Linear Mixed Models with Marginally Symmetric Nonparametric Random Effects

Linear mixed models (LMMs) are used as an important tool in the data analysis of repeated measures and longitudinal studies. The most common form of LMMs utilize a normal distribution to model the random effects. Such assumptions can often lead to misspecification errors when the random effects are not normal. One approach to remedy the misspecification errors is to utilize a point-mass distribution to model the random effects; this is known as the nonparametric maximum likelihood-fitted (NPML) model. The NPML model is flexible but requires a large number of parameters to characterize the random-effects distribution. It is often natural to assume that the random-effects distribution be at least marginally symmetric. The marginally symmetric NPML (MSNPML) random-effects model is introduced, which assumes a marginally symmetric point-mass distribution for the random effects. Under the symmetry assumption, the MSNPML model utilizes half the number of parameters to characterize the same number of point masses as the NPML model; thus the model confers an advantage in economy and parsimony. An EM-type algorithm is presented for the maximum likelihood (ML) estimation of LMMs with MSNPML random effects; the algorithm is shown to monotonically increase the log-likelihood and is proven to be convergent to a stationary point of the log-likelihood function in the case of convergence. Furthermore, it is shown that the ML estimator is consistent and asymptotically normal under certain conditions, and the estimation of quantities such as the random-effects covariance matrix and individual a posteriori expectations is demonstrated

Maximum Likelihood Estimation of Triangular and Polygonal Distributions

Triangular distributions are a well-known class of distributions that are often used as elementary example of a probability model. In the past, enumeration and order statistic-based methods have been suggested for the maximum likelihood (ML) estimation of such distributions. A novel parametrization of triangular distributions is presented. The parametrization allows for the construction of an MM (minorization--maximization) algorithm for the ML estimation of triangular distributions. The algorithm is shown to both monotonically increase the likelihood evaluations, and be globally convergent. Using the parametrization is then applied to construct an MM algorithm for the ML estimation of polygonal distributions. This algorithm is shown to have the same numerical properties as that of the triangular distribution. Numerical simulation are provided to demonstrate the performances of the new algorithms against established enumeration and order statistics-based methods

Iteratively-Reweighted Least-Squares Fitting of Support Vector Machines: A Majorization--Minimization Algorithm Approach

Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an alternative approach to SVM fitting via the majorization--minimization (MM) paradigm. Algorithms that are derived via MM algorithm constructions can be shown to monotonically decrease their objectives at each iteration, as well as be globally convergent to stationary points. We demonstrate the construction of iteratively-reweighted least-squares (IRLS) algorithms, via the MM paradigm, for SVM risk minimization problems involving the hinge, least-square, squared-hinge, and logistic losses, and 1-norm, 2-norm, and elastic net penalizations. Successful implementations of our algorithms are presented via some numerical examples

The Return of Religion? The Paradox of Faith-based Welfare Provision in a Secular Age

