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As the parameters of a map are varied an attractor may vary continuously in the Hausdorff metric. The purpose of this paper is to explore the continuation of chaotic attractors. We argue that this is not a helpful concept for smooth unimodal maps for which periodic windows fill parameter space densely, but that for many families of piecewise-smooth maps it provides a way to think about changing structures within parameter regions of robust chaos and form a stronger notion of robustness. We obtain conditions for the continuity of an attractor and demonstrate the results with coupled skew tent maps, the Lozi map and the border-collision normal form. [ABSTRACT FROM AUTHOR]

Increasing data volumes delivered by a new generation of radio interferometers require computationally efficient and robust calibration algorithms. In this paper, we propose distributed calibration as a way of improving both computational cost as well as robustness in calibration. We exploit the data parallelism across frequency that is inherent in radio astronomical observations that are recorded as multiple channels at different frequencies. Moreover, we also exploit the smoothness of the variation of calibration parameters across frequency. Data parallelism enables us to distribute the computing load across a network of compute agents. Smoothness in frequency enables us to reformulate calibration as a consensus optimization problem. With this formulation, we enable flow of information between compute agents calibrating data at different frequencies, without actually passing the data, and thereby improving robustness. We present simulation results to show the feasibility as well as the advantages of distributed calibration as opposed to conventional calibration. [ABSTRACT FROM AUTHOR]

We propose a new robust hypothesis test for (possibly non-linear) constraints on M-estimators with possibly non-differentiable estimating functions. The proposed test employs a random normalizing matrix computed from recursive M-estimators to eliminate the nuisance parameters arising from the asymptotic covariance matrix. It does not require consistent estimation of any nuisance parameters, in contrast with the conventional heteroscedasticity-autocorrelation consistent (HAC)-type test and the Kiefer-Vogelsang-Bunzel (KVB)-type test. Our test reduces to the KVB-type test in simple location models with ordinary least-squares estimation, so the error in the rejection probability of our test in a Gaussian location model is [ABSTRACT FROM AUTHOR]

Motivated by aging research, we propose an estimator of the effect of a time-varying exposure on an outcome in longitudinal studies with dropout and truncation by death. We use an inverse-probability weighted (IPW) estimator to derive a doubly robust augmented inverse-probability weighted (AIPW) estimator. IPW estimation involves weights for the exposure mechanism, dropout, and mortality; AIPW estimation additionally involves estimating data-generating models via regression. We demonstrate that the estimators identify a causal contrast that is a function of principal strata effects under a set of assumptions. Simulations show that AIPW estimation is unbiased when weights or outcome regressions are correct, and that AIPW estimation is more efficient than IPW estimation when all models are correct. We apply the method to a study of vitamin D and gait speed among older adults. [ABSTRACT FROM PUBLISHER]

Empirical Bayes methods have been extensively used for microarray data analysis by modeling the large number of unknown parameters as random effects. Empirical Bayes allows borrowing information across genes and can automatically adjust for multiple testing and selection bias. However, the standard empirical Bayes model can perform poorly if the assumed working prior deviates from the true prior. This paper proposes a new rank-conditioned inference in which the shrinkage and confidence intervals are based on the distribution of the error conditioned on rank of the data. Our approach is in contrast to a Bayesian posterior, which conditions on the data themselves. The new method is almost as efficient as standard Bayesian methods when the working prior is close to the true prior, and it is much more robust when the working prior is not close. In addition, it allows a more accurate (but also more complex) non-parametric estimate of the prior to be easily incorporated, resulting in improved inference. The new method’s prior robustness is demonstrated via simulation experiments. Application to a breast cancer gene expression microarray dataset is presented. Our R package rank.Shrinkage provides a ready-to-use implementation of the proposed methodology. [ABSTRACT FROM PUBLISHER]

Recently proposed outlier robust small area estimators can be substantially biased when outliers are drawn from a distribution that has a different mean from that of the rest of the survey data. This naturally leads one to consider an outlier robust bias correction for these estimators. We develop this idea, proposing two different analytical mean-squared error estimators for the ensuing bias-corrected outlier robust estimators. Simulations based on realistic outlier-contaminated data show that the bias correction proposed often leads to more efficient estimators. Furthermore, the mean-squared error estimation methods proposed appear to perform well with a variety of outlier robust small area estimators. [ABSTRACT FROM AUTHOR]

