parameter expansion to accelerate em the px em algorithm summary the em algorithm and its extensions are popular tools for modal estimation but ar e often criticised for their slow convergence we propose a new method that can often make em much faster the intuitive idea is to use a covariance adjustment to correct the analysis of the m step capitalising on extra information captured in the imputed complete data the way we accomplish this is by parameter expansion we expand the complete data model while preserving the observed data model and use the expanded complete data model to generate em this parameter expanded ei m px em algorithm shares the simplicity and stability of ordinary em but has a faster rate of convergence since its m step performs a more efficient analysis the px em algorithm is illustrated for the multivariate t distribution a random effects model factor analysis probit regression and a poisson imaging model

estimation of adjusted rate differences using additive negative binomial regression rate differences are an important effect measure in biostatistics and provide an alternative perspective to rate ratios when the data are event counts observed during an exposure period adjusted rate differences may be estimated using an identity link poisson generalised linear model also known as additive poisson regression a problem with this approach is that the assumption of equality of mean and variance rarely holds in real data which often show overdispersion an additive negative binomial model is the natural alternative to account for this however standard model fitting methods are often unable to cope with the constrained parameter space arising from the non negativity restrictions of the additive model in this paper we propose a novel solution to this problem using a variant of the expectation conditional maximisation either algorithm our method provides a reliable way to fit an additive negative binomial regression model and also permits flexible generalisations using semi parametric regression functions we illustrate the method using a placebo controlled clinical trial of fenofibrate treatment in patients with type ii diabetes where the outcome is the number of laser therapy courses administered to treat diabetic retinopathy an r package is available that implements the proposed method copyright 2016 john wiley sons ltd

a deletion contraction algorithm for the characteristic polynomial of a multigraph expression du polynome caracteristique d un multigraphe fini g en termes de polynomes caracteristiques des modifications locales de g application de la formule obtenue a l etude des plus grandes valeurs propres de certains graphes theta

nonparametric modeling of longitudinal covariance structure in functional mapping of quantitative trait loci estimation of the covariance structure of longitudinal processes is a fundamental prerequisite for the practical deployment of functional mapping designed to study the genetic regulation and network of quantitative variation in dynamic complex traits we present a nonparametric approach for estimating the covariance structure of a quantitative trait measured repeatedly at a series of time points specifically we adopt huang et al s 2006 biometrika 93 85 98 approach of invoking the modified cholesky decomposition and converting the problem into modeling a sequence of regressions of responses a regularized covariance estimator is obtained using a normal penalized likelihood with an l 2 penalty this approach embedded within a mixture likelihood framework leads to enhanced accuracy precision and flexibility of functional mapping while preserving its biological relevance simulation studies are performed to reveal the statistical properties and advantages of the proposed method a real example from a mouse genome project is analyzed to illustrate the utilization of the methodology the new method will provide a useful tool for genome wide scanning for the existence and distribution of quantitative trait loci underlying a dynamic trait important to agriculture biology and health sciences

c algebras of toeplitz type associated with algebraic number fields we associate with the ring r of algebraic integers in a number field a c algebra mathfrak t r it is an extension of the ring c algebra mathfrak a r studied previously by the first named author in collaboration with x li in contrast to mathfrak a r it is functorial under homomorphisms of rings it can also be defined using the left regular representation of the ax b semigroup r rtimes r times on ell 2 r rtimes r times the algebra mathfrak t r carries a natural one parameter automorphism group sigma t t in mathbb r we determine its kms structure the technical difficulties that we encounter are due to the presence of the class group in the case where r is not a principal ideal domain in that case for a fixed large inverse temperature the simplex of kms states splits over the class group the partition functions are partial dedekind zeta functions we prove a result characterizing the asymptotic behavior of quotients of such partial zeta functions which we then use to show uniqueness of the beta kms state for each inverse temperature beta in 1 2

variable selection in linear mixed effects models this paper is concerned with the selection and estimation of fixed and random effects in linear mixed effects models we propose a class of nonconcave penalized profile likelihood methods for selecting and estimating important fixed effects to overcome the difficulty of unknown covariance matrix of random effects we propose to use a proxy matrix in the penalized profile likelihood we establish conditions on the choice of the proxy matrix and show that the proposed procedure enjoys the model selection consistency where the number of fixed effects is allowed to grow exponentially with the sample size we further propose a group variable selection strategy to simultaneously select and estimate important random effects where the unknown covariance matrix of random effects is replaced with a proxy matrix we prove that with the proxy matrix appropriately chosen the proposed procedure can identify all true random effects with asymptotic probability one where the dimension of random effects vector is allowed to increase exponentially with the sample size monte carlo simulation studies are conducted to examine the finite sample performance of the proposed procedures we further illustrate the proposed procedures via a real data example

