Parametric Bootstrap Approach Research Articles

A fiducial p-value approach for comparing heteroscedastic regression models

ABSTRACTTo study the equality of regression coefficients in several heteroscedastic regression models, we propose a fiducial-based test, and theoretically examine the frequency property of the proposed test. We numerically compare the performance of the proposed approach with the parametric bootstrap (PB) approach. Simulation results indicate that the fiducial approach controls the Type I error rates satisfactorily regardless of the number of regression models and sample sizes, whereas the PB approach tends to be a little of liberal in some scenarios. Finally, the proposed approach is applied to an analysis of a real dataset for illustration.

A statistical approach for evaluating the effectiveness of heartworm preventive drugs: what does 100% efficacy really mean?

BackgroundInitial studies of heartworm preventive drugs all yielded an observed efficacy of 100% with a single dose, and based on these data the US Food and Drug Administration (FDA) required all products to meet this standard for approval. Those initial studies, however, were based on just a few strains of parasites, and therefore were not representative of the full assortment of circulating biotypes. This issue has come to light in recent years, where it has become common for studies to yield less than 100% efficacy. This has changed the landscape for the testing of new products because heartworm efficacy studies lack the statistical power to conclude that finding zero worms is different from finding a few worms.MethodsTo address this issue, we developed a novel statistical model, based on a hierarchical modeling and parametric bootstrap approach that provides new insights to assess multiple sources of variability encountered in heartworm drug efficacy studies. Using the newly established metrics we performed both data simulations and analyzed actual experimental data.ResultsOur results suggest that an important source of modeling variability arises from variability in the parasite establishment rate between dogs; not accounting for this can overestimate the efficacy in more than 40% of cases. We provide strong evidence that ZoeMo-2012 and JYD-34, which both were established from the same source dog, have differing levels of susceptibility to moxidectin. In addition, we provide strong evidence that the differences in efficacy seen in two published studies using the MP3 strain were not due to randomness, and thus must be biological in nature.ConclusionOur results demonstrate how statistical modeling can improve the interpretation of data from heartworm efficacy studies by providing a means to identify the true efficacy range based on the observed data. Importantly, these new insights should help to inform regulators on how to move forward in establishing new statistically and scientifically valid requirements for efficacy in the registration of new heartworm preventative products. Furthermore, our results provide strong evidence that heartworm ‘strains’ can change their susceptibility phenotype over short periods of time, providing further evidence that a wide diversity of susceptibility phenotypes exists among naturally circulating biotypes of D. immitis.

Water Table Uncertainties due to Uncertainties in Structure and Properties of an Unconfined Aquifer.

We consider two sources of geology-related uncertainty in making predictions of the steady-state water table elevation for an unconfined aquifer. That is the uncertainty in the depth to base of the aquifer and in the hydraulic conductivity distribution within the aquifer. Stochastic approaches to hydrological modeling commonly use geostatistical techniques to account for hydraulic conductivity uncertainty within the aquifer. In the absence of well data allowing derivation of a relationship between geophysical and hydrological parameters, the use of geophysical data is often limited to constraining the structural boundaries. If we recover the base of an unconfined aquifer from an analysis of geophysical data, then the associated uncertainties are a consequence of the geophysical inversion process. In this study, we illustrate this by quantifying water table uncertainties for the unconfined aquifer formed by the paleochannel network around the Kintyre Uranium deposit in Western Australia. The focus of the Bayesian parametric bootstrap approach employed for the inversion of the available airborne electromagnetic data is the recovery of the base of the paleochannel network and the associated uncertainties. This allows us to then quantify the associated influences on the water table in a conceptualized groundwater usage scenario and compare the resulting uncertainties with uncertainties due to an uncertain hydraulic conductivity distribution within the aquifer. Our modeling shows that neither uncertainties in the depth to the base of the aquifer nor hydraulic conductivity uncertainties alone can capture the patterns of uncertainty in the water table that emerge when the two are combined.