For centuries, churches were the main institutional providers of welfare in Europe before the state took over this role in the late 19th century. The influence of modernization theory meant that modern welfare state theorists increasingly regarded religion and its impact on welfare as a relic from the distant past. It was anticipated that modern, differentiated, and industrialized societies would see the decline and inevitable disappearance of religious welfare provision along with religiosity. Surprisingly, however, at the beginning of the 21st century in many modern industrialized societies, religious institutions are increasingly becoming involved in welfare provision again. The religion blind classic welfare state literature offers no explanation for this phenomenon. This present paper argues that the resurgence of faith-based welfare providers is the reversal of a phenomenon that occurred in the late 19th century when modern states started to strip religious providers of their prerogatives in welfare provision. The result was the ascendance of the modern state and the demise of religion in the late 19th century. The return of welfare to religious providers can therefore be interpreted as the beginning of the demise of the modern state.Jahrhundertelang war die Kirche der Hauptwohlfahrtsträger in Europa, bevor der Staat im späten 19. Jahrhundert diese Aufgabe übernahm. Der Einfluss der Modernisierungstheorie bedeutete, dass Theoretiker des modernen Wohlfahrtsstaates Religion und ihre Auswirkung auf Sozialhilfe zunehmend als ein Relikt der Vergangenheit ansahen. Man erwartete, dass in modernen, differenzierten und industrialisierten Gesellschaften der Rückgang und das unausweichliche Verschwinden kirchlicher Wohlfahrtsleistungen mit einem Zerfall an Religiosität einhergingen. Allerdings engagieren sich seit Beginn des 21. Jahrhunderts in vielen Industrienationen überraschenderweise wieder kirchliche Einrichtungen vermehrt in der Sozialfürsorge. Die klassische Literatur zum Wohlfahrtsstaat blendet die Kirche aus und liefert daher keinerlei Erklärung für dieses Phänomen. Der vorliegende Beitrag argumentiert, dass das Neuaufleben konfessioneller Wohlfahrtsanbieter das Phänomen des späten 19. Jahrhunderts wieder umkehrt, als moderne Staaten begannen, den kirchlichen Wohlfahrtsträgern die Privilegien der Sozialhilfe zu entziehen. Das Ergebnis war der Aufstieg des modernen Wohlfahrtsstaates und der Niedergang der Religion im späten 19. Jahrhundert. Das Wiedererstarken kirchlicher Wohlfahrtspflege kann daher als der Beginn des Zerfalls des modernen Staates erachtet werden.1 Contents 1 The renaissance of faith-based welfare 2 Classic welfare state theory and religion 3 Religion and welfare with Christian democracy 4 Religion and welfare without Christian democracy 5 The empirics of faith-based welfare provision 6 Substitution 7 The reversal thesis 8 Conclusion Reference

Mixtures of Spatial Spline Regressions

We present an extension of the functional data analysis framework for univariate functions to the analysis of surfaces: functions of two variables. The spatial spline regression (SSR) approach developed can be used to model surfaces that are sampled over a rectangular domain. Furthermore, combining SSR with linear mixed effects models (LMM) allows for the analysis of populations of surfaces, and combining the joint SSR-LMM method with finite mixture models allows for the analysis of populations of surfaces with sub-family structures. Through the mixtures of spatial splines regressions (MSSR) approach developed, we present methodologies for clustering surfaces into sub-families, and for performing surface-based discriminant analysis. The effectiveness of our methodologies, as well as the modeling capabilities of the SSR model are assessed through an application to handwritten character recognition

A Block Minorization--Maximization Algorithm for Heteroscedastic Regression

The computation of the maximum likelihood (ML) estimator for heteroscedastic regression models is considered. The traditional Newton algorithms for the problem require matrix multiplications and inversions, which are bottlenecks in modern Big Data contexts. A new Big Data-appropriate minorization--maximization (MM) algorithm is considered for the computation of the ML estimator. The MM algorithm is proved to generate monotonically increasing sequences of likelihood values and to be convergent to a stationary point of the log-likelihood function. A distributed and parallel implementation of the MM algorithm is presented and the MM algorithm is shown to have differing time complexity to the Newton algorithm. Simulation studies demonstrate that the MM algorithm improves upon the computation time of the Newton algorithm in some practical scenarios where the number of observations is large

Does Massive MIMO Fail in Ricean Channels?

Massive multiple-input multiple-output (MIMO) is now making its way to the standardization exercise of future 5G networks. Yet, there are still fundamental questions pertaining to the robustness of massive MIMO against physically detrimental propagation conditions. On these grounds, we identify scenarios under which massive MIMO can potentially fail in Ricean channels, and characterize them physically, as well as, mathematically. Our analysis extends and generalizes a stream of recent papers on this topic and articulates emphatically that such harmful scenarios in Ricean fading conditions are unlikely and can be compensated using any standard scheduling scheme. This implies that massive MIMO is intrinsically effective at combating interuser interference and, if needed, can avail of the base-station scheduler for further robustness.Comment: IEEE Wireless Communications Letters, accepte