maximum likelihood estimation via the ecm algorithm a general framework two major reasons for the popularity of the em algorithm are that its maximum step involves only complete data maximum likelihood estimation which is often computationally simple and that its convergence is stable with each iteration increasing the likelihood when the associated complete data maximum likelihood estimation itself is complicated em is less attractive because the m step is computationally unattractive in many cases however complete data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

penalized maximum likelihood image reconstruction using space alternating generalized em algorithms most expectation maximization em type algorithms for penalized maximum likelihood image reconstruction converge slowly particularly when one incorporates additive background effects such as scatter random coincidences dark current or cosmic radiation in addition regularizing smoothness penalties or priors introduce parameter coupling rendering intractable the m steps of most em type algorithms this paper presents space alternating generalized em sage algorithms for image reconstruction which update the parameters sequentially using a sequence of small hidden data spaces rather than simultaneously using one large complete data space the sequential update decouples the m step so the maximization can typically be performed analytically we introduce new hidden data spaces that are less informative than the conventional complete data space for poisson data and that yield significant improvements in convergence rate this acceleration is due to statistical considerations not numerical overrelaxation methods so monotonic increases in the objective function are guaranteed we provide a general global convergence proof for sage methods with nonnegativity constraints

spectral regularization algorithms for learning large incomplete matrices we use convex relaxation techniques to provide a sequence of regularized low rank solutions for large scale matrix completion problems using the nuclear norm as a regularizer we provide a simple and very efficient convex algorithm for minimizing the reconstruction error subject to a bound on the nuclear norm our algorithm soft impute iteratively replaces the missing elements with those obtained from a soft thresholded svd with warm starts this allows us to efficiently compute an entire regularization path of solutions on a grid of values of the regularization parameter the computationally intensive part of our algorithm is in computing a low rank svd of a dense matrix exploiting the problem structure we show that the task can be performed with a complexity of order linear in the matrix dimensions our semidefinite programming algorithm is readily scalable to large matrices for example soft impute takes a few hours to compute low rank approximations of a 106 x 106 incomplete matrix with 107 observed entries and fits a rank 95 approximation to the full netflix training set in 3 3 hours our methods achieve good training and test errors and exhibit superior timings when compared to other competitive state of the art techniques

regression models for identifying noise sources in magnetic resonance images stochastic noise susceptibility artifacts magnetic field and radiofrequency inhomogeneities and other noise components in magnetic resonance images mris can introduce serious bias into any measurements made with those images we formally introduce three regression models including a rician regression model and two associated normal models to characterize stochastic noise in various magnetic resonance imaging modalities including diffusion weighted imaging dwi and functional mri fmri estimation algorithms are introduced to maximize the likelihood function of the three regression models we also develop a diagnostic procedure for systematically exploring mr images to identify noise components other than simple stochastic noise and to detect discrepancies between the fitted regression models and mri data the diagnostic procedure includes goodness of fit statistics measures of influence and tools for graphical display the goodness of fit statistics can assess the key assumptions of the three r

an oriented hypergraphic approach to algebraic graph theory abstract an oriented hypergraph is a hypergraph where each vertex edge incidence is given a label of 1 or 1 we define the adjacency incidence and laplacian matrices of an oriented hypergraph and study each of them we extend several matrix results known for graphs and signed graphs to oriented hypergraphs new matrix results that are not direct generalizations are also presented finally we study a new family of matrices that contains walk information

iterative automated record linkage using mixture models the goal of record linkage is to link quickly and accurately records that correspond to the same person or entity whereas certain patterns of agreements and disagreements on variables are more likely among records pertaining to a single person than among records for different people the observed patterns for pairs of records can be viewed as arising from a mixture of matches and nonmatches mixture model estimates can be used to partition record pairs into two or more groups that can be labeled as probable matches links and probable nonmatches nonlinks a method is proposed and illustrated that uses marginal information in the database to select mixture models identifies sets of records for clerks to review based on the models and marginal information incorporates clerically reviewed data as they become available into estimates of model parameters and classifies pairs as links nonlinks or in need of further clerical review the procedure is illustrated with five datasets from the u s bureau

a characterization of oriented hypergraphic balance via signed weak walks abstract an oriented hypergraph is a hypergraph where each vertex edge incidence is given a label of 1 or 1 and each adjacency is signed the negative of the product of the incidences an oriented hypergraph is balanced if the product of the adjacencies in each circle is positive we provide a combinatorial interpretation for entries of k th power of the oriented hypergraphic laplacian via the number of signed weak walks of length k using closed weak walks we prove a new characterization of balance for oriented hypergraphs and matrices that generalizes harary s theorem for signed graphs