Deriving acute and chronic predicted no effect concentrations of pharmaceuticals and personal care products based on species sensitivity distributions

Pharmaceuticals and personal care products (PPCPs), as emerging contaminants, have been detected in various environmental matrices and caused adverse effects on human health and the ecosystem. But water quality criterias (WQCs) of PPCPs for protecting aquatic environment are lacking, which hinders the environmental management of these emerging contaminants. In the present study, in order to support their WQC derivation, acute and chronic hazardous concentrations for 5% of species (HC5s) of some frequently detected PPCPs in China were calculated based on acute and chronic species sensitivity distributions (SSDs), respectively, using both parametric (log-normal and log-logistic) and nonparametric bootstrap approaches. The groups of aquatic species used in SSDs included planktons, zooplanktons, invertebrates and vertebrates. Acute and chronic predicted no effect concentrations (PNECs) were derived from the HC5s. The acute PNECs of the selected PPCPs were in a range from 1.1 to 4993μg/L. While the chronic PNECs were one or two orders of magnitude lower than the acute PNECs, with a range from 0.02 to 298μg/L. Among these PPCPs, the compound with the highest acute effect on the aquatic environment was clarithromycin while erythromycin was the one with the highest chronic toxicity effect. Among the studied PPCPs, erythromycin caused a relatively higher aquatic ecological risk in China. This study helps derive WQCs of PPCPs in the aquatic environment, which is essential for environmental managment of these emerging contaminants.

Bootstrap adjustments of signed scoring rule root statistics

ABSTRACTScoring rules give rise to methods for statistical inference and are useful tools to achieve robustness or reduce computations. Scoring rule inference is generally performed through first-order approximations to the distribution of the scoring rule estimator or of the ratio-type statistic. In order to improve the accuracy of first-order methods even in simple models, we propose bootstrap adjustments of signed scoring rule root statistics for a scalar parameter of interest in presence of nuisance parameters. The method relies on the parametric bootstrap approach that avoids onerous calculations specific of analytical adjustments. Numerical examples illustrate the accuracy of the proposed method.

Parametric bootstrap inferences for unbalanced panel data models

ABSTRACTThis article presents parametric bootstrap (PB) approaches for hypothesis testing and interval estimation for the regression coefficients of panel data regression models with incomplete panels. Some simulation results are presented to compare the performance of the PB approaches with the approximate inferences. Our studies show that the PB approaches perform satisfactorily for various sample sizes and parameter configurations, and the performance of PB approaches is mostly better than the approximate methods with respect to the coverage probabilities and the Type I error rates. The PB inferences have almost exact coverage probabilities and Type I error rates. Furthermore, the PB procedure can be simply carried out by a few simulation steps, and the derivation is easier to understand and to be extended to the multi-way error component regression models with unbalanced panels. Finally, the proposed approaches are illustrated by using a real data example.

Simultaneous confidence intervals for comparing several inverse Gaussian means under heteroscedasticity

ABSTRACTRecently, Zhang [Simultaneous confidence intervals for several inverse Gaussian populations. Stat Probab Lett. 2014;92:125–131] proposed simultaneous pairwise confidence intervals (SPCIs) based on the fiducial generalized pivotal quantity concept to make inferences about the inverse Gaussian means under heteroscedasticity. In this paper, we propose three new methods for constructing SPCIs to make inferences on the means of several inverse Gaussian distributions when scale parameters and sample sizes are unequal. One of the methods results in a set of classic SPCIs (in the sense that it is not simulation-based inference) and the two others are based on a parametric bootstrap approach. The advantages of our proposed methods over Zhang’s (2014) method are: (i) the simulation results show that the coverage probability of the proposed parametric bootstrap approaches is fairly close to the nominal confidence coefficient while the coverage probability of Zhang’s method is smaller than the nominal confidence coefficient when the number of groups and the variance of groups are large and (ii) the proposed set of classic SPCIs is conservative in contrast to Zhang’s method.

Density Forecasts With Midas Models

In this paper we derive a general parametric bootstrapping approach to compute density forecasts for various types of mixed-data sampling (MIDAS) regressions. We consider both classical and unrestricted MIDAS regressions with and without an autoregressive component. First, we compare the forecasting performance of the dierent MIDAS models in Monte Carlo simulation experiments. We nd that the results in terms of point and density forecasts are coherent. Moreover, the results do not clearly indicate a superior performance of one of the models under scrutiny when the persistence of the low frequency variable is low. Some dierences are instead more evident when the persistence is high, for which the ARMIDAS and the AR-U-MIDAS produce better forecasts. Second, in an empirical exercise we evaluate density forecasts for quarterly US output growth, exploiting information from typical monthly series. We nd that MIDAS models provide accurate and timely density forecasts.