A rate model is proposed for a modulated renewal process comprising a single long sequence, where the covariate process may not capture the dependencies in the sequence as in standard intensity models. We consider partial likelihood-based inferences under a semiparametric multiplicative rate model, which has been widely studied in the context of independent and identical data. Under an intensity model, gap times in a single long sequence may be used naively in the partial likelihood, with variance estimation utilizing the observed information matrix. Under a rate model, the gap times cannot be treated as independent and studying the partial likelihood is much more challenging. We employ a mixing condition in the application of limit theory for stationary sequences to obtain consistency and asymptotic normality. The estimator’s variance is quite complicated, owing to the unknown gap times dependence structure. We adapt block bootstrapping and cluster variance estimators to the partial likelihood. Simulation studies and an analysis of a semiparametric extension of a popular model for neural spike train data demonstrate the practical utility of the rate approach in comparison with the intensity approach. [ABSTRACT FROM AUTHOR]

A dynamic treatment regime is a list of sequential decision rules for assigning treatment based on a patient’s history. Q- and A-learning are two main approaches for estimating the optimal regime, i.e., that yielding the most beneficial outcome in the patient population, using data from a clinical trial or observational study. Q-learning requires postulated regression models for the outcome, while A-learning involves models for that part of the outcome regression representing treatment contrasts and for treatment assignment. We propose an alternative to Q- and A-learning that maximizes a doubly robust augmented inverse probability weighted estimator for population mean outcome over a restricted class of regimes. Simulations demonstrate the method’s performance and robustness to model misspecification, which is a key concern. [ABSTRACT FROM AUTHOR]

Assumptions of normality in most animal breeding applications may make inferences vulnerable to the presence of outliers. Heavy-tail densities are viable alternatives to normal distributions and provide robustness against unusual or outlying observations when used to model the densities of residual effects. Our objective is to compare estimates of genetic parameters by fitting multivariate normal (MN) or heavy-tail distributions [multivariate Student's / (MS/) and multivariate slash (MS)] for residuals in data of body birth weight (BBW), weaning (WW), and yearling (YW) weight traits in beef cattle. A total of 17,019 weight records for BBW, WW, and YW from 1998 through 2010 from a large commercial cow/calf operation in the sand hills of Nebraska were analyzed. Models included fixed effects of contemporary group and sire breed whereas animal and maternal effects were random and the degrees of freedom (v) was treated as unknown for MS/ and MS. Model comparisons using deviance information criteria (DIC) favored MS/ over MS and MN models, respectively. The posterior means [and 95% posterior probability intervals (PPI)] of v for the MS/ and MS models were 5.28 (4.80, 5.85) and 1.88 (1.76, 2.00), respectively. Smaller values of posterior densities of v for MS/ and MS models confirm that the assumption of normally distributed residuals is not adequate for the analysis of BBW, WW, and YW datasets. Posterior mean (PM) and posterior median (PD) estimates of direct and maternal genetic variances were the same and posterior densities of these parameters were found to be symmetric. The 95% PPI estimates from MN and MS/ models for BBW did not overlap, which indicates significant difference between PM estimates from MN or MS/ models. The observed antagonistic relationship between additive direct and additive maternal effects indicated that genetic evaluation and selection strategies will be sensitive to the assumed model for residuals. [ABSTRACT FROM AUTHOR]

. Motivated by a practical application, the paper investigates robust estimation of economic indicators from survey samples based on a semiparametric Pareto tail model. Economic performance is typically measured by a set of indicators, which are often estimated from survey data-the motivating example being the European indicators on social exclusion and poverty computed from the well-known European Union statistics on income and living conditions survey. Since economic data typically contain variables with heavily tailed distributions and additional extreme outliers, the idea is to use robust Pareto tail modelling to detect the extreme outliers and to reduce their influence on the indicators. In the survey context, however, sample weights need to be considered when modelling the tail with a Pareto distribution such that the true distribution on the population level is accurately reflected. Therefore, the main methodological contribution is to adapt commonly used robust estimators for the parameters of the Pareto distribution to take sample weights into account. The resulting approach for robust estimation of indicators is then evaluated by means of a simulation study and applied in the context of estimating the Gini coefficient from the survey data. [ABSTRACT FROM AUTHOR]

. Subsampling and block-based bootstrap methods have been used in a wide range of inference problems for time series. To accommodate the dependence, these resampling methods involve a bandwidth parameter, such as the subsampling window width and block size in the block-based bootstrap. In empirical work, using different bandwidth parameters could lead to different inference results, but traditional first-order asymptotic theory does not capture the choice of the bandwidth. We propose to adopt the fixed b approach, as advocated by Kiefer and Vogelsang in the heteroscedasticity-auto-correlation robust testing context, to account for the influence of the bandwidth on inference. Under the fixed b asymptotic framework, we derive the asymptotic null distribution of the p-values for subsampling and the moving block bootstrap, and further propose a calibration of the traditional small- b-based confidence intervals (regions or bands) and tests. Our treatment is fairly general as it includes both finite dimensional parameters and infinite dimensional parameters, such as the marginal distribution function. Simulation results show that the fixed b approach is more accurate than the traditional small b approach in terms of approximating the finite sample distribution, and that the calibrated confidence sets tend to have smaller coverage errors than the uncalibrated counterparts. [ABSTRACT FROM AUTHOR]