a split and merge bayesian variable selection approach for ultrahigh dimensional regression summary we propose a bayesian variable selection approach for ultrahigh dimensional linear regression based on the strategy of split and merge the approach proposed consists of two stages split the ultrahigh dimensional data set into a number of lower dimensional subsets and select relevant variables from each of the subsets and aggregate the variables selected from each subset and then select relevant variables from the aggregated data set since the approach proposed has an embarrassingly parallel structure it can be easily implemented in a parallel architecture and applied to big data problems with millions or more of explanatory variables under mild conditions we show that the approach proposed is consistent i e the true explanatory variables can be correctly identified by the approach as the sample size becomes large extensive comparisons of the approach proposed have been made with penalized likelihood approaches such as the lasso elastic net sure independence screening and iterative sure independence screening the numerical results show that the approach proposed generally outperforms penalized likelihood approaches the models selected by the approach tend to be more sparse and closer to the true model

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

latent variable models for mixed discrete and continuous outcomes we propose a latent variable model for mixed discrete and continuous outcomes the model accommodates any mixture of outcomes from an exponential family and allows for arbitrary covariate effects as well as direct modelling of covariates on the latent variable an em algorithm is proposed for parameter estimation and estimates of the latent variables are produced as a by product of the analysis a generalized likelihood ratio test can be used to test the significance of covariates affecting the latent outcomes this method is applied to birth defects data where the outcomes of interest are continuous measures of size and binary indicators of minor physical anomalies infants who were exposed in utero to anticonvulsant medications are compared with controls

nuclearity of semigroup c algebras and the connection to amenability abstract we study c algebras associated with subsemigroups of groups for a large class of such semigroups including positive cones in quasi lattice ordered groups and left ore semigroups we describe the corresponding semigroup c algebras as c algebras of inverse semigroups groupoid c algebras and full corners in associated group crossed products these descriptions allow us to characterize nuclearity of semigroup c algebras in terms of faithfulness of left regular representations and amenability of group actions moreover we also determine when boundary quotients of semigroup c algebras are uct kirchberg algebras this leads to a unified approach to cuntz algebras and ring c algebras

on the laplacian coefficients of signed graphs abstract let g be a signed graph where g is its underlying graph and its sign function defined on edges of g a signed graph the subgraph of is its signed tu subgraph if the signed graph induced by the vertices of consists of trees and or unbalanced unicyclic signed graphs let l d g a be the laplacian of in this paper we express the coefficient of the laplacian characteristic polynomial of based on the signed tu subgraphs of and establish the relation between the laplacian characteristic polynomial of a signed graph with adjacency characteristic polynomials of its signed line graph and signed subdivision graph as an application we identify the signed unicyclic graphs having extremal coefficients of the laplacian characteristic polynomial

bias reduction of maximum likelihood estimates summary it is shown how in regular parametric problems the first order term is removed from the asymptotic bias of maximum likelihood estimates by a suitable modification of the score function in exponential families with canonical parameterization the effect is to penalize the likelihood by the jeffreys invariant prior in binomial logistic models poisson log linear models and certain other generalized linear models the jeffreys prior penalty function can be imposed in standard regression software using a scheme of iterative adjustments to the data

the dynamic expectation conditional maximization either algorithm summary the expectation conditional maximization either ecme algorithm has proven to be an effective way of accelerating the expectation maximization algorithm for many problems recognizing the limitation of using prefixed acceleration subspaces in the ecme algorithm we propose a dynamic ecme decme algorithm which allows the acceleration subspaces to be chosen dynamically the simplest decme implementation is what we call decme 1 which uses the line that is determined by the two most recent estimates as the acceleration subspace the investigation of decme 1 leads to an efficient simple stable and widely applicable decme implementation which uses two dimensional acceleration subspaces and is referred to as decme 2 the fast convergence of decme 2 is established by the theoretical result that in a small neighbourhood of the maximum likelihood estimate it is equivalent to a conjugate direction method the remarkable accelerating effect of decme 2 and its variant is also demonstrated with several numerical examples

mixtures of multivariate power exponential distributions summary an expanded family of mixtures of multivariate power exponential distributions is introduced while fitting heavy tails and skewness have received much attention in the model based clustering literature recently we investigate the use of a distribution that can deal with both varying tail weight and peakedness of data a family of parsimonious models is proposed using an eigen decomposition of the scale matrix a generalized expectation maximization algorithm is presented that combines convex optimization via a minorization maximization approach and optimization based on accelerated line search algorithms on the stiefel manifold lastly the utility of this family of models is illustrated using both toy and benchmark data

