Bayesian parametric bootstrap for models with intractable likelihoods

In this paper it is demonstrated how the Bayesian parametric bootstrap can be adapted to models with intractable likelihoods. The approach is most appealing when the semi-automatic approximate Bayesian computation (ABC) summary statistics are selected. After a pilot run of ABC, the likelihood-free parametric bootstrap approach requires very few model simulations to produce an approximate posterior, which can be a useful approximation in its own right. An alternative is to use this approximation as a proposal distribution in ABC algorithms to make them more efficient. In this paper, the parametric bootstrap approximation is used to form the initial importance distribution for the sequential Monte Carlo and the ABC importance and rejection sampling algorithms. The new approach is illustrated through a simulation study of the univariate g-and- k quantile distribution, and is used to infer parameter values of a stochastic model describing expanding melanoma cell colonies.

Orthogonal projections and bootstrap resampling procedures in the study of infraspecific variation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bootstrap confidence regions for canonical variates: Application to studies of evolutionary differentiation

Theory recently developed to construct confidence regions based on the parametric bootstrap is applied to add inferential information to graphical displays of sample centroids in canonical variate analysis. Problems of morphometric differentiation among subspecies and species are addressed using numerical resampling procedures.

POOR PERFORMANCE OF BOOTSTRAP CONFIDENCE INTERVALS FOR THE LOCATION OF A QUANTITATIVE TRAIT LOUCS

The aim of many genetic studies is to locate the genomic regions (called quantitative trait loci, QTLs) that contribute to variation in a quantitative trait (such as body weight). Confidence intervals for the locations of QTLs are particularly important for the design of further experiments to identify the gene or genes responsible for the effect. Likelihood support intervals are the most widely used method to obtain confidence intervals for QTL location, but the non-parametric bootstrap has also been recommended. Through extensive computer simulation, we show that bootstrap confidence intervals are poorly behaved and so should not be used in this context. The profile likelihood (or LOD curve) for QTL location has a tendency to peak at genetic markers, and so the distribution of the maximum likelihood estimate (MLE) of QTL location has the unusual feature of point masses at genetic markers; this contributes to the poor behavior of the bootstrap. Likelihood support intervals and approximate Bayes credible intervals, on the other hand, are shown to behave appropriately.

Bootstrap for Critical Branching Process with Non-Stationary Immigration

2000 Mathematics Subject Classification: Primary 60J80, Secondary 62F12, 60G99.

Studies on Binary Time Series Models with Applications to Empirical Macroeconomics and Finance

This thesis studies binary time series models and their applications in empirical macroeconomics and finance. In addition to previously suggested models, new dynamic extensions are proposed to the static probit model commonly used in the previous literature. In particular, we are interested in probit models with an autoregressive model structure. In Chapter 2, the main objective is to compare the predictive performance of the static and dynamic probit models in forecasting the U.S. and German business cycle recession periods. Financial variables, such as interest rates and stock market returns, are used as predictive variables. The empirical results suggest that the recession periods are predictable and dynamic probit models, especially models with the autoregressive structure, outperform the static model. Chapter 3 proposes a Lagrange Multiplier (LM) test for the usefulness of the autoregressive structure of the probit model. The finite sample properties of the LM test are considered with simulation experiments. Results indicate that the two alternative LM test statistics have reasonable size and power in large samples. In small samples, a parametric bootstrap method is suggested to obtain approximately correct size. In Chapter 4, the predictive power of dynamic probit models in predicting the direction of stock market returns are examined. The novel idea is to use recession forecast (see Chapter 2) as a predictor of the stock return sign. The evidence suggests that the signs of the U.S. excess stock returns over the risk-free return are predictable both in and out of sample. The new "error correction" probit model yields the best forecasts and it also outperforms other predictive models, such as ARMAX models, in terms of statistical and economic goodness-of-fit measures. Chapter 5 generalizes the analysis of univariate models considered in Chapters 2 4 to the case of a bivariate model. A new bivariate autoregressive probit model is applied to predict the current state of the U.S. business cycle and growth rate cycle periods. Evidence of predictability of both cycle indicators is obtained and the bivariate model is found to outperform the univariate models in terms of predictive power.

