Publication Bias in Meta-Analysis: Confidence Intervals for Rosenthal's Fail-Safe Number

The purpose of the present paper is to assess the efficacy of confidence intervals for Rosenthal's fail-safe number. Although Rosenthal's estimator is highly used by researchers, its statistical properties are largely unexplored. First of all, we developed statistical theory which allowed us to produce confidence intervals for Rosenthal's fail-safe number.This was produced by discerning whether the number of studies analysed in a meta-analysis is fixed or random. Each case produces different variance estimators. For a given number of studies and a given distribution, we provided five variance estimators. Confidence intervals are examined with a normal approximation and a nonparametric bootstrap. The accuracy of the different confidence interval estimates was then tested by methods of simulation under different distributional assumptions. The half normal distribution variance estimator has the best probability coverage. Finally, we provide a table of lower confidence intervals for Rosenthal's estimator.Comment: Published in the International Scholarly Research Notices in December 201

Contour regression: A general approach to dimension reduction

We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of small variation in the response. These directions span the orthogonal complement of the minimal space relevant for the regression and can be extracted according to two measures of variation in the response, leading to simple and general contour regression (SCR and GCR) methodology. In comparison with existing sufficient dimension reduction techniques, this contour-based methodology guarantees exhaustive estimation of the central subspace under ellipticity of the predictor distribution and mild additional assumptions, while maintaining \sqrtn-consistency and computational ease. Moreover, it proves robust to departures from ellipticity. We establish population properties for both SCR and GCR, and asymptotic properties for SCR. Simulations to compare performance with that of standard techniques such as ordinary least squares, sliced inverse regression, principal Hessian directions and sliced average variance estimation confirm the advantages anticipated by the theoretical analyses. We demonstrate the use of contour-based methods on a data set concerning soil evaporation.Comment: Published at http://dx.doi.org/10.1214/009053605000000192 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Inference for the neighborhood inequality index

The neighborhood inequality (NI) index measures aspects of spatial inequality in the distribution of incomes within a city. The NI index is a population average of the normalized income gap between each individual's income (observed at a given location in the city) and the incomes of the neighbors located within a certain distance range. The approach overcomes the Modiable Areal Units Problem affecting local inequality measures. This paper provides minimum bounds for the NI index standard error and shows that unbiased estimators can be identied under fairly common hypothesis in spatial statistics. Results from a Monte Carlo study support the relevance of the approximations. Rich income data are then used to infer about trends of neighborhood inequality in Chicago, IL over the last 35 years

Bayesian inference for group-level cortical surface image-on-scalar-regression with Gaussian process priors

In regression-based analyses of group-level neuroimage data researchers typically fit a series of marginal general linear models to image outcomes at each spatially-referenced pixel. Spatial regularization of effects of interest is usually induced indirectly by applying spatial smoothing to the data during preprocessing. While this procedure often works well, resulting inference can be poorly calibrated. Spatial modeling of effects of interest leads to more powerful analyses, however the number of locations in a typical neuroimage can preclude standard computation with explicitly spatial models. Here we contribute a Bayesian spatial regression model for group-level neuroimaging analyses. We induce regularization of spatially varying regression coefficient functions through Gaussian process priors. When combined with a simple nonstationary model for the error process, our prior hierarchy can lead to more data-adaptive smoothing than standard methods. We achieve computational tractability through Vecchia approximation of our prior which, critically, can be constructed for a wide class of spatial correlation functions and results in prior models that retain full spatial rank. We outline several ways to work with our model in practice and compare performance against standard vertex-wise analyses. Finally we illustrate our method in an analysis of cortical surface fMRI task contrast data from a large cohort of children enrolled in the Adolescent Brain Cognitive Development study

Approaches for Outlier Detection in Sparse High-Dimensional Regression Models

Modern regression studies often encompass a very large number of potential predictors, possibly larger than the sample size, and sometimes growing with the sample size itself. This increases the chances that a substantial portion of the predictors is redundant, as well as the risk of data contamination. Tackling these problems is of utmost importance to facilitate scientific discoveries, since model estimates are highly sensitive both to the choice of predictors and to the presence of outliers. In this thesis, we contribute to this area considering the problem of robust model selection in a variety of settings, where outliers may arise both in the response and the predictors. Our proposals simplify model interpretation, guarantee predictive performance, and allow us to study and control the influence of outlying cases on the fit. First, we consider the co-occurrence of multiple mean-shift and variance-inflation outliers in low-dimensional linear models. We rely on robust estimation techniques to identify outliers of each type, exclude mean-shift outliers, and use restricted maximum likelihood estimation to down-weight and accommodate variance-inflation outliers into the model fit. Second, we extend our setting to high-dimensional linear models. We show that mean-shift and variance-inflation outliers can be modeled as additional fixed and random components, respectively, and evaluated independently. Specifically, we perform feature selection and mean-shift outlier detection through a robust class of nonconcave penalization methods, and variance-inflation outlier detection through the penalization of the restricted posterior mode. The resulting approach satisfies a robust oracle property for feature selection in the presence of data contamination – which allows the number of features to exponentially increase with the sample size – and detects truly outlying cases of each type with asymptotic probability one. This provides an optimal trade-off between a high breakdown point and efficiency. Third, focusing on high-dimensional linear models affected by meanshift outliers, we develop a general framework in which L0-constraints coupled with mixed-integer programming techniques are used to perform simultaneous feature selection and outlier detection with provably optimal guarantees. In particular, we provide necessary and sufficient conditions for a robustly strong oracle property, where again the number of features can increase exponentially with the sample size, and prove optimality for parameter estimation and the resulting breakdown point. Finally, we consider generalized linear models and rely on logistic slippage to perform outlier detection and removal in binary classification. Here we use L0-constraints and mixed-integer conic programming techniques to solve the underlying double combinatorial problem of feature selection and outlier detection, and the framework allows us again to pursue optimality guarantees. For all the proposed approaches, we also provide computationally lean heuristic algorithms, tuning procedures, and diagnostic tools which help to guide the analysis. We consider several real-world applications, including the study of the relationships between childhood obesity and the human microbiome, and of the main drivers of honey bee loss. All methods developed and data used, as well as the source code to replicate our analyses, are publicly available