estimating and using propensity scores with partially missing data abstract investigators in observational studies have no control over treatment assignment as a result large differences can exist between the treatment and control groups on observed covariates which can lead to badly biased estimates of treatment effects propensity score methods are an increasingly popular method for balancing the distribution of the covariates in the two groups to reduce this bias for example using matching or subclassification sometimes in combination with model based adjustment to estimate propensity scores which are the conditional probabilities of being treated given a vector of observed covariates we must model the distribution of the treatment indicator given these observed covariates much work has been done in the case where covariates are fully observed we address the problem of calculating propensity scores when covariates can have missing values in such cases which commonly arise in practice the pattern of missing covariates can be prognostically important and

sure independence screening in generalized linear models with np dimensionality ultrahigh dimensional variable selection plays an increasingly important role in contemporary scientific discoveries and statistical research among others fan and lv 2008 propose an independent screening framework by ranking the marginal correlations they showed that the correlation ranking procedure possesses a sure independence screening property within the context of the linear model with gaussian covariates and responses in this paper we propose a more general version of the independent learning with ranking the maximum marginal likelihood estimates or the maximum marginal likelihood itself in generalized linear models we show that the proposed methods with fan and lv 2008 as a very special case also possess the sure screening property with vanishing false selection rate the conditions under which that the independence learning possesses a sure screening is surprisingly simple this justifies the applicability of such a simple method in a wide spectrum we quantify explicitly the extent to which the dimensionality can be reduced by independence screening which depends on the interactions of the covariance matrix of covariates and true parameters simulation studies are used to illustrate the utility of the proposed approaches in addition we supported in part by grant nsf grants dms 0714554 and dms 0704337 the bulk of the work was conducted when rui song was a postdoctoral research fellow at princeton university the authors would like to thank the associate editor and two referees for their constructive comments that improve the presentation and the results of the paper ams 2000 subject classifications primary 68q32 62j12 secondary 62e99 60f10

semigroup crossed products and the toeplitz algebras of nonabelian groups abstract we consider the quasi lattice ordered groups g p recently introduced by nica we realise their universal toeplitz algebra as a crossed product b p p by a semigroup of endomorphisms and show that the toeplitz representation is faithful precisely when an amenability condition is satisfied we then show directly that many interesting free products are amenable the final result contains theorems of cuntz and dinh on the uniqueness of toeplitz cuntz algebras as special cases

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

a characterization of oriented hypergraphic laplacian and adjacency matrix coefficients abstract an oriented hypergraph is an oriented incidence structure that generalizes and unifies graph and hypergraph theoretic results by examining its locally signed graphic substructure in this paper we obtain a combinatorial characterization of the coefficients of the characteristic polynomials of oriented hypergraphic laplacian and adjacency matrices via a signed hypergraphic generalization of basic figures of graphs additionally we provide bounds on the determinant and permanent of the laplacian matrix characterize the oriented hypergraphs in which the upper bound is sharp and demonstrate that the lower bound is never achieved

ring c algebras we associate reduced and full c algebras to arbitrary rings and study the inner structure of these ring c algebras as a result we obtain conditions for them to be purely infinite and simple we also discuss several examples originally our motivation comes from algebraic number theory

an imputation regularized optimization algorithm for high dimensional missing data problems and beyond missing data are frequently encountered in high dimensional problems but they are usually difficult to deal with by using standard algorithms such as the expectation maximization algorithm and its variants to tackle this difficulty some problem specific algorithms have been developed in the literature but there still lacks a general algorithm this work is to fill the gap we propose a general algorithm for high dimensional missing data problems the algorithm works by iterating between an imputation step and a regularized optimization step at the imputation step the missing data are imputed conditionally on the observed data and the current estimates of parameters and at the regularized optimization step a consistent estimate is found via the regularization approach for the minimizer of a kullback leibler divergence defined on the pseudocomplete data for high dimensional problems the consistent estimate can be found under sparsity constraints the consistency of the averaged estimate for the true parameter can be established under quite general conditions the algorithm is illustrated by using high dimensional gaussian graphical models high dimensional variable selection and a random coefficient model

semigroup c algebras of ax b semigroups we study semigroup c algebras of ax b semigroups over integral domains the goal is to generalize several results about c algebras of ax b semigroups over rings of algebraic integers we prove results concerning k theory and structural properties like the ideal structure or pure infiniteness our methods allow us to treat ax b semigroups over a large class of integral domains containing all noetherian integrally closed domains and coordinate rings of affine varieties over infinite fields

