the bivariate probit model maximum likelihood estimation pseudo true parameters and partial identification abstract this paper examines the notion of identification by functional form for two equation triangular systems for binary endogenous variables by providing a bridge between the literature on the recursive bivariate probit model and that on partial identification we evaluate the impact of functional form on the performance of quasi maximum likelihood estimators and investigate the practical importance of available instruments in both cases of correct and incorrect distributional specification finally we calculate average treatment effect bounds and demonstrate how properties of the estimators are explicable via a link between the notion of pseudo true parameters and the concepts of partial identification

a new skewed link model for dichotomous quantal response data abstract the logit probit and student t links are widely used in modeling dichotomous quantal response data most of the commonly used link functions are symmetric except the complementary log log link however in some applications the overall fit can be significantly improved by the use of an asymmetric link in this article we propose a new skewed link model for analyzing binary response data with covariates introducing a skewed distribution for the underlying latent variable we develop a class of asymmetric link models for binary response data using a bayesian approach we first characterize the propriety of the posterior distributions using standard improper priors we further propose informative priors using historical data from a similar previous study we examine the proposed method through a large scale simulation study and use data from a prostate cancer study to demonstrate the use of historical data in bayesian model fitting and comparison of skewed link models

the heteroscedastic graded response model with a skewed latent trait testing statistical and substantive hypotheses related to skewed item category functions the graded response model grm samejima estimation of ability using a response pattern of graded scores psychometric monograph no 17 richmond va the psychometric society 1969 can be derived by assuming a linear regression of a continuous variable z on the trait to underlie the ordinal item scores takane de leeuw in psychometrika 52 393 408 1987 traditionally a normal distribution is specified for z implying homoscedastic error variances and a normally distributed in this paper we present the heteroscedastic grm with skewed latent trait which extends the traditional grm by incorporation of heteroscedastic error variances and a skew normal latent trait an appealing property of the extended grm is that it includes the traditional grm as a special case this enables specific tests on the normality assumption of z we show how violations of normality in z can lead to asymmetrical category response functions the ability to test this normality assumption is beneficial from both a statistical and substantive perspective in a simulation study we show the viability of the model and investigate the specificity of the effects we apply the model to a dataset on affect and a dataset on alexithymia

convex linear combinations of compositions summary when a sampled target composition is suspected of being a mixture of different compositions from a number of independent sources the question of the nature of the mixing mechanism arises for the resolution of this question several models involving convex linear mixtures of compositions are considered and in particular the distributional problem of describing the pattern of variability of the target compositions given information about the source distributions is resolved in terms of approximations involving logistic normal and logistic skew normal distributions the quality of these approximations is shown to be satisfactory through a series of simulations briefly reported the modelling and subsequent statistical inference are motivated by an illustrative application to investigating the nature of pollution at three fishing locations in a scottish loch

hidden markov models with nonelliptically contoured state densities hidden markov models hmms are a popular approach for modeling sequential data comprising continuous attributes in such applications the observation emission densities of the hmm hidden states are typically modeled by means of elliptically contoured distributions usually multivariate gaussian or student s t densities however elliptically contoured distributions cannot sufficiently model heavy tailed or skewed populations which are typical in many fields such as the financial and the communication signal processing domain employing finite mixtures of such elliptically contoured distributions to model the hmm state densities is a common approach for the amelioration of these issues nevertheless the nature of the modeled data often requires postulation of a large number of mixture components for each hmm state which might have a negative effect on both model efficiency and the training data set s size required to avoid overfitting to resolve these issues in this paper we advocate for the utilization of a nonelliptically contoured distribution the multivariate normal inverse gaussian mnig distribution for modeling the observation densities of hmms as we experimentally demonstrate our selection allows for more effective modeling of skewed and heavy tailed populations in a simple and computationally efficient manner

distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution summary a fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry and to generate a whole set of non symmetric densities the approach is sufficiently general to encompass some recent proposals in the literature variously related to the skew normal distribution the special case of skew elliptical densities is examined in detail establishing connections with existing similar work the final part of the paper specializes further to a form of multivariate skew t density likelihood inference for this distribution is examined and it is illustrated with numerical examples