Motivation: Metabolic engineering algorithms provide means to optimize a biological process leading to the improvement of a biotechnological interesting molecule. Therefore, it is important to understand how to act in a metabolic pathway in order to have the best results in terms of productions. In this work, we present a computational framework that searches for optimal and robust microbial strains that are able to produce target molecules. Our framework performs three tasks: it evaluates the parameter sensitivity of the microbial model, searches for the optimal genetic or fluxes design and finally calculates the robustness of the microbial strains. We are capable to combine the exploration of species, reactions, pathways and knockout parameter spaces with the Pareto-optimality principle.Results: Our framework provides also theoretical and practical guidelines for design automation. The statistical cross comparison of our new optimization procedures, performed with respect to currently widely used algorithms for bacteria (e.g. Escherichia coli) over different multiple functions, reveals good performances over a variety of biotechnological products.Availability: http://www.dmi.unict.it/nicosia/pathDesign.html.Contact: nicosia@dmi.unict.it or pl219@cam.ac.ukSupplementary information: Supplementary data are available at Bioinformatics online. [ABSTRACT FROM PUBLISHER]

Motivation: Biochemical reaction networks in the form of coupled ordinary differential equations (ODEs) provide a powerful modeling tool for understanding the dynamics of biochemical processes. During the early phase of modeling, scientists have to deal with a large pool of competing nonlinear models. At this point, discrimination experiments can be designed and conducted to obtain optimal data for selecting the most plausible model. Since biological ODE models have widely distributed parameters due to, e.g. biologic variability or experimental variations, model responses become distributed. Therefore, a robust optimal experimental design (OED) for model discrimination can be used to discriminate models based on their response probability distribution functions (PDFs).Results: In this work, we present an optimal control-based methodology for designing optimal stimulus experiments aimed at robust model discrimination. For estimating the time-varying model response PDF, which results from the nonlinear propagation of the parameter PDF under the ODE dynamics, we suggest using the sigma-point approach. Using the model overlap (expected likelihood) as a robust discrimination criterion to measure dissimilarities between expected model response PDFs, we benchmark the proposed nonlinear design approach against linearization with respect to prediction accuracy and design quality for two nonlinear biological reaction networks. As shown, the sigma-point outperforms the linearization approach in the case of widely distributed parameter sets and/or existing multiple steady states. Since the sigma-point approach scales linearly with the number of model parameter, it can be applied to large systems for robust experimental planning.Availability: An implementation of the method in MATLAB/AMPL is available at http://www.uni-magdeburg.de/ivt/svt/person/rf/roed.html.Contact: flassig@mpi-magdeburg.mpg.deSupplementary information: Supplementary data are are available at Bioinformatics online. [ABSTRACT FROM PUBLISHER]

Summary Pilot phases of a randomized clinical trial often suggest that a parametric model may be an accurate description of the trial's longitudinal trajectories. However, parametric models are often not used for fear that they may invalidate tests of null hypotheses of equality between the experimental groups. Existing work has shown that when, for some types of data, certain parametric models are used, the validity for testing the null is preserved even if the parametric models are incorrect. Here, we provide a broader and easier to check characterization of parametric models that can be used to (i) preserve nonparametric validity of testing the null hypothesis, i.e., even when the models are incorrect, and (ii) increase power compared to the non- or semiparametric bounds when the models are close to correct. We demonstrate our results in a clinical trial of depression in Alzheimer's patients. [ABSTRACT FROM AUTHOR]

Summary Generalized linear models are a widely used method to obtain parametric estimates for the mean function. They have been further extended to allow the relationship between the mean function and the covariates to be more flexible via generalized additive models. However, the fixed variance structure can in many cases be too restrictive. The extended quasilikelihood (EQL) framework allows for estimation of both the mean and the dispersion/variance as functions of covariates. As for other maximum likelihood methods though, EQL estimates are not resistant to outliers: we need methods to obtain robust estimates for both the mean and the dispersion function. In this article, we obtain functional estimates for the mean and the dispersion that are both robust and smooth. The performance of the proposed method is illustrated via a simulation study and some real data examples. [ABSTRACT FROM AUTHOR]