the ecme algorithm a simple extension of em and ecm with faster monotone convergence a generalisation of the ecm algorithm meng rubin 1993 which is itselfan extension of the em algorithm dempster laird rubin 1977 can be obtained by replacing some cm steps of ecm which maximise the constrained expected complete data loglikelihood function with steps that maximise the correspondingly constrained actual likelihood function this algorithm which we call ecme algorithm for expectation conditional maximisation either shares with both em and ecm their stable monotone convergence and basic simplicity of implementation relative to competing faster converging methods moreover ecme can have a substantially faster convergence rate than either em or ecm measured using either the number of iterations or actual computer time

type iii1 equilibrium states of the toeplitz algebra of the affine semigroup over the natural numbers abstract we complete the analysis of kms states of the toeplitz algebra t n n of the affine semigroup over the natural numbers recently studied by raeburn and the first author by showing that for every inverse temperature in the critical interval 1 2 the unique kms state is of type iii1 we prove this by reducing the type classification from t n n to that of the symmetric part of the bost connes system with a shift in inverse temperature to carry out this reduction we first obtain a parametrization of the nica spectrum of n n in terms of an adelic space combining a characterization of traces on crossed products due to the second author with an analysis of the action of n n on the nica spectrum we can also recover all the kms states of t n n originally computed by raeburn and the first author our computation sheds light on why there is a free transitive circle action on the extremal kms states for 2 that does not ostensibly come from an action of t on the c algebra

an equivalent measure of partial correlation coefficients for high dimensional gaussian graphical models gaussian graphical models ggms are frequently used to explore networks such as gene regulatory networks among a set of variables under the classical theory of ggms the construction of gaussian graphical networks amounts to finding the pairs of variables with nonzero partial correlation coefficients however this is infeasible for high dimensional problems for which the number of variables is larger than the sample size in this article we propose a new measure of partial correlation coefficient which is evaluated with a reduced conditional set and thus feasible for high dimensional problems under the markov property and adjacency faithfulness conditions the new measure of partial correlation coefficient is equivalent to the true partial correlation coefficient in construction of gaussian graphical networks based on the new measure of partial correlation coefficient we propose a multiple hypothesis test based method for the construction of gaussian graphical networks furthermore we establish

high dimensional variable selection with reciprocal l1 regularization during the past decade penalized likelihood methods have been widely used in variable selection problems where the penalty functions are typically symmetric about 0 continuous and nondecreasing in 0 we propose a new penalized likelihood method reciprocal lasso or in short rlasso based on a new class of penalty functions that are decreasing in 0 discontinuous at 0 and converge to infinity when the coefficients approach zero the new penalty functions give nearly zero coefficients infinity penalties in contrast the conventional penalty functions give nearly zero coefficients nearly zero penalties e g lasso and smoothly clipped absolute deviation scad or constant penalties e g l0 penalty this distinguishing feature makes rlasso very attractive for variable selection it can effectively avoid to select overly dense models we establish the consistency of the rlasso for variable selection and coefficient estimation under both the low and high dimensional settings since the r

pattern alternating maximization algorithm for missing data in high dimensional problems we propose a novel and efficient algorithm for maximizing the observed log likelihood of a multivariate normal data matrix with missing values we show that our procedure based on iteratively regressing the missing on the observed variables generalizes the standard em algorithm by alternating between different complete data spaces and performing the e step incrementally in this non standard setup we prove numerical convergence to a stationary point of the observed log likelihood for high dimensional data where the number of variables may greatly exceed sample size we perform regularization using a lasso type penalty this introduces sparsity in the regression coefficients used for imputation permits fast computation and warrants competitive performance in terms of estimating the missing entries we show on simulated and real data that the new method often improves upon other modern imputation techniques such as k nearest neighbors imputation nuclear norm minimization or a penalized likelihood approach with an l1 penalty on the concentration matrix

spectral properties of complex unit gain graphs abstract a complex unit gain graph is a graph where each orientation of an edge is given a complex unit which is the inverse of the complex unit assigned to the opposite orientation we extend some fundamental concepts from spectral graph theory to complex unit gain graphs we define the adjacency incidence and laplacian matrices and study each of them the main results of the paper are eigenvalue bounds for the adjacency and laplacian matrices

