robust kalman filter based on a generalized maximum likelihood type estimator a new robust kalman filter is proposed that detects and bounds the influence of outliers in a discrete linear system including those generated by thick tailed noise distributions such as impulsive noise besides outliers induced in the process and observation noises we consider in this paper a new type called structural outliers for a filter to be able to counter the effect of these outliers observation redundancy in the system is necessary we have therefore developed a robust filter in a batch mode regression form to process the observations and predictions together making it very effective in suppressing multiple outliers a key step in this filter is a new prewhitening method that incorporates a robust multivariate estimator of location and covariance the other main step is the use of a generalized maximum likelihood type gm estimator based on schweppe s proposal and the huber function which has a high statistical efficiency at the gaussian distribution and a positive breakdown point in regression the latter is defined as the largest fraction of contamination for which the estimator yields a finite maximum bias under contamination this gm estimator enables our filter to bound the influence of residual and position where the former measures the effects of observation and innovation outliers and the latter assesses that of structural outliers the estimator is solved via the iteratively reweighted least squares irls algorithm in which the residuals are standardized utilizing robust weights and scale estimates finally the state estimation error covariance matrix of the proposed gm kalman filter is derived from its influence function simulation results revealed that our filter compares favorably with the h filter in the presence of outliers

using angles to identify concentrated multivariate outliers this article describes a procedure for the detection of multivariate outliers based on the analysis of certain angular properties of the observations the method is simple exploratory in nature and particularly well suited for the detection of concentrated contamination patterns in which the outliers appear to form a cluster separated from the sample it is shown that it presents good properties for the identification of contaminations on high dimensional sample spaces and for high contamination levels including some cases in which methods based on robust estimators the minimum covariance determinant and minimum volume ellipsoid estimators the stahel donoho estimator or other recent proposals may fail the use of the procedure is illustrated through several examples

hyper markov laws in the statistical analysis of decomposable graphical models this paper introduces and investigates the notion of a hyper markov law which is a probability distribution over the set of probability measures on a multivariate space that i is concentrated on the set of markov probabilities over some decomposable graph and ii satisfies certain conditional independence restrictions related to that graph a stronger version of this hyper markov property is also studied our analysis starts by reconsidering the properties of markov probabilities using an abstract approach which thereafter proves equally applicable to the hyper markov case next it is shown constructively that hyper markov laws exist that they appear as sampling distributions of maximum likelihood estimators in decomposable graphical models and also that they form natural conjugate prior distributions for a bayesian analysis of these models as examples we construct a range of specific hyper markov laws including the hyper multinomial hyper dirichlet and the hyper wishart and inverse wishart laws these laws occur naturally in connection with the analysis of decomposable log linear and covariance selection models

uniform approach to linear and nonlinear interrelation patterns in multivariate time series currently a variety of linear and nonlinear measures is in use to investigate spatiotemporal interrelation patterns of multivariate time series whereas the former are by definition insensitive to nonlinear effects the latter detect both nonlinear and linear interrelation in the present contribution we employ a uniform surrogate based approach which is capable of disentangling interrelations that significantly exceed random effects and interrelations that significantly exceed linear correlation the bivariate version of the proposed framework is explored using a simple model allowing for separate tuning of coupling and nonlinearity of interrelation to demonstrate applicability of the approach to multivariate real world time series we investigate resting state functional magnetic resonance imaging rsfmri data of two healthy subjects as well as intracranial electroencephalograms ieeg of two epilepsy patients with focal onset seizures the main findings are that for our rsfmri data interrelations can be described by linear cross correlation rejection of the null hypothesis of linear ieeg interrelation occurs predominantly for epileptogenic tissue as well as during epileptic seizures

retrospective prospective symmetry in the likelihood and bayesian analysis of case control studies summary prentice pyke 1979 established that the maximum likelihood estimate of an odds ratio in a case control study is the same as would be found by fitting a logistic regression in other words for this specific target the incorrect prospective model is inferentially equivalent to the correct retrospective model similar results have been obtained for other models and conditions have also been identified under which the corresponding bayesian property holds namely that the posterior distribution of the odds ratio is the same whether it is computed using the prospective or the retrospective likelihood in this article we demonstrate how these results follow directly from certain parameter independence properties of the models and priors and identify prior laws that support such reverse analysis for both standard and stratified designs somekeywords case controlstudy conditionalindependence hypermarkovlaw logisticregression retrospective likelihood

bayesian analysis of case control studies a bayesian approach to the estimation of an odds ratio from case control data is considered the exact posterior density of the odds ratio and its moments are derived a log normal approximation to the density is shown to be adequate for practical purposes mechanisms for setting prior parameters are discussed and some examples are presented

parameter priors for directed acyclic graphical models and the characterization of several probability distributions we develop simple methods for constructing parameter priors for model choice among directed acyclic graphical dag models in particular we introduce several assumptions that permit the construction of parameter priors for a large number of dag models from a small set of assessments we then present a method for directly computing the marginal likelihood of every dag model given a random sample with no missing observations we apply this methodology to gaussian dag models which consist of a recursive set of linear regression models we show that the only parameter prior for complete gaussian dag models that satisfies our assumptions is the normal wishart distribution our analysis is based on the following new characterization of the wishart distribution let w be an n times n n ge 3 positive definite symmetric matrix of random variables and f w be a pdf of w then f w is a wishart distribution if and only if w 11 w 12 w 22 1 w 12 is independent of w 12 w 22 for every block partitioning w 11 w 12 w 12 w 22 of w similar characterizations of the normal and normal wishart distributions are provided as well

confidence sets for a multivariate distribution on etudie une version multivariable alternative de la bande de confiance unidimensionnelle de kolmogorov smirnov qui preserve l invariance affine

the masking breakdown point of multivariate outlier identification rules abstract in this article we consider simultaneous outlier identification rules for multivariate data generalizing the concept of so called outlier identifiers as presented by davies and gather for the case of univariate samples such multivariate outlier identifiers are based on estimators of location and covariance therefore it seems reasonable that characteristics of the estimators influence the behavior of outlier identifiers several authors mentioned that using estimators with low finite sample breakdown point is not recommended for identifying outliers to give a formal explanation we investigate how the finite sample breakdown points of estimators used in these identification rules influence the masking behavior of the rules

on the stahel donoho estimator and depth weighted means of multivariate data the depth of multivariate data can be used to construct weighted means as robust estimators of location the use of projection depth leads to the stahel donoho estimator as a special case in contrast to maximal depth estimators the depth weighted means are shown to be asymptotically normal under appropriate conditions met by depth functions commonly used in the current literature we also confirm through a finite sample study that the stahel donoho estimator achieves a desirable balance between robustness and efficiency at gaussian models

asymptotic behaviour of s estimates of multivariate location parameters and dispersion matrices it is shown under appropriate conditions that rousseeuw s minimum volume estimator and other s estimators of multivariate location and dispersion parameters are consistent under certain differentiability conditions the estimates are asymptotically normally distributed with a norming factor of n 1 2

a distribution free m estimator of multivariate scatter the existence and uniqueness of a limiting form of a huber type m estimator of multivariate scatter is established under certain conditions on the observed sample these conditions hold with probability one when sampling randomly from a continuous multivariate distribution the existence of the estimator is proven by showing that it is the limiting point of a specific algorithm hence the proof is constructive for continuous populations the estimator of multivariate scatter is shown to be strongly consistent and asymptotically normal an important property of the estimator is that its asymptotic distribution is distribution free with respect to the class of continuous elliptically distributed populations this distribution free property also holds for the finite sample size distribution when the location parameter is known in addition the estimator is the most robust estimator of the scatter matrix of an elliptical distribution in the sense of minimizing the maximum asymptotic variance

a characterization of the dirichlet distribution through global and local parameter independence we provide a new characterization of the dirichlet distribution let theta ij 1 leq i leq k 1 leq j leq n be positive random variables that sum to unity define theta i cdot sigma j 1 n theta ij theta i cdot theta i cdot i 1 k 1 theta j i theta ij sigma j theta ij and theta j i theta j i j 1 n 1 we prove that if theta i cdot theta j 1 dots theta j k are mutually independent and theta cdot j theta i 1 dots theta i n are mutually independent where theta cdot j and theta i j are defined analogously and each parameter set has a strictly positive pdf then the pdf of theta ij is dirichlet this characterization implies that under assumptions made by several previous authors for selecting a bayesian network structure out of a set of candidate structures a dirichlet prior on the parameters is inevitable

regression and ordered categorical variables read before the royal statistical society by professor r l plackett on behalf of the late professor anderson at a meeting organized by the research section on wednesday october 5th 1983 professor j b copas in the chair summary a general approach to regression modelling for ordered categorical response variables y is given which is equally applicable to ordered and unordered y the regressor variables xt xi x may be continuous or categorical the method is based on the logistic family which contains a hierarchy of regression models ranging from ordered to unordered models ordered properties of the former the stereotype model are established the choice between models is made empirically on the basis of model fit this is particularly important for assessed ordered categorical response variables where it is not obvious a priori whether or not the ordering is relevant to the regression relationship model simplification is investigated in terms of whether or not the response categories are distinguishable with respect to x the models are fitted iteratively using the method of maximum likelihood examples are given

a note on tyler s modification of the mad for the stahel donoho estimator in 1994 tyler proposed a modification of the mad in order to achieve the maximal possible finite sample breakdown point for the stahel donoho estimator based upon the median and the modified mad a proof is not given however and as far as we know has not been published yet moreover there seems to be an error concerning the exact definition of the modified mad which is needed to achieve this goal for the sake of theoretical completeness and in order to correct this error we calculate the finite sample breakdown point of modifications of the mad and point out which of these modifications lead to a stahel donoho estimator with maximal finite sample breakdown point

finite sample breakdown points of projection based multivariate location and scatter statistics finite sample breakdown points are obtained for two classes of projection based multivariate location and scatter statistics the stahel donoho statistics and the maronna yohai statistics the definition of these multivariate statistics are dependent on the value of location and scale statistics for all univariate projections of the data and consequently their properties depend on the nature of the corresponding univariate location and scale statistics used on the projected data the finite sample breakdown points of the multivariate statistics though are not directly related to those of the corresponding univariate location and scale statistics a uniform finite sample breakdown point concept is needed the median and the median absolute deviation about the median m a d are one possible choice for the univariate location and scale statistics respectively for sparse data sets in high dimensions though it is not recommended that the m a d be used as the univariate scale statistic for the projected data since its uniform finite sample breakdown point is shown to be much less than optimum a simple modification to the m a d however is shown to alleviate this problem for various reasons one may wish to consider univariate location and scale statistics other than the median and the m a d respectively a very broad and natural class of univariate location and scale statistics to consider for the projected data is the simultaneous m estimates of location and scale new results on their breakdown properties are given in this paper implicit formulas for the breakdown points of monotonic simultaneous m estimates of location and scale are known and they tend to imply rather low breakdown points for smooth choices of the defining weight functions it is shown here that this phenomenon does not occur for a large class of nonmonotonic simultaneous m estimates of location and scale furthermore explicit rather than implicit expressions for the uniform finite sample breakdown points are given for these nonmonotonic m estimates

reliable detection of directional couplings using rank statistics to detect directional couplings from time series various measures based on distances in reconstructed state spaces were introduced these measures can however be biased by asymmetries in the dynamics structure noise color or noise level which are ubiquitous in experimental signals using theoretical reasoning and results from model systems we identify the various sources of bias and show that most of them can be eliminated by an appropriate normalization we furthermore diminish the remaining biases by introducing a measure based on ranks of distances this rank based measure outperforms existing distance based measures concerning both sensitivity and specificity for directional couplings therefore our findings are relevant for a reliable detection of directional couplings from experimental signals

the behavior of the stahel donoho robust multivariate estimator abstract the stahel donoho estimators t v of multivariate location and scatter are defined as a weighted mean and a weighted covariance matrix with weights of the form w r where w is a weight function and r is a measure of outlyingness obtained by considering all univariate projections of the data it has a high breakdown point for all dimensions and order n consistency the asymptotic bias of v for point mass contamination for suitable weight functions is compared with that of rousseeuw s minimum volume ellipsoid mve estimator a simulation shows that for a suitable w t and v exhibit high efficiency for both normal and cauchy distributions and are better than their competitors for normal data with point mass contamination the performances of the estimators for detecting outliers are compared for both a real and a synthetic data set

