. A CAR family for conditional autoregressive random effects was implemented. Eigen decomposition of the matrix describing the spatial structure (e.g. the neighborhood matrix) was used to transform the CAR random effectsinto an independent, but heteroscedastic, gaussian random effect. A linear predictor is fitted for the random effect variance to estimate the parameters in the CAR model.This gives a computationally efficient algorithm for moderately sized problems (e.g. n<5000).

Influence Assessment in an Heteroscedastic Errors-in-Variables Model

The main goal of this article is to consider influence assessment in models with error-prone observations and variances of the measurement errors changing across observations. The techniques enable to identify potential influential elements and also to quantify the effects of perturbations in these elements on some results of interest. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease.

A Generalized Regression Methodology for Bivariate Heteroscedastic Data

We present a methodology for reducing a straight line fitting regression problem to a Least Squares minimization one. This is accomplished through the definition of a measure on the data space that takes into account directional dependences of errors, and the use of polar descriptors for straight lines. This strategy improves the robustness by avoiding singularities and non-describable lines. The methodology is powerful enough to deal with non-normal bivariate heteroscedastic data error models, but can also supersede classical regression methods by making some particular assumptions. An implementation of the methodology for the normal bivariate case is developed and evaluated.

Managing uncertainty in complex stochastic models: design and emulation of a Rabies model

In this paper we present a novel method for emulating a stochastic, or random output, computer model and show its application to a complex rabies model. The method is evaluated both in terms of accuracy and computational efficiency on synthetic data and the rabies model. We address the issue of experimental design and provide empirical evidence on the effectiveness of utilizing replicate model evaluations compared to a space-filling design. We employ the Mahalanobis error measure to validate the heteroscedastic Gaussian process based emulator predictions for both the mean and (co)variance. The emulator allows efficient screening to identify important model inputs and better understanding of the complex behaviour of the rabies model.

Characterization Of Microsatellite Markers Developed From Prosopis Rubriflora And Prosopis Ruscifolia (leguminosae - Mimosoideae), Legume Species That Are Used As Models For Genetic Diversity Studies In Chaquenian Areas Under Anthropization In South America.

Prosopis rubriflora and Prosopis ruscifolia are important species in the Chaquenian regions of Brazil. Because of the restriction and frequency of their physiognomy, they are excellent models for conservation genetics studies. The use of microsatellite markers (Simple Sequence Repeats, SSRs) has become increasingly important in recent years and has proven to be a powerful tool for both ecological and molecular studies. In this study, we present the development and characterization of 10 new markers for P. rubriflora and 13 new markers for P. ruscifolia. The genotyping was performed using 40 P. rubriflora samples and 48 P. ruscifolia samples from the Chaquenian remnants in Brazil. The polymorphism information content (PIC) of the P. rubriflora markers ranged from 0.073 to 0.791, and no null alleles or deviation from Hardy-Weinberg equilibrium (HW) were detected. The PIC values for the P. ruscifolia markers ranged from 0.289 to 0.883, but a departure from HW and null alleles were detected for certain loci; however, this departure may have resulted from anthropic activities, such as the presence of livestock, which is very common in the remnant areas. In this study, we describe novel SSR polymorphic markers that may be helpful in future genetic studies of P. rubriflora and P. ruscifolia.