Probabilistic inversion of airborne electromagnetic data for basement conductors

Probabilistic inversion of airborne electromagnetic data is often approximated by a layered earth using a computationally efficient 1D kernel. If the underlying framework accounts for prior beliefs on spatial correlation, the inversion will be able to recover spatially coherent interfaces and associated uncertainties. Greenfield exploration using airborne electromagnetic data, however, often seeks to identify discrete economical targets. In mature exploration provinces, such bodies are frequently obscured by thick, conductive regolith, and the response of such economic basement conductors presents a challenge to any layered earth inversion. A well-known computationally efficient way to approximate the response of a basement conductor is to use a thin plate. Here we have extended a Bayesian parametric bootstrap approach, so that the basement of a spatially varying layered earth can contain a thin plate. The resulting Bayesian framework allowed for the inversion of basement conductors and associated uncertainties, but more importantly, the use of model selection concepts to determine if the data supports a basement conductor model or not. Recovered maps of basement conductor probabilities show the expected patterns in uncertainty; for example, a decrease in target probability with increasing depth. Such maps of target probabilities generated using the thin plate approximation are a potentially valuable source of information for the planning of exploration activity, such as the targeting of drillholes to confirm the existence of a discrete conductor in a greenfield exploration scenario. We have used a field data set from northwest Queensland, Australia, to illustrate how the approach allowed inversion for a basement conductor and related uncertainties in a spatially variable layered earth, using the information from multiple survey lines and prior beliefs of geology.

Parametric bootstrap inferences for panel data models

ABSTRACTThis article presents parametric bootstrap (PB) approaches for hypothesis testing and interval estimation for the regression coefficients and the variance components of panel data regression models with complete panels. The PB pivot variables are proposed based on sufficient statistics of the parameters. On the other hand, we also derive generalized inferences and improved generalized inferences for variance components in this article. Some simulation results are presented to compare the performance of the PB approaches with the generalized inferences. Our studies show that the PB approaches perform satisfactorily for various sample sizes and parameter configurations, and the performance of PB approaches is mostly the same as that of generalized inferences with respect to the expected lengths and powers. The PB inferences have almost exact coverage probabilities and Type I error rates. Furthermore, the PB procedure can be simply carried out by a few simulation steps, and the derivation is easier to understand and to be extended to the incomplete panels. Finally, the proposed approaches are illustrated by using a real data example.

Parametric bootstrap inferences for the growth curve models with intraclass correlation structure

ABSTRACTThis paper presents parametric bootstrap (PB) approaches for hypothesis testing and interval estimation of the fixed effects and the variance component in the growth curve models with intraclass correlation structure. The PB pivot variables are proposed based on the sufficient statistics of the parameters. Some simulation results are presented to compare the performance of the proposed approaches with the generalized inferences. Our studies show that the PB approaches perform satisfactorily for various cell sizes and parameter configurations, and tends to outperform the generalized inferences with respect to the coverage probabilities and powers. The PB approaches not only have almost exact coverage probabilities and Type I error rates, but also have the shorter expected lengths and the higher powers. Furthermore, the PB procedure can be simply carried out by a few simulation steps. Finally, the proposed approaches are illustrated by using a real data example.

Hypothesis Testing for Mixture Model Selection

ABSTRACTGaussian mixture models with eigen-decomposed covariance structures, i.e. the Gaussian parsimonious clustering models (GPCM), make up the most popular family of mixture models for clustering and classification. Although the GPCM family has been used for almost 20 years, selecting the best member of the family in a given situation remains a troublesome problem. Likelihood ratio (LR) tests are developed to tackle this problem; given a number of mixture components, these LR tests compare each member of the family to the heteroscedastic model under the alternative hypothesis. Along the way, a novel maximum likelihood estimation procedure is developed for two members of the GPCM family. Simulations show that the reference distribution provides a reasonable approximation for the LR statistics when the sample size is not too small and when the mixture components are separate enough; accordingly, in the remaining configurations, a parametric bootstrap approach is also discussed and evaluated. Furthermore, a closed testing procedure, having the defined LR tests as local tests, is considered to assess, in a straightforward way, a unique model in the general family. In contrast with the information criteria that are often employed in the literature as ‘black boxes’, it is only based on one subjective element, the significance level, whose meaning is clear to everyone. Simulation results are presented to investigate the performance of the procedure in situations with gradual departure from the homoscedastic model and its robustness with respect to elliptical departures from normality in each mixture component. Finally, the advantages of the procedure are illustrated via applications to some well-known data sets.

Dynamic Bayesian Network Modeling of the Interplay between EGFR and Hedgehog Signaling.

Aberrant activation of sonic Hegdehog (SHH) signaling has been found to disrupt cellular differentiation in many human cancers and to increase proliferation. The SHH pathway is known to cross-talk with EGFR dependent signaling. Recent studies experimentally addressed this interplay in Daoy cells, which are presumable a model system for medulloblastoma, a highly malignant brain tumor that predominately occurs in children. Currently ongoing are several clinical trials for different solid cancers, which are designed to validate the clinical benefits of targeting the SHH in combination with other pathways. This has motivated us to investigate interactions between EGFR and SHH dependent signaling in greater depth. To our knowledge, there is no mathematical model describing the interplay between EGFR and SHH dependent signaling in medulloblastoma so far. Here we come up with a fully probabilistic approach using Dynamic Bayesian Networks (DBNs). To build our model, we made use of literature based knowledge describing SHH and EGFR signaling and integrated gene expression (Illumina) and cellular location dependent time series protein expression data (Reverse Phase Protein Arrays). We validated our model by sub-sampling training data and making Bayesian predictions on the left out test data. Our predictions focusing on key transcription factors and p70S6K, showed a high level of concordance with experimental data. Furthermore, the stability of our model was tested by a parametric bootstrap approach. Stable network features were in agreement with published data. Altogether we believe that our model improved our understanding of the interplay between two highly oncogenic signaling pathways in Daoy cells. This may open new perspectives for the future therapy of Hedghog/EGF-dependent solid tumors.

Pairwise likelihood inference for multivariate ordinal responses with applications to customer satisfaction

A common practice in customer satisfaction analysis is to administer surveys where subjects are asked to express opinions on a number of statements, or satisfaction scales, by use of ordered categorical responses. Motivated by this application, we propose a pseudo‐likelihood approach to estimate the dependence structure among multivariate categorical variables. As it is commonly carried out in this area, we assume that the responses are related to latent continuous variables that are truncated to induce categorical responses. A Gaussian likelihood is assumed for the latent variables leading to the so‐called ordered probit model. Because the calculation of the exact likelihood is computationally demanding, we adopt an approximate solution based on pairwise likelihood. To asses the performance of the approach, simulation studies are conducted comparing the proposed method with standard likelihood methods. A parametric bootstrap approach to evaluate the variance of the maximum pairwise likelihood estimator is proposed and discussed. An application to customer satisfaction survey is performed showing the effectiveness of the approach in the presence of covariates and under other generalizations of the model. Copyright © 2015 John Wiley & Sons, Ltd.

Parametric bootstrap goodness-of-fit testing for Wehrly–Johnson bivariate circular distributions

The Wehrly---Johnson family of bivariate circular distributions is by far the most general one currently available for modelling data on the torus. It allows complete freedom in the specification of the marginal circular densities as well as the binding circular density which regulates any dependence that might exist between them. We propose a parametric bootstrap approach for testing the goodness-of-fit of Wehrly---Johnson distributions when the forms of their marginal and binding densities are assumed known. The approach admits the use of any test for toroidal uniformity, and we consider versions of it incorporating three such tests. Simulation is used to illustrate the operating characteristics of the approach when the underlying distribution is assumed to be bivariate wrapped Cauchy. An analysis of wind direction data recorded at a Texan weather station illustrates the use of the proposed goodness-of-fit testing procedure.