asymptotic robustness study of the polychoric correlation estimation asymptotic robustness against misspecification of the underlying distribution for the polychoric correlation estimation is studied the asymptotic normality of the pseudo maximum likelihood estimator is derived using the two step estimation procedure the t distribution assumption and the skew normal distribution assumption are used as alternatives to the normal distribution assumption in a numerical study the numerical results show that the underlying normal distribution can be substantially biased even though skewness and kurtosis are not large the skew normal assumption generally produces a lower bias than the normal assumption thus it is worth using a non normal distributional assumption if the normal assumption is dubious

linear mixed models for skew normal independent bivariate responses with an application to periodontal disease bivariate clustered correlated data often encountered in epidemiological and clinical research are routinely analyzed under a linear mixed model framework with underlying normality assumptions of the random effects and within subject errors however such normality assumptions might be questionable if the data set particularly exhibit skewness and heavy tails using a bayesian paradigm we use the skew normal independent sni distribution as a tool for modeling clustered data with bivariate non normal responses in a linear mixed model framework the sni distribution is an attractive class of asymmetric thick tailed parametric structure which includes the skew normal distribution as a special case we assume that the random effects follows multivariate skew normal independent distributions and the random errors follow symmetric normal independent distributions which provides substantial robustness over the symmetric normal process in a linear mixed model framework specific distributions obtained as special cases viz the skew t the skew slash and the skew contaminated normal distributions are compared along with the default skew normal density the methodology is illustrated through an application to a real data which records the periodontal health status of an interesting population using periodontal pocket depth ppd and clinical attachment level cal

efficient estimation of large portfolio loss probabilities in t copula models we consider the problem of accurately measuring the credit risk of a portfolio consisting of loans bonds and other financial assets one particular performance measure of interest is the probability of large portfolio losses over a fixed time horizon we revisit the so called t copula that generalizes the popular normal copula to allow for extremal dependence among defaults by utilizing the asymptotic description of how the rare event occurs we derive two simple simulation algorithms based on conditional monte carlo to estimate the probability that the portfolio incurs large losses under the t copula we further show that the less efficient estimator exhibits bounded relative error an extensive simulation study demonstrates that both estimators outperform existing algorithms we then discuss a generalization of the t copula model that allows the multivariate defaults to have an asymmetric distribution lastly we show how the estimators proposed for the t copula can be modified to estimate the portfolio risk under the skew t copula model

mean variance skewness efficient surfaces stein s lemma and the multivariate extended skew student distribution abstract recent advances in stein s lemma imply that under elliptically symmetric distributions all rational investors will select a portfolio which lies on markowitz mean variance efficient frontier this paper describes extensions to stein s lemma for the case when a random vector has the multivariate extended skew student distribution under this distribution rational investors will select a portfolio which lies on a single mean variance skewness efficient hyper surface the same hyper surface arises under a broad class of models in which returns are defined by the convolution of a multivariate elliptically symmetric distribution and a multivariate distribution of non negative random variables efficient portfolios on the efficient surface may be computed using quadratic programming

model comparison of coordinate free multivariate skewed distributions with an application to stochastic frontiers we consider classes of multivariate distributions which can model skewness and are closed under orthogonal transformations we review two classes of such distributions proposed in the literature and focus our attention on a particular yet quite flexible subclass of one of these classes members of this subclass are defined by affine transformations of univariate skewed distributions that ensure the existence of a set of coordinate axes along which there is independence and the marginals are known analytically the choice of an appropriate m dimensional skewed distribution is then restricted to the simpler problem of choosing m univariate skewed distributions we introduce a bayesian model comparison setup for selection of these univariate skewed distributions the analysis does not rely on the existence of moments allowing for any tail behaviour and uses equivalent priors on the common characteristics of the different models finally we apply this framework to multi output stochastic frontiers using data from dutch dairy farms

on robustness of the normal theory based asymptotic distributions of three reliability coefficient estimates this paper studies the asymptotic distributions of three reliability coefficient estimates sample coefficient alpha the reliability estimate of a composite score following a factor analysis and the estimate of the maximal reliability of a linear combination of item scores following a factor analysis results indicate that the asymptotic distribution for each of the coefficient estimates obtained based on a normal sampling distribution is still valid within a large class of nonnormal distributions therefore a formula for calculating the standard error of the sample coefficient alpha recently obtained by van zyl neudecker and nel applies to other reliability coefficients and can still be used even with skewed and kurtotic data such as are typical in the social and behavioral sciences

bivariate random effect model using skew normal distribution with application to hiv rna correlated data arise in a longitudinal studies from epidemiological and clinical research random effects models are commonly used to model correlated data mostly in the longitudinal data setting we assume that the random effects and within subject errors are normally distributed however the normality assumption may not always give robust results particularly if the data exhibit skewness in this paper we develop a bayesian approach to bivariate mixed model and relax the normality assumption by using a multivariate skew normal distribution specifically we compare various potential models and illustrate the procedure using a real data set from hiv study

a heckman selection t model sample selection arises often in practice as a result of the partial observability of the outcome of interest in a study in the presence of sample selection the observed data do not represent a random sample from the population even after controlling for explanatory variables that is data are missing not at random thus standard analysis using only complete cases will lead to biased results heckman introduced a sample selection model to analyze such data and proposed a full maximum likelihood estimation method under the assumption of normality the method was criticized in the literature because of its sensitivity to the normality assumption in practice data such as income or expenditure data often violate the normality assumption because of heavier tails we first establish a new link between sample selection models and recently studied families of extended skew elliptical distributions then this allows us to introduce a selection t slt model which models the error distribution using a st

the multivariate skew normal distribution summary the paper extends earlier work on the so called skew normal distribution a family of distributions including the normal but with an extra parameter to regulate skewness the present work introduces a multivariate parametric family such that the marginal densities are scalar skew normal and studies its properties with special emphasis on the bivariate case

random overlap structures properties and applications to spin glasses random overlap structures rost s are random elements on the space of probability measures on the unit ball of a hilbert space where two measures are identified if they differ by an isometry in spin glasses they arise as natural limits of gibbs measures under the appropriate algebra of functions we prove that the so called cavity mapping on the space of rost s is continuous leading to a proof of the stochastic stability conjecture for the limiting gibbs measures of a large class of spin glass models similar arguments yield the proofs of a number of other properties of rost s that may be useful in future attempts at proving the ultrametricity conjecture lastly assuming that the ultrametricity conjecture holds the setup yields a constructive proof of the parisi formula for the free energy of the sherrington kirkpatrick model by making rigorous a heuristic of aizenman sims and starr

estimation and prediction in linear mixed models with skew normal random effects for longitudinal data this paper extends the classical linear mixed model by considering a multivariate skew normal assumption for the distribution of random effects we present an efficient hybrid ecme nr algorithm for the computation of maximum likelihood estimates of parameters a score test statistic for testing the existence of skewness preference among random effects is developed the technique for the prediction of future responses under this model is also investigated the methodology is illustrated through an application to framingham cholesterol data and a simulation study

conjugate bayes for probit regression via unified skew normal distributions regression models for dichotomous data are ubiquitous in statistics besides being useful for inference on binary responses these methods serve also as building blocks in more complex formulations such as density regression nonparametric classification and graphical models within the bayesian framework inference proceeds by updating the priors for the coefficients typically set to be gaussians with the likelihood induced by probit or logit regressions for the responses in this updating the apparent absence of a tractable posterior has motivated a variety of computational methods including markov chain monte carlo routines and algorithms which approximate the posterior despite being routinely implemented markov chain monte carlo strategies face mixing or time inefficiency issues in large p and small n studies whereas approximate routines fail to capture the skewness typically observed in the posterior this article proves that the posterior distribution for the probit coefficients has a unified skew normal kernel under gaussian priors such a novel result allows efficient bayesian inference for a wide class of applications especially in large p and small to moderate n studies where state of the art computational methods face notable issues these advances are outlined in a genetic study and further motivate the development of a wider class of conjugate priors for probit models along with methods to obtain independent and identically distributed samples from the unified skew normal posterior

a new kurtosis matrix with statistical applications abstract the number of fourth order moments which can be obtained from a random vector rapidly increases with the vector s dimension scalar measures of multivariate kurtosis may not satisfactorily capture the fourth order structure and matrix measures of multivariate kurtosis are called for in this paper we propose a kurtosis matrix derived from the dominant eigenpair of the fourth standardized moment we show that it is the best symmetric positive semidefinite kronecker square root approximation to the fourth standardized moment additional properties are derived for realizations from garch and reversible random processes statistical applications include independent component analysis and projection pursuit the star product of matrices highlights the connection between the proposed kurtosis matrix and other kurtosis matrices which appeared in the statistical literature a simulation study assesses the practical relevance of theoretical results in the paper

semiparametric mean field variational bayes general principles and numerical issues we introduce the term semiparametric mean field variational bayes to describe the relaxation of mean field variational bayes in which some density functions in the product density restriction are pre specified to be members of convenient parametric families this notion has appeared in various guises in the mean field variational bayes literature during its history and we endeavor to unify this important topic we lay down a general framework and explain how previous relevant methodologies fall within this framework a major contribution is elucidation of numerical issues that impact semiparametric mean field variational bayes in practice

a note on mar identifying restrictions model comparison and sensitivity analysis in pattern mixture models with and without covariates for incomplete data summary pattern mixture modeling is a popular approach for handling incomplete longitudinal data such models are not identifiable by construction identifying restrictions is one approach to mixture model identification little 1995 journal of the american statistical association 90 1112 1121 little and wang 1996 biometrics 52 98 111 thijs et al 2002 biostatistics 3 245 265 kenward molenberghs and thijs 2003 biometrika 90 53 71 daniels and hogan 2008 in missing data in longitudinal studies strategies for bayesian modeling and sensitivity analysis and is a natural starting point for missing not at random sensitivity analysis thijs et al 2002 biostatistics 3 245 265 daniels and hogan 2008 in missing data in longitudinal studies strategies for bayesian modeling and sensitivity analysis however when the pattern specific models are multivariate normal identifying restrictions corresponding to missing at random mar may not exist furthermore identification strategies can be problematic in models with covariates e g baseline covariates with time invariant coefficients in this article we explore conditions necessary for identifying restrictions that result in mar to exist under a multivariate normality assumption and strategies for identifying sensitivity parameters for sensitivity analysis or for a fully bayesian analysis with informative priors in addition we propose alternative modeling and sensitivity analysis strategies under a less restrictive assumption for the distribution of the observed response data we adopt the deviance information criterion for model comparison and perform a simulation study to evaluate the performances of the different modeling approaches we also apply the methods to a longitudinal clinical trial problems caused by baseline covariates with time invariant coefficients are investigated and an alternative identifying restriction based on residuals is proposed as a solution

a semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error summary a common objective in longitudinal studies is to characterise the relationship between a failure time process and time independent and time dependent covariates timedependent covariates are generally available as longitudinal data collected periodically during the course of the study we assume that these data follow a linear mixed effects model with normal measurement error and that the hazard of failure depends both on the underlying random effects describing the covariate process and other time independent covariates through a proportional hazards relationship a routine assumption is that the random effects are normally distributed however this need not hold in practice within this framework we develop a simple method for estimating the proportional hazards model parameters that requires no assumption on the distribution of the random effects large sample properties are discussed and finite sample performance is assessed and compared to competing methods via simulation

robustness in real life a study of clinical laboratory data previous studies have evaluated the performance of robust estimators of location using computer generated distributions this paper describes how distributions commonly seen in biomedical research differ from the simulated distributions and compares the performance of six families of estimators using samples from four biomedical distributions the biomedical distributions can be asymmetric and have shorter tails and other anomalies such as digit preferences which are not modeled in simulation studies the four biomedical distributions studied differ markedly from the models previously studied and these differences strongly affect the robust estimators in such situations the trimmed mean provides an improvement over the sample mean and its performance is more stable than that of estimators whose psi functions have steeply descending tails the central value and dispersion of each of the estimators are evaluated

bifurcation analysis in an approachable haematopoietic stem cells model a haematopoietic stem cells model hsc with one delay is considered at first we investigate the stability and existence of hopf bifurcations by analyzing the distribution of the roots of associated characteristic equation then an explicit formula for determining the stability and the direction of periodic solutions bifurcating from hopf bifurcations is derived using the normal form theory and center manifold argument finally some numerical simulations are carried out for supporting the analytic results

conditional estimation for generalized linear models when covariates are subject specific parameters in a mixed model for longitudinal measurements the relationship between a primary endpoint and features of longitudinal profiles of a continuous response is often of interest and a relevant framework is that of a generalized linear model with covariates that are subject specific random effects in a linear mixed model for the longitudinal measurements naive implementation by imputing subject specific effects from individual regression fits yields biased inference and several methods for reducing this bias have been proposed these require a parametric normality assumption on the random effects which may be unrealistic adapting a strategy of stefanski and carroll 1987 biometrika74 703 716 we propose estimators for the generalized linear model parameters that require no assumptions on the random effects and yield consistent inference regardless of the true distribution the methods are illustrated via simulation and by application to a study of bone mineral density in women transitioning to menopause

semiparametric bayesian latent variable regression for skewed multivariate data for many real life studies with skewed multivariate responses the level of skewness and association structure assumptions are essential for evaluating the covariate effects on the response and its predictive distribution we present a novel semiparametric multivariate model and associated bayesian analysis for multivariate skewed responses similar to multivariate gaussian densities this multivariate model is closed under marginalization allows a wide class of multivariate associations and has meaningful physical interpretations of skewness levels and covariate effects on the marginal density other desirable properties of our model include the markov chain monte carlo computation through available statistical software and the assurance of consistent bayesian estimates of the parameters and the nonparametric error density under a set of plausible prior assumptions we illustrate the practical advantages of our methods over existing alternatives via simulation studies and the analysis of a clinical study on periodontal disease

renyi entropy and complexity measure for skew gaussian distributions and related families abstract in this paper we provide the renyi entropy and complexity measure for a novel flexible class of skew gaussian distributions and their related families as a characteristic form of the skew gaussian shannon entropy we give closed expressions considering a more general class of closed skew gaussian distributions and the weighted moments estimation method in addition closed expressions of renyi entropy are presented for extended skew gaussian and truncated skew gaussian distributions finally additional inequalities for skew gaussian and extended skew gaussian renyi and shannon entropies are reported

statistical applications of the multivariate skew normal distribution azzalini and dalla valle have recently discussed the multivariate skew normal distribution which extends the class of normal distributions by the addition of a shape parameter the first part of the present paper examines further probabilistic properties of the distribution with special emphasis on aspects of statistical relevance inferential and other statistical issues are discussed in the following part with applications to some multivariate statistics problems illustrated by numerical examples finally a further extension is described which introduces a skewing factor of an elliptical density

predicting false discovery proportion under dependence we present a flexible framework for predicting error measures in multiple testing situations under dependence our approach is based on modeling the distribution of the probit transform of the p values by mixtures of multivariate skew normal distributions the model can incorporate dependence among p values and it allows for shape restrictions on the p value density a nonparametric bayesian scheme for estimating the components of the mixture model is outlined and markov chain monte carlo algorithms are developed these lead to the prediction of false discovery proportion and related credible bands an expression for the positive false discovery rate for dependent observations is also derived the power of the mixture model in estimation of key quantities in multiple testing is illustrated by a simulation study a dataset on kidney transplant is also analyzed using the methods developed

closed form reml estimators and sample size determination for mixed effects models for repeated measures under monotone missingness we derive the closed form restricted maximum likelihood estimator and kenward roger s variance estimator for fixed effects in the mixed effects model for repeated measures mmrm when the missing data pattern is monotone as an important application of the analytic result we present the formula for calculating the power of treatment comparison using the wald t test with the kenward roger adjusted variance estimate in mmrm it allows adjustment for baseline covariates without the need to specify the covariate distribution in randomized trials a simple two step procedure is proposed to determine the sample size needed to achieve the targeted power the proposed method performs well for both normal and moderately non normal data even in small samples n 20 in simulations an antidepressant trial is analyzed for illustrative purposes copyright 2017 john wiley sons ltd

modeling spatial processes with unknown extremal dependence class abstractmany environmental processes exhibit weakening spatial dependence as events become more extreme well known limiting models such as max stable or generalized pareto processes cannot capture this which can lead to a preference for models that exhibit a property known as asymptotic independence however weakening dependence does not automatically imply asymptotic independence and whether the process is truly asymptotically in dependent is usually far from clear the distinction is key as it can have a large impact upon extrapolation that is the estimated probabilities of events more extreme than those observed in this work we present a single spatial model that is able to capture both dependence classes in a parsimonious manner and with a smooth transition between the two cases the model covers a wide range of possibilities from asymptotic independence through to complete dependence and permits weakening dependence of extremes even under asymptotic dependence censored likelihood based

value of information analysis and bayesian inversion for closed skew normal distributions applications to seismic amplitude variation with offset data abstractinformation analysis can be used in the context of reservoir decisions under uncertainty to evaluate whether additional data e g seismic data are likely to be useful in impacting the decision such evaluation of geophysical information sources depends on input modeling assumptions we studied results for bayesian inversion and value of information analysis when the input distributions are skewed and non gaussian reservoir parameters and seismic amplitudes are often skewed and using models that capture the skewness of distributions the input assumptions are less restrictive and the results are more reliable we examined the general methodology for value of information analysis using closed skew normal sn distributions as an example we found a numerical case with porosity and saturation as reservoir variables and computed the value of information for seismic amplitude variation with offset intercept and gradient all modeled with closed sn distributions sensitivity of the value of informa

locally efficient semiparametric estimators for generalized skew elliptical distributions we consider a class of generalized skew normal distributions that is useful for selection modeling and robustness analysis and derive a class of semiparametric estimators for the location and scale parameters of the central part of the model we show that these estimators are consistent and asymptotically normal we present the semiparametric efficiency bound and derive the locally efficient estimator that achieves this bound if the model for the skewing function is correctly specified the estimators that we propose are consistent and asymptotically normal even if the model for the skewing function is misspecified and we compute the loss of efficiency in such cases we conduct a simulation study and provide an illustrative example our method is applicable to generalized skew elliptical distributions

hopf bifurcation in differential equations with delay for tumor immune system competition model this paper deals with the qualitative analysis of the solutions to a model that refers to the competition between the immune system and an aggressive host such as a tumor the model which describes this competition is governed by a system of differential equations with one delay it is shown that the dynamics depends crucially on the time delay parameter by using the time delay as a parameter of bifurcation the analysis is focused on the hopf bifurcation problem to predict the occurrence of a limit cycle bifurcating from the nontrivial steady state the obtained results depict the oscillations given by simulations see m galach int j appl math comput sci 13 2003 pp 395 406 which are observed in reality see d kirschner and j c panetta j math biol 37 1998 pp 235 252 it is suggested to examine by laboratory experiments how to employ these results for control of tumor growth

ica based on asymmetry we build a new approach to ica which is based on the data asymmetry instead of densities with heavy tails we use asymmetric ones split gaussians we verified our approach on images sound and eeg data in the case of source signal reconstructing our approach gives better results independent component analysis ica one of the basic tools in data analysis aims to find a coordinate system in which the components of the data are independent most of existing methods are based on the minimization of the function of fourth order moment kurtosis skewness third order moment has received much less attention in this paper we present a competitive approach to ica based on the split gaussian distribution which is well adapted to asymmetric data consequently we obtain a method which works better than the classical approaches especially in the case when the underlying density is not symmetric which is a typical situation in the color distribution in images

asymptotic form of the kullback leibler divergence for multivariate asymmetric heavy tailed distributions abstract an asymptotic expression for the kullback leibler kl divergence measure of multivariate skew t distributions mst is derived this novel class of flexible family distributions incorporates a shape and degree of freedom parameters in order to manipulate the skewness and heavy tail presence of the data respectively the quadratic form expressions of mst models are used to provide asymptotic measures additional inequalities for mst entropy and simulation studies are reported finally the expected values of the kl divergence of a sample correlation matrix obtained by pearson s correlation coefficient are discussed

skew normal antedependence models for skewed longitudinal data antedependence models also known as transition models have proven to be useful for longitudinal data exhibiting serial correlation especially when the variances and or same lag correlations are time varying statistical inference procedures associated with normal antedependence models are well developed and have many nice properties but they are not appropriate for longitudinal data that exhibit considerable skewness we propose two direct extensions of normal antedependence models to skew normal antedependence models the first is obtained by imposing antedependence on a multivariate skew normal distribution and the second is a sequential autoregressive model with skew normal innovations for both models necessary and sufficient conditions for formula see text th order antedependence are established and likelihood based estimation and testing procedures for models satisfying those conditions are developed the procedures are applied to simulated data and to real data from a study of cattle growth

a stein type lemma for the multivariate generalized hyperbolic distribution abstract when two variables are bivariate normally distributed stein s 1973 1981 seminal lemma provides a convenient expression for the covariance of the first variable with a function of the second the lemma has proven to be useful in various disciplines including statistics probability decision theory and finance in finance however asset returns do not always display symmetry but may exhibit skewness this observation led adcock 2007 2010 2014 to develop stein s type lemmas for certain multivariate distributions that are consistent with simaan s 1987 1993 setting for asset returns in this paper we depart from simaan s setting and develop a new stein s type lemma in the setting of a mean variance mixture model for returns as a particular application we show that expected utility maximizers select portfolios that are mean variance skewness efficient

gaussian process regression with skewed errors abstract in statistical literature the gaussian process is used as a prior process to treat a non linear regression from a bayesian viewpoint with normally distributed error terms in this paper we modify the gaussian process regression gpr model by assuming the error terms of the gpr model follow a skew normal distribution instead of the normal distribution we refer to this new modification as the gaussian process regression with skewed errors gprse a key advantage of our model is that the well known gpr model is a subclass of the gprse model most importantly we derive its predictive distribution for a new input location in a closed form moreover the marginal likelihood of the gprse model is derived and is used to train the model hyper parameters we also conduct simulation experiments to demonstrate the efficiency of our proposed approach compared to the gpr model

a model of immune system with time dependent immune reactivity abstract in this paper we deal with the marchuk model of an immune system among the main parameters of the model are the coefficients which describe the state of infected organism and the rate of production of antibodies in the classical model these coefficients are constants we consider the case when these coefficients are time dependent in particular we are interested in the case of periodic coefficients which can describe periodic changes of the immune reactivity due to periodic changes of the environment we examine the asymptotic behaviour of solutions under some assumptions we prove that the solutions tend to periodic functions we also present the results of numerical simulations to illustrate the behaviour of solutions

a class of asymmetric pathway distributions and an entropy interpretation abstract asymmetric distributions are widely used in probability modeling and statistical analysis recently various asymmetric distributions are being developed by many researchers for modeling various data sets in real life contexts in the present paper we introduce a new class of q type asymmetric distributions which include q analogues of asymmetric laplace exponential power weibull etc and corresponding standard distributions as special cases also we show that this pathway model can be obtained by optimizing mathai s generalized entropy with more general setup which is a generalization of various entropy measures due to shannon and others

quadratic forms in skew normal variates in this paper first a characterization of the multivariate skew normal distribution is given then the joint moment generating functions of two quadratic forms and a linear compound and a quadratic form in skew normal variates have been derived and conditions for their independence are given distribution of the ratios of quadratic forms in skew normal variates has also been studied

stability and bifurcations for the chronic state in marchuk s model of an immune system in the paper we present known and new results concerning stability and the hopf bifurcation for the positive steady state describing a chronic disease in marchuk s model of an immune system we describe conditions guaranteeing local stability or instability of this state in a general case and for very strong immune system we compare these results with the results known in the literature we show that the positive steady state can be stable only for very specific parameter values stability analysis is illustrated by mikhailov s hodographs and numerical simulations conditions for the hopf bifurcation and stability of arising periodic orbit are also studied these conditions are checked for arbitrary chosen realistic parameter values numerical examples of arising due to the hopf bifurcation periodic solutions are presented

analysis of small sample size studies using nonparametric bootstrap test with pooled resampling method experimental studies in biomedical research frequently pose analytical problems related to small sample size in such studies there are conflicting findings regarding the choice of parametric and nonparametric analysis especially with non normal data in such instances some methodologists questioned the validity of parametric tests and suggested nonparametric tests in contrast other methodologists found nonparametric tests to be too conservative and less powerful and thus preferred using parametric tests some researchers have recommended using a bootstrap test however this method also has small sample size limitation we used a pooled method in nonparametric bootstrap test that may overcome the problem related with small samples in hypothesis testing the present study compared nonparametric bootstrap test with pooled resampling method corresponding to parametric nonparametric and permutation tests through extensive simulations under various conditions and using real data examples the nonparametric pooled bootstrap t test provided equal or greater power for comparing two means as compared with unpaired t test welch t test wilcoxon rank sum test and permutation test while maintaining type i error probability for any conditions except for cauchy and extreme variable lognormal distributions in such cases we suggest using an exact wilcoxon rank sum test nonparametric bootstrap paired t test also provided better performance than other alternatives nonparametric bootstrap test provided benefit over exact kruskal wallis test we suggest using nonparametric bootstrap test with pooled resampling method for comparing paired or unpaired means and for validating the one way analysis of variance test results for non normal data in small sample size studies copyright 2017 john wiley sons ltd

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

modeling non stationary asymmetric lens blur by normal sinh arcsinh model images acquired by a camera show lens blur due to imperfection in the optical system even when images are properly focused lens blur is non stationary in a sense that the amount of blur depends on pixel locations in a sensor lens blur is also asymmetric in a sense that the amount of blur is different in the radial and tangential directions and also in the inward and outward radial directions this paper presents parametric blur kernel models based on the normal sinh arcsinh distribution function the proposed models can provide flexible shapes of blur kernels with a different symmetry and skewness to model complicated lens blur due to optical aberration in a properly focused images accurately blur of single focal length lenses is estimated and the accuracy of the models is compared with the existing parametric blur models an advantage of the proposed models is demonstrated through deblurring experiments