Non-monophyly of fish in the Sinipercidae (Perciformes) as inferred from cytochrome b gene

The sinipercids represent a group of 12 species of freshwater percoid fish, including nine in Siniperca and three species in Coreoperca. Despite several classification attempts and a preliminary molecular phylogeny, the phylogenetic relationships and systematic position of sinipercids remained still unsolved. The complete cytochrome b gene sequences from nine sinipercid species four non-sinipercid fish species were cloned, and a total of 12 cyt b sequences from 10 species of sinipercids and 11 cyt b sequences from 10 species of non-sinipercid fish also in Perciformes were included in the phylogenetic analysis. As expected, the two genera Siniperca and Coreoperca within sinipercids are recovered as monophyletic. However, nine species representing Moronidae, Serranidae, Centropomidae, Acropomatidae, Emmelichtyidae, Siganidae and Centrarchidae included in the present study are all nested between Coreoperca and Siniperca, which provides marked evidence for a non-monophyly of sinipercid fishes. Coreoperca appears to be closest to Centrachus representing the family Centrarchidae. Coreoperca whiteheadi and C. herzi are sibling species, which together are closely related to C. kawamebari. In the Siniperca, the node between S. roulei and the remaining species is the most ancestral, followed by that of S. fortis. S. chuatsi and S. kneri are sibling species, sister to S. obscura. However, the sinipercids do not seem to have a very clear phylogenetic history, for different methods of phylogenetic reconstruction result in different tree topologies, and the only conclusive result in favor of a paraphyletic origin of the two sinipercid genera is the parametric bootstrap test. The paraphyly of Sinipercidae may suggest that the "synapomorphs" such as cycloid scales, upon which this family is based, were independently derived at least twice within sinipercid fishes, and further study should be carried out to include the other two Siniperca species and to incorporate other genes.

Evolution of the rbcS gene family in Solanaceae: concerted evolution and gain and loss of introns, with a description of new statistical guidelines for determining the number of unique gene copies.

Thesis (Ph.D.)--University of Washington, 2014

New methods for meta-analysis under a fixed effects framework, with frequentist and Bayesian estimation.

Thesis (Ph.D.)--University of Washington, 2015

Simulation-Based Finite and Large Sample Tests in Multivariate Regressions.

In the context of multivariate linear regression (MLR) models, it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection. In this paper, we propose a general method for constructing exact tests of possibly nonlinear hypotheses on the coefficients of MLR systems. For the case of uniform linear hypotheses, we present exact distributional invariance results concerning several standard test criteria. These include Wilks' likelihood ratio (LR) criterion as well as trace and maximum root criteria. The normality assumption is not necessary for most of the results to hold. Implications for inference are two-fold. First, invariance to nuisance parameters entails that the technique of Monte Carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses. Second, the invariance property of the latter statistic is exploited to derive general nuisance-parameter-free bounds on the distribution of the LR statistic for arbitrary hypotheses. Even though it may be difficult to compute these bounds analytically, they can easily be simulated, hence yielding exact bounds Monte Carlo tests. Illustrative simulation experiments show that the bounds are sufficiently tight to provide conclusive results with a high probability. Our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation-based test methods (e.g., the parametric bootstrap) which may be applied when the bounds are not conclusive.

Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics

The technique of Monte Carlo (MC) tests [Dwass (1957), Barnard (1963)] provides an attractive method of building exact tests from statistics whose finite sample distribution is intractable but can be simulated (provided it does not involve nuisance parameters). We extend this method in two ways: first, by allowing for MC tests based on exchangeable possibly discrete test statistics; second, by generalizing the method to statistics whose null distributions involve nuisance parameters (maximized MC tests, MMC). Simplified asymptotically justified versions of the MMC method are also proposed and it is shown that they provide a simple way of improving standard asymptotics and dealing with nonstandard asymptotics (e.g., unit root asymptotics). Parametric bootstrap tests may be interpreted as a simplified version of the MMC method (without the general validity properties of the latter).

Actuarial applications of multivariate phase-type distributions : model calibration and credibility

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Inférence robuste à la présence des valeurs aberrantes dans les enquêtes