Motivation: Monoclonal antibodies (mAbs) are among the most powerful and important tools in biology and medicine. MAb development is of great significance to many research and clinical applications. Therefore, objective mAb classification is essential for categorizing and comparing mAb panels based on their reactivity patterns in different cellular species. However, typical flow cytometric mAb profiles present unique modeling challenges with their non-Gaussian features and intersample variations. It makes accurate mAb classification difficult to do with the currently used kernel-based or hierarchical clustering techniques.Results: To address these challenges, in the present study we developed a formal two-step framework called mAbprofiler for systematic, parametric characterization of mAb profiles. Further, we measured the reactivity of hundreds of new antibodies in diverse tissues using flow cytometry, which we successfully classified using mAbprofiler.First, mAbprofiler fits a mAb's flow cytometric histogram with a finite mixture model of skew t distributions that is robust against non-Gaussian features, and constructs a precise, smooth and mathematically rigorous profile. Then it performs novel curve clustering of the fitted mAb profiles using a skew t mixture of non-linear regression model that can handle intersample variation. Thus, mAbprofiler provides a new framework for identifying robust mAb classes, all well defined by distinct parametric templates, which can be used for classifying new mAb samples. We validated our classification results both computationally and empirically using mAb profiles of known classification.Availability and Implementation: A demonstration code in R is available at the journal website. The R code implementing the full framework is available from the author website – http://amath.nchu.edu.tw/www/teacher/tilin/softwareContact: saumyadipta_pyne@dfci.harvard.eduSupplementary Information: Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

There are copula-based statistical models in the literature for regression with dependent data such as clustered and longitudinal overdispersed counts, for which parameter estimation and inference are straightforward. For situations where the main interest is in the regression and other univariate parameters and not the dependence, we propose a “weighted scores method”, which is based on weighting score functions of the univariate margins. The weight matrices are obtained initially fitting a discretized multivariate normal distribution, which admits a wide range of dependence. The general methodology is applied to negative binomial regression models. Asymptotic and small-sample efficiency calculations show that our method is robust and nearly as efficient as maximum likelihood for fully specified copula models. An illustrative example is given to show the use of our weighted scores method to analyze utilization of health care based on family characteristics. [ABSTRACT FROM PUBLISHER]

BSTRACT [ABSTRACT FROM AUTHOR]

In many practical problems, a hypothesis testing involves a nuisance parameter which appears only under the alternative hypothesis.(1977,Biometrika64,247–254) proposed the maximum of the score statistics over the whole range of the nuisance parameter as a test statistic for this type of hypothesis testing.(1999,Biometrics55,883–886) studied two other simpler maximum test statistics, the maximum of the score statistics at two extreme points of the nuisance parameter, and the maximum of the score statistics at three points of the nuisance parameter including the two extreme points. In this article, we compare the powers of these three maximum-type statistics in the context of three genetic problems. [ABSTRACT FROM AUTHOR]

Summary: Here we present INRICH (INterval enRICHment analysis), a pathway-based genome-wide association analysis tool that tests for enriched association signals of predefined gene-sets across independent genomic intervals. INRICH has wide applicability, fast running time and, most importantly, robustness to potential genomic biases and confounding factors. Such factors, including varying gene size and single-nucleotide polymorphism density, linkage disequilibrium within and between genes and overlapping genes with similar annotations, are often not accounted for by existing gene-set enrichment methods. By using a genomic permutation procedure, we generate experiment-wide empirical significance values, corrected for the total number of sets tested, implicitly taking overlap of sets into account. By simulation we confirm a properly controlled type I error rate and reasonable power of INRICH under diverse parameter settings. As a proof of principle, we describe the application of INRICH on the NHGRI GWAS catalog.Availability: A standalone C++ program, user manual and datasets can be freely downloaded from: http://atgu.mgh.harvard.edu/inrich/.Contact: shaun@atgu.mgh.harvard.eduSupplementary information: Supplementary data are available at Bioinformatics online. [ABSTRACT FROM PUBLISHER]

. We study the heteroscedastic partially linear single-index model with an unspecified error variance function, which allows for high dimensional covariates in both the linear and the single-index components of the mean function. We propose a class of consistent estimators of the parameters by using a proper weighting strategy. An interesting finding is that the linearity condition which is widely assumed in the dimension reduction literature is not necessary for methodological or theoretical development: it contributes only to the simplification of non-optimal consistent estimation. We also find that the performance of the usual weighted least square type of estimators deteriorates when the non-parametric component is badly estimated. However, estimators in our family automatically provide protection against such deterioration, in that the consistency can be achieved even if the baseline non-parametric function is completely misspecified. We further show that the most efficient estimator is a member of this family and can be easily obtained by using non-parametric estimation. Properties of the estimators proposed are presented through theoretical illustration and numerical simulations. An example on gender discrimination is used to demonstrate and to compare the practical performance of the estimators. [ABSTRACT FROM AUTHOR]