the nontruncated marginal of a truncated bivariate normal distribution inference is considered for the marginal distribution ofx when x y has a truncated bivariate normal distribution they variable is truncated but only thex values are observed the relationship of this distribution to azzalini s skew normal distribution is obtained method of moments and maximum likelihood estimation are compared for the three parameter azzalini distribution samples that are uniformative about the skewness of this distribution may occur even for largen profile likelihood methods are employed to describe the uncertainty involved in parameter estimation a sample of 87 otis test scores is shown to be well described by this model

backward bifurcation of an epidemic model with saturated treatment function an epidemic model with saturated incidence rate and saturated treatment function is studied here the treatment function adopts a continuous and differentiable function which can describe the effect of delayed treatment when the number of infected individuals is getting larger and the medical condition is limited the global dynamics of the model indicate that the basic reproduction number being the unity is a strict threshold for disease eradication when such effect is weak however it is shown that a backward bifurcation will take place when this delayed effect for treatment is strong therefore driving the basic reproduction number below the unity is not enough to eradicate the disease and a critical value at the turning point is deduced as a new threshold some sufficient conditions for the disease free equilibrium and the endemic equilibrium being globally asymptotically stable are also obtained mathematical results in this paper suggest that giving the patients timely treatment improving the cure efficiency and decreasing the infective coefficient are all valid methods for the control of disease

the multivariate g and h distribution in this article we consider a generalization of the univariate g and h distribution to the multivariate situation with the aim of providing a flexible family of multivariate distributions that incorporate skewness and kurtosis the approach is to modify the underlying random variables and their quantiles directly giving rise to a family of distributions in which the quantiles rather than the densities are the foci of attention using the ideas of multivariate quantiles we show how to fit multivariate data to our multivariate g and h distribution this provides a more flexible family than the skew normal and skew elliptical distributions when quantiles are of principal interest unlike those families the distribution of quadratic forms from the multivariate g and h distribution depends on the underlying skewness we illustrate our methods on australian athletes data as well as on some wind speed data from the northwest pacific

likelihood inferences on semiparametric odds ratio model a flexible semiparametric odds ratio model has been proposed to unify and to extend both the log linear model and the joint normal model for data with a mix of discrete and continuous variables the semiparametric odds ratio model is particularly useful for analyzing biased sampling designs however statistical inference of the model has not been systematically studied when more than one nonparametric component is involved in the model in this article we study the maximum semiparametric likelihood approach to estimation and inference of the semiparametric odds ratio model we show that the maximum semiparametric likelihood estimator of the odds ratio parameter is consistent and asymptotically normally distributed we also establish statistical inference under a misspecified semiparametric odds ratio model which is important when handling weak identifiability in conditionally specified models under biased sampling designs we use simulation studies to demonstrate that the proposed approaches have satis

a variational bayesian approach for inverse problems with skew t error distributions in this work we develop a novel robust bayesian approach to inverse problems with data errors following a skew t distribution a hierarchical bayesian model is developed in the inverse problem setup the bayesian approach contains a natural mechanism for regularization in the form of a prior distribution and a lasso type prior distribution is used to strongly induce sparseness we propose a variational type algorithm by minimizing the kullback leibler divergence between the true posterior distribution and a separable approximation the proposed method is illustrated on several two dimensional linear and nonlinear inverse problems e g cauchy problem and permeability estimation problem

correlation curves measures of association as functions of covariate values for experiments where the strength of association between a response variable y and a covariate x is different over different regions of values for the covariate x we propose local nonparametric dependence functions which measure the strength of association between y and x as a function of x x our dependence functions are extensions of galton s idea of strength of co relation from the bivariate normal case to the nonparametric case in particular a dependence function is obtained by expressing the usual galton pearson correlation coefficient in terms of the regression line slope 3 and the residual variance o 2 and then replacing 3 and 72 by a nonparametric regression slope 13 x and a nonparametric residual variance o 2 x var yix respectively our local dependence functions are standardized nonparametric regression curves which provide universal scale free measures of the strength of the relationship between variables in nonlinear models they share most of the properties of the correlation coefficient and they reduce to the usual correlation coefficient in the bivariate normal case for this reason we call them correlation curves we show that in a certain sense they quantify lehmann s notion of regression dependence finally the correlation curve concept is illustrated using data from a study of the relationship between cholesterol levels x and triglyceride concentrations y of heart patients