a bayesian semiparametric model for case control studies with errors in variables summary we develop a model and a numerical estimation scheme for a bayesian approach to inference in case control studies with errors in covariables the model proposed in this paper is based on a nonparametric model for the unknown joint distribution for the missing data the observed covariates and the proxy this nonparametric distribution defines the measurement error component of the model which relates the missing covariates x with a proxy w the oxymoron nonparametric bayes refers to a class of flexible mixture distributions for the likelihood of disease given covariates we choose a logistic regression model by using a parametric disease model and nonparametric exposure model we obtain robust interpretable results quantifying the effect of exposure

asymptotics of reweighted estimators of multivariate location and scatter we investigate the asymptotic behavior ofa weighted sample mean and covariance where the weights are determined by the mahalanobis distances with respect to initial robust estimators we derive an explicit expansion for the weighted estimators from this expansion it can be seen that reweighting does not improve the rate ofconvergence ofthe initial estimators we also show that ifone uses smooth s estimators to determine the weights the weighted estimators are asymptotically normal finally we will compare the efficiency and local robustness of the reweighted s estimators with two other improvements of s estimators estimators and constrained m estimators

granger causality in multivariate time series using a time ordered restricted vector autoregressive model granger causality has been used for the investigation of the inter dependence structure of the underlying systems of multivariate time series in particular the direct causal effects are commonly estimated by the conditional granger causality index cgci in the presence of many observed variables and relatively short time series cgci may fail because it is based on vector autoregressive models var involving a large number of coefficients to be estimated in this paper the var is restricted by a scheme that modifies the recently developed method of backward in time selection bts of the lagged variables and the cgci is combined with bts further the proposed approach is compared favorably to other restricted var representations such as the top down strategy the bottom up strategy and the least absolute shrinkage and selection operator lasso in terms of sensitivity and specificity of cgci this is shown by using simulations of linear and nonlinear low and high dimensional systems and different time series lengths for nonlinear systems cgci from the restricted var representations are compared with analogous nonlinear causality indices further cgci in conjunction with bts and other restricted var representations is applied to multichannel scalp electroencephalogram eeg recordings of epileptic patients containing epileptiform discharges cgci on the restricted var and bts in particular could track the changes in brain connectivity before during and after epileptiform discharges which was not possible using the full var representation

influence function and maximum bias of projection depth based estimators location estimators induced from depth functions increasingly have been pursued and studied in the literature among them are those induced from projection depth functions these projection depth based estimators have favorable properties among their competitors in particular they possess the best possible finite sample breakdown point robustness however robustness of estimators cannot be revealed by the finite sample breakdown point alone the influence function gross error sensitivity maximum bias and contamination sensitivity are also important aspects of robustness in this article we study these other robustness aspects of two types of projection depth based estimators projection medians and projection depth weighted means the latter includes the stahel donoho estimator as a special case exact maximum bias the influence function and contamination and gross error sensitivity are derived and studied for both types of estimators sharp upper bounds for the maximum bias and the influence functions are established comparisons based on these robustness criteria reveal that the projection depth based estimators enjoy desirable local as well as global robustness and are very competitive among their competitors

bayesian analysis of case control studies with categorical covariates in a case control study the appropriate likelihood is the retrospective likelihood i e the likelihood of exposure given disease for the classical frequentist analysis the prospective likelihood i e the likelihood of disease given exposure and the retrospective likelihood produce the same odds ratio estimators for exposure and so logistic regression may be used for both the bayesian analysis is not so simple but the bayesian framework for case control studies offers flexible possibilities for the hierarchical modelling that is needed in many contexts we review the bayesian approaches to the analysis of case control studies developed so far show how to extend these approaches to the situation of a study with any number of categorical or discretised continuous exposure variables and identifying suitable priors we then show how the resulting models may be fitted using markov chain monte carlo methods and provide an illustration based on genotype data

information from the maximized likelihood function suppose x x1 xj is a random sample of either scalar or vector observations from a density f x c where w e q is partitioned into a set 0 01 or of parameters of direct interest and 4 4 1 4 q of nuisance parameters the log likelihood function l x w i logf xi w is assumed to have continuous first and second derivatives on the parameter space q and to have a global maximum at an interior point a i of q at which the likelihood equations are satisfied the information in the sample is defined as minus the matrix of second partial derivatives of the log likelihood that is

robust estimates of location and dispersion for high dimensional datasets the computing times of high breakdown point estimates of multivariate location and scatter increase rapidly with the number of variables which makes them impractical for high dimensional datasets such as those used in data mining we propose an estimator of location and scatter based on a modified version of the gnanadesikan kettenring robust covariance estimate we compare its behavior with that of the stahel donoho sd and rousseeuw and van driessen s fast mcd fmcd estimates in simulations with contaminated multivariate normal data our estimate is almost as good as sd and clearly better than fmcd it is much faster than both especially for large dimension we give examples with real data with dimensions between 5 and 93 in which the proposed estimate is as good as or better than sd and fmcd at detecting outliers and other structures with much shorter computing times

equivalence of prospective and retrospective models in the bayesian analysis of case control studies summary the natural likelihood to use for a case control study is a retrospective likelihood i e a likelihood based on the probability of exposure given disease status prentice pyke 1979 showed that when a logistic regression form is assumed for the probability of disease given exposure the maximum likelihood estimators and asymptotic covariance matrix of the log odds ratios obtained from the retrospective likelihood are the same as those obtained from the prospective likelihood i e that based on probability of disease given exposure we prove a similar result for the posterior distribution of the log odds ratios in a bayesian analysis this means that the bayesian analysis of case control studies may be done using a relatively simple model the logistic regression model which treats data as though generated prospectively and which does not involve nuisance parameters for the exposure distribution

projection estimates of multivariate location in this paper we study the maximum asymptotic bias of the projection estimate for multivariate location based on univariate estimates of location and dispersion in particular we study the projection estimate that uses the median and median absolute deviation about the median mad as univariate location and dispersion estimates respectively this estimator may be considered a natural affine equivariant multivariate median for spherical distributions the maximum bias of this estimate depends only on the marginal distributions and not on the dimension and is approximately twice the maximum bias of the univariate median we also show that for multivariate normal distributions its maximum bias compares favorably with those of the donoho stahel minimum volume ellipsoid and minimum covariance determinant estimates in all these cases the maximum bias increases with the dimension p

multinomial inverse regression for text analysis text data including speeches stories and other document forms are often connected to sentiment variables that are of interest for research in marketing economics and elsewhere it is also very high dimensional and difficult to incorporate into statistical analyses this article introduces a straightforward framework of sentiment sufficient dimension reduction for text data multinomial inverse regression is introduced as a general tool for simplifying predictor sets that can be represented as draws from a multinomial distribution and we show that logistic regression of phrase counts onto document annotations can be used to obtain low dimensional document representations that are rich in sentiment information to facilitate this modeling a novel estimation technique is developed for multinomial logistic regression with very high dimensional response in particular independent laplace priors with unknown variance are assigned to each regression coefficient and we detail an efficient routine for ma

elliptical graphical modelling we propose elliptical graphical models based on conditional uncorrelatedness as a gen eralization of gaussian graphical models by letting the population distribution be elliptical instead of normal allowing the tting of data with arbitrarily heavy tails we study the class of propor tionally ane equivariant scatter estimators and show how they can be used to perform elliptical graphical modelling leading to a new class of partial correlation estimators and analogues of the classical deviance test general expressions for the asymptotic variance of partial correlation esti mators unconstrained and under decomposable models are given and the asymptotic chi square approximation of the pseudo deviance test statistic is proved the feasibility of our approach is demonstrated by a simulation study using among others tyler s scatter estimator which is distribution free within the elliptical model our approach provides a robustication of gauss ian graphical modelling the latter is likelihood based and known to be very sensitive to model misspecication and outlying observations 1 introduction and notation the statistical theory of undirected graphical models for continuous variables is usually based on the assumption of multivariate normality in practice data may deviate from the normal model in various ways outliers and heavy tails pose a problem of particular gravity they frequently occur and the normal likelihood methods such as the sample covariance matrix are very susceptible to them our objective is to deal with heavy tailed data and to safeguard graphical modelling against the impact of faulty outliers we restrict our attention to the case where we have only continuous variables and only undirected edges joint multivariate normality is often assumed in this situation and the statistical methodology is called gaussian graphical modelling we propose the class of elliptical distributions as a more general model and call our approach elliptical graphical modelling the lack of robustness of gaussian graphical modelling has been noted by several authors four proposals of robust approaches to gaussian graphical modelling are known to us becker 2005 and gottard and pacillo 2010 suggest replacing the sample covariance matrix by the reweighted minimum covariance determinant estimator miyamura and kano 2006 propose an alternative m type estimation and finegold drton arxiv 1009 3669 consider robustied versions of the graphical lasso by friedman et al 2008 this article delivers a systematic treatment of the plug in approach used in the rst two ref erences we show that the sample covariance matrix may be replaced by any ane equivariant

unmasking multivariate outliers and leverage points abstract detecting outliers in a multivariate point cloud is not trivial especially when there are several outliers the classical identification method does not always find them because it is based on the sample mean and covariance matrix which are themselves affected by the outliers that is how the outliers get masked to avoid the masking effect we propose to compute distances based on very robust estimates of location and covariance these robust distances are better suited to expose the outliers in the case of regression data the classical least squares approach masks outliers in a similar way also here the outliers may be unmasked by using a highly robust regression method finally a new display is proposed in which the robust regression residuals are plotted versus the robust distances this plot classifies the data into regular observations vertical outliers good leverage points and bad leverage points several examples are discussed

equivalence between conditional and mixture approaches to the rasch model and matched case control studies with applications analyses of data using rasch models including the special case of matched case control studies are common applications of conditional likelihood in which the usual inferential procedures are applied only after conditioning on an approximately ancillary statistic another common approach to the analysis of rasch models is to integrate the nuisance parameters over a mixing distribution using the marginal likelihood obtained as the basis for inference we show that the full conditional likelihood can always be obtained exactly via the marginal approach given a particular choice of mixing distribution and derive necessary and sufficient conditions for the two approaches to agree previous work has shown that with sufficient flexibility in the mixing distribution the maxima of the marginal and conditional likelihoods will be equivalent under concordance criteria our argument requires no such criteria and for any dataset guarantees the equivalence of the whole of the two likelihoods not just their maxi

a class of locally and globally robust regression estimates abstract we present a new class of regression estimates called generalized estimates these estimates are defined by minimizing the scale of the weighted residuals with weights that penalize high leverage observations like the estimates the generalized estimates utilize for their definition two loss functions 1 and 2 which together with the weights can be chosen to achieve simultaneously high breakdown point finite gross error sensitivity and high efficiency we recommend however choosing these functions so as to control the bias behavior of the estimate for a large range of possible contaminations and then boosting the efficiency by a simple least squares reweighting step the generalized estimate with loss functions 1 and 2 is related to the hill ryan gm estimate with a loss function which is a linear combination of 1 and r in fact both estimates have the same influence function and asymptotic distribution under the central model we show that a certain generalized estima

comparison of six methods for the detection of causality in a bivariate time series in this comparative study six causality detection methods were compared namely the granger vector autoregressive test the extended granger test the kernel version of the granger test the conditional mutual information transfer entropy the evaluation of cross mappings between state spaces and an assessment of predictability improvement due to the use of mixed predictions seven test data sets were analyzed linear coupling of autoregressive models a unidirectional connection of two h enon systems a unidirectional connection of chaotic systems of r ossler and lorenz type and of two different r ossler systems an example of bidirectionally connected two species systems a fishery model as an example of two correlated observables without a causal relationship and an example of mediated causality we tested not only 20 phantom rule 0 16em 0ex 000 points long clean time series but also noisy and short variants of the data the standard and the extended granger tests worked only for the autoregressive models the remaining methods were more successful with the more complex test examples although they differed considerably in their capability to reveal the presence and the direction of coupling and to distinguish causality from mere correlation

