an exact test for multiple inequality and equality constraints in the linear regression model abstract in this article we consider the linear regression model y x e where e is n 0 2i in this context we derive exact tests of the form h r r versus k rk for the case in which 2 is unknown we extend these results to consider hypothesis tests of the form h r1 r1 and r2 r2 versus k rk for each of these hypotheses tests we derive several equivalent forms of the test statistics using the duality theory of the quadratic programming for both tests we derive their exact distribution as a weighted sum of snedecor s f distributions normalized by the numerator degrees of freedom of each f distribution of the sum a methodology for computing critical values as well as probability values for the tests is discussed the relationship between this testing framework and the multivariate one sided hypothesis testing literature is also discussed in this context we show that for any size of the hypothesis test h 0 versus k rk the test statistic and critical value obtained a

a likelihood ratio test for mtp_2 within binary variables multivariate totally positive mtp 2 binary distributions have been studied in many fields such as statistical mechanics computer storage and latent variable models we show that mtp 2 is equivalent to the requirement that the parameters of a saturated log linear model belong to a convex cone and we provide a fisher scoring algorithm for maximum likelihood estimation we also show that the asymptotic distribution of the log likelihood ratio is a mixture of chi squares a distribution known as chi bar squared in the literature on order restricted inference for this we derive tight bounds which turn out to have very simple forms a potential application of this method is for item response theory irt models which are used in educational assessment to analyse the responses of a group of subjects to a collection of questions items an important issue within irt is whether the joint distribution of the manifest variables is compatible with a single latent variable representation satisfying local independence and monotonicity which in turn imply that the joint distribution of item responses is mtp 2

structural modeling and psychometrika an historical perspective on growth and achievements the field of linear structural equation modeling with continuous variables is reviewed trends in psychometric theory and data analysis across the five decades of publication ofpsychometrika are discussed especially the clarification of concepts of population and sample explication of the parametric structure of models delineation of concepts of exploratory and confirmatory data analysis expansion of statistical theory in psychometrics estimation via optimization of an explicit objective function and implementation of general function minimization methods developments in the ideas of factor analysis latent variables as well as structural and causal modeling are noted some major conceptual achievements involving general covariance structure representations multiple population models and moment structures are reviewed the major statistical achievements of normal theory generalized least squares estimation elliptical and distribution free estimation and higher moment estimation are discussed computer programs that implement some of the theoretical developments are described

testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown suppose that an order restriction is imposed among several p variate normal mean vectors we are interested in testing the homogeneity of these mean vectors under this restriction this problem is a multivariate extension of bartholomew s biometrika 46 1959 36 48 when the covariance matrices are known this problem has been studied by sasabuchi inutsuka and kulatunga hiroshima math j 22 1992 551 560 sasabuchi kulatunga and saito amer j math management sci 18 1998 131 158 and some others in the present paper we consider the case when the covariance matrices are common but unknown we propose a test statistic study its upper tail probability under the null hypothesis and estimate its critical points

a test for a multiple isotonic regression problem summary a new procedure for testing the homogeneity of normal mean vectors versus order restricted alternatives is proposed and its performance discussed

a multivariate multisample quantile test for ordered alternatives abstract we propose and study a multivariate c sample rank test for order restricted alternatives when the underlying distributions have a contaminated component an example concerning lens opacity in adults is presented the asymptotic distributions are obtained under local mixture alternatives and pitman efficiencies are calculated an empirical power study is also included

a priori error estimates for three dimensional parabolic optimal control problems with pointwise control in this paper we provide an a priori error analysis for parabolic optimal control problems with a pointwise dirac type control in space on three dimensional domains the two dimensional case was treated in d leykekhman and b vexler siam j numer anal 51 2013 pp 2797 2821 however the three dimensional case is technically much more involved to approximate the problem we use standard continuous piecewise linear elements in space and the piecewise constant discontinuous galerkin method in time despite low regularity of the state equation we establish mathcal o sqrt k h order of convergence rate for the control in the l 2 norm this result improves almost twice the previously known estimate in w gong m hinze and z zhou siam j control optim 52 2014 pp 97 119 and in addition does not require any relationship between the time step k and the mesh size h the main technical tools are discrete maximal parabolic regularity results and the best approximation type estim

on the finite element method for elliptic problems with degenerate and singular coefficients we consider dirichlet boundary value problems for second order elliptic equations over polygonal domains the coefficients of the equations under consideration degenerate at an inner point of the domain or behave singularly in the neighborhood of that point this behavior may cause singularities in the solution the solvability of the problems is proved in weighted sobolev spaces and their approximation by finite elements is studied this study includes regularity results graded meshes and inverse estimates applications of the theory to some problems appearing in quantum mechanics are given numerical results are provided which illustrate the theory and confirm the predicted rates of convergence of the finite element approximations for quasi uniform meshes

high order local rate of convergence by mesh refinement in the finite element method we seek approximations of the solution u of the neumann problem for the equation lu f in q with special emphasis on high order accuracy at a given point xo e f2 here q is a bounded domain in rn n 2 with smooth boundary and l is a second order uniformly elliptic differential operator with smooth coefficients an approximate solution uh is determined by the standard galerkin method in a space of continuous piecewise polynomials of degree at most r 1 on a partition ah xo a of u here h is a global mesh size parameter and a is the degree of a certain systematic refinement of the mesh around the given point x0 where larger a s mean finer mesh and a 0 corresponds to the quasi uniform case with no refinement it is proved that for suitable sufficiently large a s the high order error estimate u uh x0 o h2 2 holds a corresponding estimate with the same order of convergence is obtained for the first order derivatives of u uh these estimates are sharp in the sense that the required degree of refinement in each case is essentially the same as is needed for the local approximation to this order near xo for the estimates to hold it is sufficient that the exact solution u have derivatives to the rth order which are bounded close to xo and square integrable in the rest of u the proof of this uses high order negative norm estimates of u uh the number of elements in the considered partitions is of the same order as in the corresponding quasi uniform ones applications of the results to other types of boundary value problems are indicated 0 introduction let i2 be a bounded domain in rn n 2 with smooth boundary aq and consider the neumann problem to find u such that n a au n au 0 1 lu ax aija ea3 au f inn au n au 0 2 an i a a nj 0 on3ai2 a i j1 aj xi here l is assumed to be uniformly elliptic with smooth coefficients n nj and n denote the exterior normal and conormal to aq respectively assume also that the bilinear form n3v w n a v w e a a e a a w avw dx received september 22 1983 revised july 23 1984 1980 mathematics subject classification primary 65n30

robust wald type tests of one sided hypotheses in the linear model abstract let us consider the linear model y x e in the usual matrix notation where the errors are iid our main objective is to develop robust wald type tests for a large class of hypotheses on by robust we mean robustness in terms of size and power against long tailed error distributions first assume that the error distribution is symmetric about the origin let l and be the least squares and a robust estimator of assume that they are asymptotically normal about with covariance matrices 2 xtx 1 and 2 xtx 1 respectively so could be an m estimator or a high breakdown point estimator robust wald type tests based on denoted by rw are studied here for testing a large class of one sided hypotheses on it is shown that the asymptotic null distribution of rw and that of the usual wald type statistic based on l denoted by w are the same this is a useful result since the critical values and procedures for computing the p values for w are directly applicable to rw as well a more impo

likelihood inference for a class of latent markov models under linear hypotheses on the transition probabilities summary for a class of latent markov models for discrete variables having a longitudinal structure we introduce an approach for formulating and testing linear hypotheses on the transition probabilities of the latent process for the maximum likelihood estimation of a latent markov model under hypotheses of this type we outline an em algorithm that is based on well known recursions in the hidden markov literature we also show that under certain assumptions the asymptotic null distribution of the likelihood ratio statistic for testing a linear hypothesis on the transition probabilities of a latent markov model against a less stringent linear hypothesis on the transition probabilities of the same model is of x2 type as a particular case we derive the asymptotic distribution of the likelihood ratio statistic between a latent class model and its latent markov version which may be used to test the hypothesis of absence of transition between latent states the approach is illustrated through a series of simulations and two applications the first of which is based on educational testing data that have been collected within the national assessment of educational progress 1996 and the second on data concerning the use of marijuana which have been collected within the national youth survey 19761980

constructing a confidence interval for the fraction who benefit from treatment using randomized trial data the fraction who benefit from treatment is the proportion of patients whose potential outcome under treatment is better than that under control inference on this parameter is challenging since it is only partially identifiable even in our context of a randomized trial we propose a new method for constructing a confidence interval for the fraction when the outcome is ordinal or binary our confidence interval procedure is pointwise consistent it does not require any assumptions about the joint distribution of the potential outcomes although it has the flexibility to incorporate various user defined assumptions our method is based on a stochastic optimization technique involving a second order asymptotic approximation that to the best of our knowledge has not been applied to biomedical studies this approximation leads to statistics that are solutions to quadratic programs which can be computed efficiently using optimization tools in simulation our method attains the nominal coverage probability or higher and can have narrower average width than competitor methods we apply it to a trial of a new intervention for stroke

testing for garch effects a one sided approach arch models often lie at the boundary of the parameter space under conditional homoskedasticity which invalidates the usual s2 distribution of lr and wald tests although lm tests are not a ected the one sided nature of the alternative hypothesis should result in more powerful tests we propose a simple one sided version of the lm test which is closely related to the kuhn tucker multiplier test we also present critical values for lr wald and one sided lm tests the results of a monte carlo comparison suggest that one sided tests are indeed more powerful than their two sided counterparts 1998 elsevier science s a all rights reserved jel classification c22

likelihood inference on the underlying structure of irt models the assumptions underlying item response theory irt models may be expressed as a set of equality and inequality constraints on the parameters of a latent class model it is well known that the same assumptions imply that the parameters of the manifest distribution have to satisfy a more complicated set of inequality constraints which however are necessary but not sufficient in this paper we describe how the theory for likelihood based inference under equality and inequality constraints may be used to test the underlying assumptions of irt models it turns out that the analysis based directly on the latent structure is simpler and more flexible in particular we indicate how several interesting extensions of the rasch model may be obtained by partial relaxation of the basic constraints an application to a data set provided by educational testing service is used to illustrate the approach

some comments on maximum likelihood and partial least squares methods abstract the paper discusses some general aspects of two estimation methods which are designed for analysis of interrelationships between indirectly and directly observable variables the paper s main object is to summarize in broad terms what appears to be known about tthe asymptotic properties of maximum likelihood and partial least squares estimators the author would be pleased if as a side effect interest is stirred up in the analysis of estimators under non textbook assumptions

estimation with overidentifying inequality moment conditions this paper derives limit distributions of empirical likelihood estimators for models in which inequality moment conditions provide overidentifying information we show that the use of this information leads to a reduction of the asymptotic mean squared estimation error and propose asymptotically uniformly valid tests and confidence sets for the parameters of interest while inequality moment conditions arise in many important economic models we use a dynamic macroeconomic model as a data generating process and illustrate our methods with instrumental variable estimators of monetary policy rules the results obtained in this paper extend to conventional gmm estimators

a conditional composite likelihood ratio test with boundary constraints summary composite likelihood has been widely used in applications the asymptotic distribution of the composite likelihood ratio statistic at the boundary of the parameter space is a complicated mixture of weighted chi 2 distributions in this paper we propose a conditional test with data dependent degrees of freedom we consider a modification of the composite likelihood which satisfies the second order bartlett identity we show that the modified composite likelihood ratio statistic given the number of estimated parameters lying on the boundary converges to a simple chi 2 distribution this conditional testing procedure is validated through simulation studies

extended maxt tests of one sided hypotheses in many statistical applications of one sided tests of multiple hypotheses researchers are often concerned not only with global tests of the intersection of individual hypotheses but also with multiple tests of individual hypotheses for example in clinical trial studies researchers often need to find out the efficacy of a treatment as well as the significance of each outcome measurement endpoint of the treatment this article proposes maxt type tests aiming at improving the global power of existing maxt tests our extended maxt tests are constructed by adding an extra component to the maximand set of existing maxt tests the added component is a weighted sum of other components some power properties relating to choices of weight are studied our simulation study shows that the proposed tests can considerably improve the global power of existing maxt tests and can also outperform many other global tests under some alternatives and or some nonnormal distributions furthermore it is shown that such g

a unified set based test with adaptive filtering for gene environment interaction analyses in genome wide gene environment interaction gxe studies a common strategy to improve power is to first conduct a filtering test and retain only the snps that pass the filtering in the subsequent gxe analyses inspired by two stage tests and gene based tests in gxe analysis we consider the general problem of jointly testing a set of parameters when only a few are truly from the alternative hypothesis and when filtering information is available we propose a unified set based test that simultaneously considers filtering on individual parameters and testing on the set we derive the exact distribution and approximate the power function of the proposed unified statistic in simplified settings and use them to adaptively calculate the optimal filtering threshold for each set in the context of gene based gxe analysis we show that although the empirical power function may be affected by many factors the optimal filtering threshold corresponding to the peak of the power curve primarily depends on the size of the gene we further propose a resampling algorithm to calculate p values for each gene given the estimated optimal filtering threshold the performance of the method is evaluated in simulation studies and illustrated via a genome wide gene gender interaction analysis using pancreatic cancer genome wide association data

a simple multivariate test for one sided alternatives abstract a simple test for multivariate normal data is proposed that has good power for alternatives where the mean vector tends to be positive the test rejects if the quadratic form of the sample mean vector exceeds its 2 critical value and the sum of the elements of the mean vector exceeds zero the proposed test is shown to have type i error rate equal to whether or not the covariance matrix is known tight bounds on the power of the proposed test are provided and the test is compared to three likelihood ratio tests

interior maximum norm estimates for finite element methods part ii we consider bilinear forms a connected with second order elliptic problems and assume that for u h in a finite element space s h we have a u u h x f x for x in s h with local compact support we give local estimates for u u h in l and w 1 of the type local best approximation plus weak outside influences plus the local size of f

on pseudolikelihood inference for semiparametric models with boundary problems consider a semiparametric model indexed by a euclidean parameter of interest and an infinite dimensional nuisance parameter in many applications pseudolikelihood provides a convenient way to infer the parameter of interest where the nuisance parameter is replaced by a consistent estimator the purpose of this paper is to establish the asymptotic behaviour of the pseudolikelihood ratio statistic under semiparametric models in particular we consider testing the hypothesis that the parameter of interest lies on the boundary of its parameter space under regularity conditions we establish the equivalence between the asymptotic distributions of the pseudolikelihood ratio statistic and a likelihood ratio statistic for a normal mean problem with a misspecified covariance matrix this result holds when the nuisance parameter is estimated at a rate slower than the usual rate in parametric models we study three examples in which the asymptotic distributions are shown to be mixtures of chi squared variables we conduct simulation studies to examine the finite sample performance of the pseudolikelihood ratio test

improved accuracy by adapted mesh refinements in the finite element method for appropriately adapted mesh refinements optimal order error estimates are proved for the finite element approximate solution of the neumann problem for the second order elliptic equation lu 8 where 8 is the dirac distribution

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

testing inequality constraints in linear econometric models abstract this paper develops three asymptotically equivalent tests for examining the validity of imposing linear inequality restrictions on the parameters of linear econometric models first we consider the model y x e where e is n 0 and the hypothesis test h r r versus k rk later we generalize this testing framework to the linear simultaneous equations model we show that the joint asymptotic distribution of these test statistics and the test statistics from the hypothesis test h r r versus k r r is a weighted sum of two sets of independent 2 distributions we also derive a useful duality relation between the multivariate inequality constraints test developed here and the multivariate one sided hypothesis test in small samples these three test statistics satisfy inequalities similar to those derived by berndt and savin 1977 for the case of equality constraints the paper also contains an illustrative application of this testing technique

on the likelihood ratio tests in bivariate acde models the ace and ade models have been heavily exploited in twin studies to identify the genetic and environmental components in phenotypes however the validity of the likelihood ratio test lrt of the existence of a variance component a key step in the use of such models has been doubted because the true values of the parameters lie on the boundary of the parameter space of the alternative model for such tests violating a regularity condition required for a lrt e g carey in behav genet 35 653 665 2005 visscher in twin res hum genet 9 490 495 2006 dominicus skrondal gjessing pedersen and palmgren behav genet 36 331 340 2006 solve the problem of testing univariate components in acde models our current work as presented in this paper resolves the issue of lrts in bivariate acde models by exploiting the theoretical frameworks of inequality constrained lrts based on cone approximations our derivation shows that the asymptotic sampling distribution of the test statistic for testing a single bivariate component in an ace or ade model is a mixture of 2 distributions of degrees of freedom dfs ranging from 0 to 3 and that for testing both the a and c or d components is one of dfs ranging from 0 to 6 these correct distributions are stochastically smaller than the 2 distributions in traditional lrts and therefore lrts based on these distributions are more powerful than those used naively formulas for calculating the weights are derived and the sampling distributions are confirmed by simulation studies several invariance properties for normal data at most missing by person are also proved potential generalizations of this work are also discussed

a repeated significance test with applications to sequential detection in sensor networks in this paper we introduce a randomly truncated sequential hypothesis test using the framework of a repeated significance test rst we study a sequential test with truncation time based on a random stopping time using the functional central limit theorem fclt for a sequence of statistics we derive a general result that can be employed in developing a repeated significance test with random sample size we present effective methods for evaluating accurate approximations for the probability of type i error and the power function numerical results are presented to evaluate the accuracy of these approximations we apply the proposed test to a decentralized sequential detection problem in sensor networks sns with communication constraints finally a sequential detection problem with measurements at random times is investigated

conditions for factor in determinacy in factor analysis the subject of factor indeterminacy has a vast history in factor analysis guttman 1955 lederman 1938 wilson 1928 it has lead to strong differences in opinion steiger 1979 the current paper gives necessary and sufficient conditions for observability of factors in terms of the parameter matrices and a finite number of variables five conditions are given which rigorously define indeterminacy it is shown that un observable factors are in determinate specifically the indeterminacy proof by guttman is extended to heywood cases the results are illustrated by two examples and implications for indeterminacy are discussed

second order sensitivity analysis and asymptotic theory of parametrized nonlinear programs in this paper we study second order differential properties of an optimal value function x it is shown that under certain conditions x possesses second order directional derivatives which can be calculated by solving corresponding quadratic programs also upper and lower bounds on these derivatives are introduced under weaker assumptions in particular we show that the second order directional derivative is infinite if the corresponding quadratic program is unbounded finally sensitivity results are applied to investigate asymptotics of estimators in parametrized nonlinear programs

positive quadrant dependence and marginal modeling in two way tables with ordered margins for a collection of two way tables where subjects are cross classified according to the same pair of ordinal categorical variables conditionally on the value of one or more discrete explanatory variables we propose a general approach to likelihood inference that combines marginal modeling with fitting and testing of inequality constraints such as those implied by the assumption that one marginal distribution is stochastically larger than the other positive dependence and stronger positive dependence the approach is based on parameterizing bivariate conditional distributions with global logits and global log odds ratios and we provide a general framework for handling models defined by equality and inequality constraints on these parameters in this way such models as marginal homogeneity proportional odds among row or columns margins and plackett distribution may be treated together with various models defined by inequality constraints on the same parameters such as for instance those implied by

testing when a parameter is on the boundary of the maintained hypothesis this paper considers testing problems where several of the standard regularity conditions fail to hold we consider the case where i parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and ii there may be a nuisance parameter that appears under the alternative hypothesis but not under the null the paper establishes the asymptotic null and local alternative distributions of quasi likelihood ratio rescaled quasi likelihood ratio wald and score tests in this case the results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models examples treated in the paper are i tests of the null hypothesis of no conditional heteroskedasticity in a garch 1 1 regression model and ii tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with possibly correlated random coefficients

the order restricted association model two estimation algorithms and issues in testing this paper presents a row column rc association model in which the estimated row and column scores are forced to be in agreement with an a priori specified ordering two efficient algorithms for finding the order restricted maximum likelihood ml estimates are proposed and their reliability under different degrees of association is investigated by a simulation study we propose testing order restricted rc models using a parametric bootstrap procedure which turns out to yield reliablep values except for situations in which the association between the two variables is very weak the use of order restricted rc models is illustrated by means of an empirical example

the finite element method for a boundary value problem with strong singularity the existence and uniqueness of the r n generalized solution for the third boundary value problem and the non self adjoint second order elliptic equation with strong singularity are established we construct a finite element method with a basis containing singular functions the rate of convergence of the approximate solution to the r n generalized solution in the norm of the sobolev weighted space is established and finally results of numerical experiments are presented

boundary crossing probabilities and statistical applications abstract this paper surveys recent results involving boundary crossing probabilities and related statistical applications the first part is concerned with problems of sequential analysis especially repeated significance tests and their application to sequential clinical trials involving survival data the second part develops the probability theory motivated by the problems of part 1 a method for computing first passage distributions of brownian motion to linear boundaries is introduced and then modified to handle problems in discrete time and those involving nonlinear boundaries the third part is concerned with fixed sample statistical problems especially change point problems which involve boundary crossing probabilities examples are given of problems for which methods of part 2 appear adequate and of problems which require new methods

finite element pointwise results on convex polyhedral domains the main goal of the paper is to establish that the l 1 norm of jumps of the normal derivative across element boundaries and the l 1 norm of the laplacian of a piecewise polynomial finite element function can be controlled by corresponding weighted discrete h 2 norm on convex polyhedral domains in the finite element literature such results are only available for piecewise linear elements in two dimensions and the extension to convex polyhedral domains is rather technical as a consequence of this result we establish almost pointwise stability of the ritz projection and the discrete resolvent estimate in l infty norm

a note on likelihood ratio tests for models with latent variables the likelihood ratio test lrt is widely used for comparing the relative fit of nested latent variable models following wilks theorem the lrt is conducted by comparing the lrt statistic with its asymptotic distribution under the restricted model a formula see text distribution with degrees of freedom equal to the difference in the number of free parameters between the two nested models under comparison for models with latent variables such as factor analysis structural equation models and random effects models however it is often found that the formula see text approximation does not hold in this note we show how the regularity conditions of wilks theorem may be violated using three examples of models with latent variables in addition a more general theory for lrt is given that provides the correct asymptotic theory for these lrts this general theory was first established in chernoff j r stat soc ser b methodol 45 404 413 1954 and discussed in both van der vaart asymptotic statistics cambridge cambridge university press 2000 and drton ann stat 37 979 1012 2009 but it does not seem to have received enough attention we illustrate this general theory with the three examples

a note on the parameter set for factor analysis models abstract necessary and sufficient conditions are given for the compactness of the parameter set of models for factor analysis together with implications for purposes of estimation

approximate tail probabilities for the maxima of some random fields abstract hogan and siegmund 1986 adapt the method developed by pickands 1969 qualls and watanabe 1973 and bickel and rosenblatt 1973 to obtain explicit large deviation approximations for the maxima of several gaussian random fields arising in statistics using a special argument for one particular case they suggest a heuristic second order approximation for that case and they show by a monte carlo experiment that the second order approximation frequently gives considerably better numerical results the purpose of this paper is to show that the method developed by woodroofe 1976 1982 for problems in one dimensional time can be adapted to study maxima of random fields overall it involves simpler computations than the previous method and consequently seems potentially capable of delivering a genuine second order approximation should one seem desirable

likelihood ratio tests with boundary constraints using data dependent degrees of freedom when the null hypothesis constrains parameters to the boundary of the parameter space the asymptotic null distribution of the likelihood ratio statistic is often a mixture of chi squared distributions giving rise to the so called chi bar test where weights can depend on the true unknown parameter and be difficult to calculate we consider the test that conditions on the observed number of null hypothesis parameters in the interior of the parameter space this approach uses simple chi squared thresholds yields conservative asymptotic type i error and is guaranteed to give power improvements over the naive approach of simply ignoring boundary constraints simulations validate the theoretical results illustrate application settings and find power comparable with but usually less than that of the chi bar test copyright 2013 oxford university press

a unified approach to likelihood inference on stochastic orderings in a nonparametric context abstract for data in a two way contingency table with ordered margins we consider various hypotheses of stochastic orders among the conditional distributions considered by rows and show that each is equivalent to requiring that an invertible transformation of the vectors of conditional row probabilities satisfies an appropriate set of linear inequalities this leads to the construction of a general algorithm for maximum likelihood estimation under multinomial sampling and provides a simple framework for deriving the asymptotic distribution of log likelihood ratio tests the usual stochastic ordering and the so called uniform and likelihood ratio orderings are considered as special cases in particular for each of these three orderings we determine the transformation required to apply the estimation algorithm we then consider testing the hypothesis that the rows are identically distributed against the alternative that they are stochastically ordered as well as testing each stochastic order against an u

asymptotic theory of overparameterized structural models abstract a theory of overparameterized structural models is presented in such a model some redundant parameters are involved the parameter vector is not identified and the information matrix is not nonsingular the minimum discrepancy function mdf test statistic is shown to have an asymptotic chi squared distribution almost everywhere for a wide class of discrepancy functions asymptotic distribution properties of the mdf estimators are investigated the factor analysis model is discussed as an example

a multivariate version of isotonic regression summary a multivariate generalization of isotonic regression is given enabling the study of statistical inference for ordered vector valued parameters or sets of ordered parameters including multivariate extensions of bartholomew s 22 and 4 2 an iterative algorithm for computing multivariate isotonic regression is proposed and studied

a multivariate change point model for statistical process control multivariate statistical process control spc carries out ongoing checks to ensure that a process is in control these checks on the process are traditionally done by t2 multivariate cusum and multivariate exponentially weighted moving average control charts these traditional spc charts assume that the in control true parameters are known exactly and use these assumed true values to set the control limits the reality however is that true parameter values are seldom if ever known exactly rather they are commonly estimated from a phase i sample it is increasingly recognized that this phase i study needs to involve large samples if the parameter estimates are to provide run behavior matching that of the known parameter situation but apart from the general undesirability of large and thus expensive studies preliminary to actual charting some industrial settings have a paucity of relevant data for estimating the process parameters an attractive alternative to traditional charting methods when mon

variance components testing in the longitudinal mixed effects model this article discusses the asymptotic behavior of likelihood ratio tests for nonzero variance components in the longitudinal mixed effects linear model described by laird and ware 1982 biometrics 38 963 974 our discussion of the large sample behavior of likelihood ratio tests for nonzero variance components is based on the results for nonstandard testing situations by self and liang 1987 journal of the american statistical association 82 605 610

robust tests of inequality constraints and one sided hypotheses in the linear model summary for the linear regression model with independent and identically distributed errors robust tests of various hypotheses on the regression parameter are developed by robust we mean robustness of size and power against long tailed error distributions which may not be symmetric the proposed test statistic denoted by fm resembles the usual f statistic the two main results are i under the null hypothesis the asymptotic distribution of fm and that of the least squares based f statistic are the same and ii the pitman asymptotic efficiency of fm relative to f is equal to the asymptotic efficiency of the corresponding m estimator relative to the least squares estimator an example and simulation results illustrate that fm has desirable robustness properties compared to f

asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints summary the analysis of moment structural models has become an important tool of investigation in behavioural educational and economic studies the chi squared largesample test is routinely employed to assess the goodness of fit of the model considered however in order to invoke the standard asymptotic distribution theory certain regularity conditions have to be met here we consider the case where the population value of the parameter vector is a boundary point of the feasible region we show that in this case the asymptotic distribution of test statistic is a mixture of chi squared distributions the problem of finding the corresponding weights is discussed

extended rc association models allowing for order restrictions and marginal modeling in the context of two way contingency tables the rc model may be seen as a way of modeling the set of log odds ratios for adjacent 2 2 subtables through row and column scores this article presents an extended class of rc models that allows simultaneous modeling of the marginal distributions and the association between two categorical variables these components are parameterized with logits and log odds ratios that may be of different types e g global or continuation to suit the nature of the data and the type of dependence of interest an algorithm for maximum likelihood estimation under equality and inequality constraints is presented the asymptotic distribution of the likelihood ratio statistic to test some interesting hypotheses is derived and extensions to multiway tables are outlined three examples are presented to highlight the features of the new approach

optimal a priori error estimates of parabolic optimal control problems with pointwise control in this paper we consider a parabolic optimal control problem with a pointwise dirac type control in space but variable in time in two space dimensions to approximate the problem we use the standard continuous piecewise linear approximation in space and the piecewise constant discontinuous galerkin method in time despite low regularity of the state equation we show almost optimal h 2 k convergence rate for the control in l 2 norm this result improves almost twice the previously known estimate in w gong m hinze and z zhou a priori error analysis for finite element approximation of parabolic optimal control problems with pointwise control tech report 2011 07 hamburger beitrage zur angewandten mathematik hamburg germany 2011

order restricted statistical tests on multinomial and poisson parameters the starshaped restriction abstract likelihood ratio statistics for i testing the homogeneity of a collection of multinomial parameters against the alternative which accounts for the restriction that those parameters are starshaped cf shaked ann statist 1979 and for ii testing the null hypothesis that this parameter vector is starshaped are considered for both tests the asymptotic distribution of the test statistic under the null hypothesis is a version of the chi bar square distribution analogous tests on a collection of poisson means are also found to have asymptotic chi bar square distributions author

testing for the multivariate stochastic order among ordered experimental groups with application to dose response studies summary the comparison of two or more ordered experimental groups based on multivariate data is common in a variety of applications such as toxicology clinical trials and drug development to name just a few in this article we develop a nonparametric methodology for analyzing such data in particular we propose a global k sample nonparametric test for order among vector valued outcomes the testing procedure can also be used in a post hoc fashion to answer questions about the ordering of subgroups and or single outcomes within any subset of experimental groups such a methodology does not currently exist in contrast with standard methodology such as multivariate analysis of variance manova and its nonparametric analogues we do not assume that the groups differ only by a location parameter or that the components of the response vector have the same marginal distributions between and across groups that is we allow for the shape of the distribution to change across groups we emphasize that our test compares the outcome distributions not just their mean tendencies and explicitly incorporates and exploits the order constraints consequently it is more powerful than the existing unordered tests the methodology is illustrated using genotoxicity data where the effect of hydrogen peroxide exposure on damage to dna is evaluated using a comet assay

hierarchical diagnostic classification models a family of models for estimating and testing attribute hierarchies although latent attributes that follow a hierarchical structure are anticipated in many areas of educational and psychological assessment current psychometric models are limited in their capacity to objectively evaluate the presence of such attribute hierarchies this paper introduces the hierarchical diagnostic classification model hdcm which adapts the log linear cognitive diagnosis model to cases where attribute hierarchies are present the utility of the hdcm is demonstrated through simulation and by an empirical example simulation study results show the hdcm is efficiently estimated and can accurately test for the presence of an attribute hierarchy statistically a feature not possible when using more commonly used dcms empirically the hdcm is used to test for the presence of a suspected attribute hierarchy in a test of english grammar confirming the data is more adequately represented by hierarchical attribute structure when compared to a crossed or nonhierarchical structure

testing for order restricted hypotheses in longitudinal data an inherent ordering we propose a quadratic score test qst based on a quadratic inference function for detecting an order in treatment effects for correlated data the quadratic inference function is similar to the negative of a log likelihood and it provides test statistics in the spirit of a x2 test for testing nested hypotheses as well as for assessing the goodness of fit of model assumptions under the null hypothesis of no order restriction it is shown that the qst statistic has a wald type asymptotic representation and that the asymptotic distribution of the qst statistic is a weighted x2 distribution furthermore an asymptotic distribution of the qst statistic under an arbitrary convex cone alternative is provided the performance of the qst is investigated through monte carlo simulation experiments analysis of the polyposis data demonstrates that the qst outperforms the wald test when data are highly correlated with a small sample size and there is a significant amount of missing data with a small number of clusters the proposed test statistic accommodates both time dependent and time independent covariates in a model

limited information estimation and testing of thurstonian models for paired comparison data under multiple judgment sampling we relate thurstonian models for paired comparisons data to thurstonian models for ranking data which assign zero probabilities to all intransitive patterns we also propose an intermediate model for paired comparisons data that assigns nonzero probabilities to all transitive patterns and to some but not all intransitive patterns