Using the Bootstrap to Account for Linkage Errors when Analysing Probabilistically Linked Categorical Data

Abstract Record linkage is the act of bringing together records that are believed to belong to the same unit (e.g., person or business) from two or more files. Record linkage is not an error-free process and can lead to linking a pair of records that do not belong to the same unit. This occurs because linking fields on the files, which ideally would uniquely identify each unit, are often imperfect. There has been an explosion of record linkage applications, particularly involving government agencies and in the field of health, yet there has been little work on making correct inference using such linked files. Naively treating a linked file as if it were linked without errors can lead to biased inferences. This article develops a method of making inferences for cross tabulated variables when record linkage is not an error-free process. In particular, it develops a parametric bootstrap approach to estimation which can accommodate the sophisticated probabilistic record linkage techniques that are widely used in practice (e.g., 1-1 linkage). The article demonstrates the effectiveness of this method in a simulation and in a real application.

Identification and quantification of heteroscedasticity in stock–recruitment relationships

Nonconstant variance (heteroscedasticity) in the stock–recruitment (S-R) relationship is proposed as an important factor in sustainable fisheries management, but its reliable estimation from noisy populations is problematic. We developed methods for both frequentist and Bayesian approaches to test whether we can accurately estimate the degree of heteroscedasticity in 90 published S-R populations. We estimated the confidence interval for the heteroscedastic regression model via a parametric bootstrap approach and the credible interval for the Bayesian method via a Markov chain Monte Carlo sampling algorithm. We found strong evidence of negative heteroscedasticity in several stocks, regardless of the statistical paradigm, the details of density dependence, and the methods used to generate the original populations. This statistical framework, together with its associated freely available software, provides an efficient and reliable setting for assessing heteroscedasticity of the S-R relationship in fisheries.

Testing the equality means of several log-normal distributions

ABSTRACTResearches propose various methods for comparing the means of two log-normal distributions. Some of these methods have been recently extended to test the equality means of several log-normal populations. Investigations show that none of the established methods is satisfactory. In this article, we provide three methods based on the computational approach test, which is a parametric bootstrap approach, for testing the means of several log-normal distributions. Further, we compare our methods with the existing methods through Monte Carlo simulation. The numerical results show that the Type I errors of these procedures are satisfactory regardless of the sample size, number of populations, and the true parameters. Finally, we explain the considered methods by real examples.

Density Forecasts with MIDAS Models

In this paper we propose a parametric block wild bootstrap approach to compute density forecasts for various types of mixed-data sampling (MIDAS) regressions. First, Monte Carlo simulations show that predictive densities for the various MIDAS models derived from the block wild bootstrap approach are more accurate, in terms of coverage rates, than predictive densities derived from either a residual-based bootstrap approach or by drawing errors from a normal distribution. This result holds irrespective of the data generating errors being normally independently distributed, serially correlated, heteroskedastic or a mixture of normal distributions. Second, in an empirical exercise we evaluate density forecasts for quarterly U.S. real output growth, exploiting information from typical monthly and weekly series. We show that the block wild bootstrapping approach, applied to the various MIDAS regressions, produces predictive densities for U.S. real output growth that are well-calibrated. Moreover, the relative accuracy, measured in terms of the logarithmic score or the continuous ranked probability score, improves for the various MIDAS specifications as more information becomes available.

Probabilistic inversion of airborne electromagnetic data under spatial constraints

Probabilistic 1D inversions of airborne electromagnetic (AEM) surveys allow an exhaustive search of model space for each station, but they often assume that there is no spatial correlation between neighboring stations. This can result in abrupt transverse model discontinuities when attempting to construct a 3D model. In contrast to this, fully spatially regularized deterministic inversions can take spatial correlation between 1D models into account, but they do not explore the model space sufficiently to be able to evaluate model robustness. The Bayesian parametric bootstrap (BPB) approach that we developed is a practical compromise between computationally expensive exhaustive search techniques and computationally efficient deterministic inversions. Using a 1D kernel, we inverted for the interfaces, layer properties, and related uncertainties, taking lateral spatial correlations and additional prior information into account. Numerical examples revealed that a BPB technique was likely to explore the model space sufficiently for nonpathological situations. Using a subset of a large AEM survey collected in northwest Australia for aquifer mapping, we show how the BPB approach can be used to produce a spatially coherent map of the base of the Broome sandstone aquifer. The recovered uncertainties, which are likely to be one of the main sources of uncertainty in any groundwater model, exhibited the well-known increase in uncertainty of a depth to interface with increasing depth to the interface.