Cette thèse comporte trois articles dont un est publié et deux en préparation. Le sujet central de la thèse porte sur le traitement des valeurs aberrantes représentatives dans deux aspects importants des enquêtes que sont : l’estimation des petits domaines et l’imputation en présence de non-réponse partielle. En ce qui concerne les petits domaines, les estimateurs robustes dans le cadre des modèles au niveau des unités ont été étudiés. Sinha & Rao (2009) proposent une version robuste du meilleur prédicteur linéaire sans biais empirique pour la moyenne des petits domaines. Leur estimateur robuste est de type «plugin», et à la lumière des travaux de Chambers (1986), cet estimateur peut être biaisé dans certaines situations. Chambers et al. (2014) proposent un estimateur corrigé du biais. En outre, un estimateur de l’erreur quadratique moyenne a été associé à ces estimateurs ponctuels. Sinha & Rao (2009) proposent une procédure bootstrap paramétrique pour estimer l’erreur quadratique moyenne. Des méthodes analytiques sont proposées dans Chambers et al. (2014). Cependant, leur validité théorique n’a pas été établie et leurs performances empiriques ne sont pas pleinement satisfaisantes. Ici, nous examinons deux nouvelles approches pour obtenir une version robuste du meilleur prédicteur linéaire sans biais empirique : la première est fondée sur les travaux de Chambers (1986), et la deuxième est basée sur le concept de biais conditionnel comme mesure de l’influence d’une unité de la population. Ces deux classes d’estimateurs robustes des petits domaines incluent également un terme de correction pour le biais. Cependant, ils utilisent tous les deux l’information disponible dans tous les domaines contrairement à celui de Chambers et al. (2014) qui utilise uniquement l’information disponible dans le domaine d’intérêt. Dans certaines situations, un biais non négligeable est possible pour l’estimateur de Sinha & Rao (2009), alors que les estimateurs proposés exhibent un faible biais pour un choix approprié de la fonction d’influence et de la constante de robustesse. Les simulations Monte Carlo sont effectuées, et les comparaisons sont faites entre les estimateurs proposés et ceux de Sinha & Rao (2009) et de Chambers et al. (2014). Les résultats montrent que les estimateurs de Sinha & Rao (2009) et de Chambers et al. (2014) peuvent avoir un biais important, alors que les estimateurs proposés ont une meilleure performance en termes de biais et d’erreur quadratique moyenne. En outre, nous proposons une nouvelle procédure bootstrap pour l’estimation de l’erreur quadratique moyenne des estimateurs robustes des petits domaines. Contrairement aux procédures existantes, nous montrons formellement la validité asymptotique de la méthode bootstrap proposée. Par ailleurs, la méthode proposée est semi-paramétrique, c’est-à-dire, elle n’est pas assujettie à une hypothèse sur les distributions des erreurs ou des effets aléatoires. Ainsi, elle est particulièrement attrayante et plus largement applicable. Nous examinons les performances de notre procédure bootstrap avec les simulations Monte Carlo. Les résultats montrent que notre procédure performe bien et surtout performe mieux que tous les compétiteurs étudiés. Une application de la méthode proposée est illustrée en analysant les données réelles contenant des valeurs aberrantes de Battese, Harter & Fuller (1988). S’agissant de l’imputation en présence de non-réponse partielle, certaines formes d’imputation simple ont été étudiées. L’imputation par la régression déterministe entre les classes, qui inclut l’imputation par le ratio et l’imputation par la moyenne sont souvent utilisées dans les enquêtes. Ces méthodes d’imputation peuvent conduire à des estimateurs imputés biaisés si le modèle d’imputation ou le modèle de non-réponse n’est pas correctement spécifié. Des estimateurs doublement robustes ont été développés dans les années récentes. Ces estimateurs sont sans biais si l’un au moins des modèles d’imputation ou de non-réponse est bien spécifié. Cependant, en présence des valeurs aberrantes, les estimateurs imputés doublement robustes peuvent être très instables. En utilisant le concept de biais conditionnel, nous proposons une version robuste aux valeurs aberrantes de l’estimateur doublement robuste. Les résultats des études par simulations montrent que l’estimateur proposé performe bien pour un choix approprié de la constante de robustesse.

The log-exponentiated Weibull regression model for interval-censored data

In interval-censored survival data, the event of interest is not observed exactly but is only known to occur within some time interval. Such data appear very frequently. In this paper, we are concerned only with parametric forms, and so a location-scale regression model based on the exponentiated Weibull distribution is proposed for modeling interval-censored data. We show that the proposed log-exponentiated Weibull regression model for interval-censored data represents a parametric family of models that include other regression models that are broadly used in lifetime data analysis. Assuming the use of interval-censored data, we employ a frequentist analysis, a jackknife estimator, a parametric bootstrap and a Bayesian analysis for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Furthermore, for different parameter settings, sample sizes and censoring percentages, various simulations are performed; in addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to a modified deviance residual in log-exponentiated Weibull regression models for interval-censored data. (C) 2009 Elsevier B.V. All rights reserved.

Improved likelihood inference in Birnbaum-Saunders regressions

The Birnbaum-Saunders regression model is commonly used in reliability studies. We address the issue of performing inference in this class of models when the number of observations is small. Our simulation results suggest that the likelihood ratio test tends to be liberal when the sample size is small. We obtain a correction factor which reduces the size distortion of the test. Also, we consider a parametric bootstrap scheme to obtain improved critical values and improved p-values for the likelihood ratio test. The numerical results show that the modified tests are more reliable in finite samples than the usual likelihood ratio test. We also present an empirical application. (C) 2009 Elsevier B.V. All rights reserved.