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

unbalanced repeated measures models with structured covariance matrices the question of how to analyze unbalanced or incomplete repeated measures data is a common problem facing analysts we address this problem through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within subject covariances models that can be fit include standard univariate and multivariate models with incomplete data random effects models and models with time series and factor analytic error structures we describe newton raphson and fisher scoring algorithms for computing maximum likelihood estimates and generalized em algorithms for computing restricted and unrestricted maximum likelihood estimates an example fitting several models to a set of growth data is included

semiparametric maximum likelihood for measurement error model regression this paper presents an em algorithm for semiparametric likelihood analysis of linear generalized linear and nonlinear regression models with measurement errors in explanatory variables a structural model is used in which probability distributions are specified for a the response and b the measurement error a distribution is also assumed for the true explanatory variable but is left unspecified and is estimated by nonparametric maximum likelihood for various types of extra information about the measurement error distribution the proposed algorithm makes use of available routines that would be appropriate for likelihood analysis of a and b if the true x were available simulations suggest that the semiparametric maximum likelihood estimator retains a high degree of efficiency relative to the structural maximum likelihood estimator based on correct distributional assumptions and can outperform maximum likelihood based on an incorrect distributional assumption the approach is illustrated on three examples with a variety of structures and types of extra information about the measurement error distribution

maximum likelihood estimation of nonlinear structural equation models the existing maximum likelihood theory and its computer software in structural equation modeling are established based on linear relationships among manifest variables and latent variables however models with nonlinear relationships are often encountered in social and behavioral sciences in this article an em type algorithm is developed for maximum likelihood estimation of a general nonlinear structural equation model to avoid computation of the complicated multiple integrals involved the e step is completed by a metropolis hastings algorithm it is shown that the m step can be completed efficiently by simple conditional maximization standard errors of the maximum likelihood estimates are obtained via louis s formula the methodology is illustrated with results from a simulation study and two real examples

variable selection in finite mixture of regression models in the applications of finite mixture of regression fmr models often many covariates are used and their contributions to the response variable vary from one component to another of the mixture model this creates a complex variable selection problem existing methods such as the akaike information criterion and the bayes information criterion are computationally expensive as the number of covariates and components in the mixture model increases in this article we introduce a penalized likelihood approach for variable selection in fmr models the new method introduces penalties that depend on the size of the regression coefficients and the mixture structure the new method is shown to be consistent for variable selection a data adaptive method for selecting tuning parameters and an em algorithm for efficient numerical computations are developed simulations show that the method performs very well and requires much less computing power than existing methods the new method is illustrated by analyzin

regression analysis with linked data record linkage or exact matching can be used to join together two files that contain information on the same individuals but lack unique personal identification codes the possibility of errors in linkage causes problems for estimating the relationships between variables on the two files the effect is analogous to the impact of measurement error a model of a linear regression relationship between variables in linked files is proposed assuming the probabilities that pairs of records are links are known an unbiased estimator of the regression coefficients is derived methods for estimating the linkage probabilities by using mixture models are discussed a consistent estimator of the covariance matrix of the proposed estimator is proposed a bootstrap estimator is used to reflect the impact of the uncertainty in record linkage model parameters on the estimators of the regression parameters a simulation study compares the performance of the proposed estimator and alternatives

semiparametric probit models with univariate and bivariate current status data summary multivariate current status data are frequently encountered in biomedical and public health studies semiparametric regression models have been extensively studied for univariate current status data but most existing estimation procedures are computationally intensive involving either penalization or smoothing techniques it becomes more challenging for the analysis of multivariate current status data in this article we study the maximum likelihood estimations for univariate and bivariate current status data under the semiparametric probit regression models we present a simple computational procedure combining the expectation maximization algorithm with the pool adjacent violators algorithm for solving the monotone constraint on the baseline function asymptotic properties of the maximum likelihood estimators are investigated including the calculation of the explicit information bound for univariate current status data as well as the asymptotic consistency and convergence rate for bivariate current status data extensive simulation studies showed that the proposed computational procedures performed well under small or moderate sample sizes we demonstrate the estimation procedure with two real data examples in the areas of diabetic and hiv research

model selection and estimation in the gaussian graphical model summary we propose penalized likelihood methods for estimating the concentration matrix in the gaussian graphical model the methods lead to a sparse and shrinkage estimator of the concentration matrix that is positive definite and thus conduct model selection and estimation simultaneously the implementation of the methods is nontrivial because of the positive definite constraint on the concentration matrix but we show that the computation can be done effectively by taking advantage of the efficient maxdet algorithm developed in convex optimization we propose a bic type criterion for the selection of the tuning parameter in the penalized likelihood methods the connection between our methods and existing methods is illustrated simulations and real examples demonstrate the competitive performance of the new methods

using em to obtain asymptotic variance covariance matrices the sem algorithm abstract the expectation maximization em algorithm is a popular and often remarkably simple method for maximum likelihood estimation in incomplete data problems one criticism of em in practice is that asymptotic variance covariance matrices for parameters e g standard errors are not automatic byproducts as they are when using some other methods such as newton raphson in this article we define and illustrate a procedure that obtains numerically stable asymptotic variance covariance matrices using only the code for computing the complete data variance covariance matrix the code for em itself and code for standard matrix operations the basic idea is to use the fact that the rate of convergence of em is governed by the fractions of missing information to find the increased variability due to missing information to add to the complete data variance covariance matrix we call this supplemented em algorithm the sem algorithm theory and particular examples reinforce the conclusion that the sem alg