testing for causality in reconstructed state spaces by an optimized mixed prediction method in this study a method of causality detection was designed to reveal coupling between dynamical systems represented by time series the method is based on the predictions in reconstructed state spaces the results of the proposed method were compared with outcomes of two other methods the granger var test of causality and the convergent cross mapping we used two types of test data the first test example is a unidirectional connection of chaotic systems of rossler and lorenz type the second one the fishery model is an example of two correlated observables without a causal relationship the results showed that the proposed method of optimized mixed prediction was able to reveal the presence and the direction of coupling and distinguish causality from mere correlation as well

model selection through sparse maximum likelihood estimation for multivariate gaussian or binary data we consider the problem of estimating the parameters of a gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse our approach is to solve a maximum likelihood problem with an added l1 norm penalty term the problem as formulated is convex but the memory requirements and complexity of existing interior point methods are prohibitive for problems with more than tens of nodes we present two new algorithms for solving problems with at least a thousand nodes in the gaussian case our first algorithm uses block coordinate descent and can be interpreted as recursive l1 norm penalized regression our second algorithm based on nesterov s first order method yields a complexity estimate with a better dependence on problem size than existing interior point methods using a log determinant relaxation of the log partition function wainwright and jordan 2006 we show that these same algorithms can be used to solve an approximate sparse maximum likelihood problem for the binary case we test our algorithms on synthetic data as well as on gene expression and senate voting records data

on the equivalence of prospective and retrospective likelihood methods in case control studies summary we present new approaches to analyzing case control studies using prospective likelihood methods in the classical framework we extend the equality of the profile likelihoods to the barndorff nielsen modified profile likelihoods for prospective and retrospective models this enables simple and accurate approximate conditional inference for stratified case control studies of moderate stratum size in the bayesian framework we provide sufficient conditions on priors for the prospective model parameters to yield a prospective marginal posterior density equal to its retrospective counterpart our results extend the prospective retrospective equivalence in the bayesian paradigm with a more general class of priors than has previously been investigated

prospective analysis of case control data under general multiplicative intercept risk models summary we show that under a general multiplicative intercept model for risk case control data can be analyzed by maximum likelihood as if they had arisen prospectively up to an unidentifiable multiplicative constant which depends on the relative sampling fractions this generalizes earlier work of anderson 1972 1979 by showing that not only the point estimates but also the standard errors based on the observed information matrix are correct when the prospective likelihood is maximized likelihood ratio testing is also valid under this broad class of risk models data on disease status from a much larger cohort are shown to add no information to the estimation of the covariate related parameters

nearest neighbor variance estimation nnve robust covariance estimation commonly proceeds by downweighting outliers in this article we measure the outlyingness of a data point by the standardized distance between the point and its kth nearest neighbor the appropriate weights for robust estimation are found by a model based mixture modeling approach that follows from considering the data cloud as a realization of a high dimensional point process to correct a potential bias when there are no outliers we introduce a boundary correction procedure that artificially adds in extra outlying points the resulting methodology is called nearest neighbor variance estimation nnve the strength of nnve is its robustness against a large proportion of noise points and against deviation from normality of the signal a consistency result for the method is established under some reasonable assumptions it is shown that the covariance estimate is bounded and that each point has only bounded influence on the final estimates nnve outperformed the popular mini

robust multivariate tolerance regions influence function and monte carlo study in this article we define a class of multivariate tolerance regions that turn out to be more resistant than the classical ones to outliers the tolerance factors are numerically evaluated under the central model and the sensitivity to deviations from the normal distribution for moderate samples is studied through a monte carlo study moreover the influence function of the coverage probability allows us to compare the sensitivity of different proposals to anomalous data finally real data examples are discussed

outlier detection for high dimensional data outlier detection is an integral component of statistical modelling and estimation for high dimensional data classical methods based on the mahalanobis distance are usually not applicable we propose an outlier detection procedure that replaces the classical minimum covariance determinant estimator with a high breakdown minimum diagonal product estimator the cut off value is obtained from the asymptotic distribution of the distance which enables us to control the type i error and deliver robust outlier detection simulation studies show that the proposed method behaves well for high dimensional data