bilinear probabilistic principal component analysis probabilistic principal component analysis ppca is a popular linear latent variable model for performing dimension reduction on 1 d data in a probabilistic manner however when used on 2 d data such as images ppca suffers from the curse of dimensionality due to the subsequently large number of model parameters to overcome this problem we propose in this paper a novel probabilistic model on 2 d data called bilinear ppca bppca this allows the establishment of a closer tie between bppca and its nonprobabilistic counterpart moreover two efficient parameter estimation algorithms for fitting bppca are also developed experiments on a number of 2 d synthetic and real world data sets show that bppca is more accurate than existing probabilistic and nonprobabilistic dimension reduction methods

the ideal structure of the hecke c algebra of bost and connes we compute explicitly the primitive ideal space of the bost connes hecke c algebra by embedding it as a full corner in a transformation group c algebra and applying a general theorem of williams this requires the computation of the quasi orbit space for the action of q on the space mathcal a f of finite adeles we then carry out a similar computation for the action of q on the space mathcal a mathcal a f times mathbb r of full adeles

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

improving on deterministic approximate bayesian inferences for mixture distributions this paper presents the branching approach which can improve deterministic implementation methods such as variational bayesian inference and expectation propagation method for bayesian mixture distributions this proposed approach utilizes a set of artificial conditions defined by using the latent variables of the mixture distribution this condition set is updated iteratively by branching based on a condition selected from the previous condition set the target approximate bayesian inference is obtained by merging the approximate conditional inferences under each condition in the condition set the proposed approach is compared with several standard implementation methods by using a numerical example and a real world example

the 2 adic ring c algebra of the integers and its representations abstract we study the 2 adic version of the ring c algebra of the integers first we work out the precise relation between the cuntz algebra o 2 and our 2 adic ring c algebra in terms of representations secondly we prove a 2 adic duality theorem identifying the crossed product arising from 2 adic affine transformations on the 2 adic numbers with the analogous crossed product algebra over the real numbers and finally as an outcome of this duality result we construct an explicit imprimitivity bimodule and prove that it transports one canonical representation into the other

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

estimating the false discovery rate using the stochastic approximation algorithm testing of multiple hypotheses involves statistics that are strongly dependent in some applications but most work on this subject is based on the assumption of independence we propose a new method for estimating the false discovery rate of multiple hypothesis tests in which the density of test scores is estimated parametrically by minimizing the kullback leibler distance between the unknown density and its estimator using the stochastic approximation algorithm and the false discovery rate is estimated using the ensemble averaging method our method is applicable under general dependence between test statistics numerical comparisons between our method and several competitors conducted on simulated and real data examples show that our method achieves more accurate control of the false discovery rate in almost all scenarios

general formulas for obtaining the mles and the asymptotic variance covariance matrix in mapping quantitative trait loci when using the em algorithm we present in this paper general formulas for deriving the maximum likelihood estimates and the asymptotic variance covariance matrix of the positions and effects of quantitative trait loci qtls in a finite normal mixture model when the em algorithm is used for mapping qtls the general formulas are based on two matrices d and q where d is the genetic design matrix characterizing the genetic effects of the qtls and q is the conditional probability matrix of qtl genotypes given flanking marker genotypes containing the information on qtl positions with the general formulas it is relatively easy to extend qtl mapping analysis to using multiple marker intervals simultaneously for mapping multiple qtls for analyzing qtl epistasis and for estimating the heritability of quantitative traits simulations were performed to evaluate the performance of the estimates of the asymptotic variances of qtl positions and effects

a direct approach to false discovery rates summary multiple hypothesis testing involves guarding against much more complicated errors than single hypothesis testing whereas we typically control the type i error rate for a single hypothesis test a compound error rate is controlled for multiple hypothesis tests for example controlling the false discovery rate fdr traditionally involves intricate sequential p value rejection methods based on the observed data whereas a sequential p value method fixes the error rate and estimates its corresponding rejection region we propose the opposite approach we fix the rejection region and then estimate its corresponding error rate this new approach offers increased applicability accuracy and power we apply the methodology to both the positive false discovery rate pfdr and fdr and provide evidence for its benefits it is shown that pfdr is probably the quantity of interest over fdr also discussed is the calculation of the q value the pfdr analogue of the p value which eliminates the need to set the error rate beforehand as is traditionally done some simple numerical examples are presented that show that this new approach can yield an increase of over eight times in power compared with the benjamini hochberg fdr method

combinatorial approach for computing the characteristic polynomial of a matrix the study of the spectrum of weighted di graphs has attracted recently much attention in the literature here we use the coates digraph as a main tool to extend in a combinatorial way some well known results from the spectral graph theory on computing the characteristic polynomial of graphs new results are related to weighted di graph and thus to any square matrix

globally convergent algorithms for maximizing a likelihood function summary in this paper we show global convergence under very general assumptions of iterative maximization procedures with cyclic fixing of groups of parameters maximizing over the remaining parameters further we show that a slightly modified newton procedure applied to the derivative of the reciprocal likelihood function in a one dimensional exponential family is globally convergent we also prove that if the distribution of the sufficient statistic is infinitely divisible then the newton method applied to the derivative of the log likelihood function converges by combining these results we obtain general globally convergent iterative procedures for maximizing the likelihood function in any regular k dimensional exponential family the likelihood function can be maximized either by successively maximizing over one parameter at a time or by maximizing in the newton direction

leptokurtic and platykurtic class of robust symmetrical and asymmetrical time series models abstract in this study we examined the well known autoregressive time series model in which innovations follow the flexible class of two piece distributions based on the scale mixtures of normal tp smn family the mentioned class of distributions is a rich class of distributions family that covers the robust symmetric asymmetric light heavy tailed distributions a key feature of this study is using a new suitable hierarchical representation of the family to obtain the maximum likelihood estimates of the model parameters via an expectation maximization em type algorithm performances and usefulness of the proposed model and estimates are shown via simulation studies and a real dataset

phase transition on the toeplitz algebra of the affine semigroup over the natural numbers abstract we show that the group q q of orientation preserving affine transformations of the rational numbers is quasi lattice ordered by its subsemigroup n n the associated toeplitz c algebra t n n is universal for isometric representations which are covariant in the sense of nica we give a presentation of t n n in terms of generators and relations and use this to show that the c algebra q n recently introduced by cuntz is the boundary quotient of q q n n in the sense of crisp and laca the toeplitz algebra t n n carries a natural dynamics which induces the one considered by cuntz on the quotient q n and our main result is the computation of the kms equilibrium states of the dynamical system t n n r for all values of the inverse temperature for 1 2 there is a unique kms state and the kms 1 state factors through the quotient map onto q n giving the unique kms state discovered by cuntz at 2 there is a phase transition and for 2 the kms states are indexed by probability measures on the circle there is a further phase transition at where the kms states are indexed by the probability measures on the circle but the ground states are indexed by the states on the classical toeplitz algebra t n

on k theoretic invariants of semigroup c algebras attached to number fields abstract we show that semigroup c algebras attached to a x b semigroups over rings of integers determine number fields up to arithmetic equivalence under the assumption that the number fields have the same number of roots of unity for finite galois extensions this means that the semigroup c algebras are isomorphic if and only if the number fields are isomorphic

spectra of cycle and path families of oriented hypergraphs abstract an oriented hypergraph is a hypergraph where each vertex edge incidence is given a label of either 1 or 1 this generalizes signed graphs to a hypergraph setting and simultaneously provides a natural definition for a signed adjacency which is used to define the adjacency and laplacian matrices many properties of these matrices are known but there are no nontrivial families of oriented hypergraphs with their spectrum determined in this paper we define and study hypergraph families that are analogous to cycles and paths in graphs and signed graphs the adjacency and laplacian eigenvalues for some of these families is determined

sparse kalman filtering approaches to realized covariance estimation from high frequency financial data estimation of the covariance matrix of asset returns from high frequency data is complicated by asynchronous returns market microstructure noise and jumps one technique for addressing both asynchronous returns and market microstructure is the kalman expectation maximization kem algorithm however the kem approach assumes log normal prices and does not address jumps in the return process which can corrupt estimation of the covariance matrix in this paper we extend the kem algorithm to price models that include jumps we propose a sparse kalman filtering approach to this problem in particular we develop a kalman expectation conditional maximization algorithm to determine the unknown covariance as well as detecting the jumps in order to promote a sparse estimate of the jumps we consider both laplace and the spike and slab jump priors numerical results using simulated data show that each of these approaches provide for improved covariance estimation relative to the kem method in a variety of settings where jumps occur

semigroup c algebras and amenability of semigroups we construct reduced and full semigroup c algebras for left cancellative semigroups our new construction covers particular cases already considered by a nica and also toeplitz algebras attached to rings of integers in number fields due to j cuntz moreover we show how left amenability of semigroups can be expressed in terms of these semigroup c algebras in analogy to the group case

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea