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

determinacy indeterminacy and dynamic misspecification in linear rational expectations models abstract this paper proposes a testing strategy for the null hypothesis that a multivariate linear rational expectations lre model may have a unique stable solution determinacy against the alternative of multiple stable solutions indeterminacy the testing problem is addressed by a misspecification type approach in which the overidentifying restrictions test obtained from the estimation of the system of euler equations of the lre model through the generalized method of moments is combined with a likelihood based test for the cross equation restrictions that the model places on its reduced form solution under determinacy the resulting test has no power against a particular class of indeterminate equilibria hence the non rejection of the null hypothesis can not be interpreted conclusively as evidence of determinacy on the other hand this test i circumvents the nonstandard inferential problem generated by the presence of the auxiliary parameters that appear under indeterminacy and that are not identifiable under determinacy ii does not involve inequality parametric restrictions and hence the use of nonstandard inference iii is consistent against the dynamic misspecification of the lre model and iv is computationally simple monte carlo simulations show that the suggested testing strategy delivers reasonable size coverage and power against dynamic misspecification in finite samples an empirical illustration focuses on the determinacy indeterminacy of a new keynesian monetary business cycle model of the us economy

fast fourier transform method for partial differential equations case study the 2 d diffusion equation abstract the solution of time dependent partial differential equations using discrete i e finite difference versions of those equations traditionally has been done by marching forward in time one time unit per step the authors here extend earlier results to higher dimensions focusing on the solution of the discrete diffusion or heat equation in 2 d and show that the solution may be found using fast fourier transform fft techniques that treat the solution as the output of a linear filter this technique is analogous to an integral method for the differential equation and is related to the green s function of the difference equation it allows the solution to be determined with a single step computation that does not require the solution at intermediate time levels the number of numerical operations is essentially independent of the time level at which the solution is desired the results of numerical examples are given and computation times are shown to be much faster than those of the traditional method for all but small time levels

testing affine term structure models in case of transaction costs we empirically analyze the impact of transaction costs on the performance of essentially affine interest rate models we test the implied euler restrictions and calculate the specification error bound of hansen and jagannathan to measure model misspecification using both short maturity and long maturity bond return data we find under the assumption of frictionless markets strong evidence of misspecification of affine yield models with up to three factors next we incorporate transaction costs in our tests the results show that the evidence of misspecification of essentially affine yield models disappears in case of monthly holding periods at market size transaction costs

on approximation of the level probabilities and associated distributions in order restricted inference summary the use of much of the distribution theory developed for order restricted inference has been limited by the lack of algorithms for the level probabilities an approximation for these which accounts for the pattern of large and small weights is developed this approximation and the equal weights approximation are examined both approximations appear to be reasonable for weight sets having a moderate amount of variability the quality of the equal weights approximation as a function of the amount of variability in the weights deteriorates more quickly for certain patterns of large and small weights than for others thus the approximation based upon the pattern of large and small weights is a significant improvement over the equal weights approximation finally siskind s 1976 approximation which can be applied if the number of parameters is not too large is discussed the chi bar squared 2 and e bar squared p2 distributions are fundamental to the theory of order restricted hypothesis tests these distributions have tail probabilities which are linear combinations of the tail probabilities of standard distributions and they depend upon the order restriction through the coefficients in these linear combinations the values of these coefficients are the probabilities that the order restricted maximum likelihood estimates of normal means assume specified numbers of distinct values which are called levels the estimates are based upon independent samples from each of the populations and depend upon the vector of relative precisions called weights of the sample means as estimates of the corresponding population means the use of these tests has been limited because these level probabilities can be virtually impossible to compute if the weights are not all equal in this paper we describe a technique for approximating the level probabilities for a linear order restriction and for unequal precisions this approximation is based upon an idea of chase 1974 and uses the pattern of large and small relative precisions it seems to be particularly good when the relative precisions have two distinct values however it seems to provide a satisfactory approximation so long as the variation in the relative precisions is not too large this is probably due to the lack of sensitivity of the level probabilities to changes in the weights the robustness was

statistical inference for stochastic dominance and for the measurement of poverty and inequality we derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty welfare and inequality this includes estimators of most of the poverty indices currently in use as well as estimators of the curves used to infer stochastic dominance of any order these curves can be used to determine whether poverty inequality or social welfare is greater in one distribution than in another for general classes of indices and for ranges of possible poverty lines we also derive the sampling distribution of the maximal poverty lines up to which we may confidently assert that poverty is greater in one distribution than in another the sampling distribution of convenient dual estimators for the measurement of poverty is also established the statistical results are established for deterministic or stochastic poverty lines as well as for paired or independent samples of incomes our results are briefly illustrated using data for four countries drawn from the luxembourg income study data bases

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

statistical inference for poverty measures with relative poverty lines relative poverty lines such as one half median income have been increasingly used in poverty studies this paper contributes to the literature by developing statistical inference for testing decomposable poverty measures with relative poverty lines the poverty lines we consider are percentages of mean income and percentages of quantiles we show that the estimates of poverty indices with relative poverty lines are asymptotically normally distributed and that the covariance structure can be consistently estimated as a consequence asymptotically distribution free statistical inference can be established in a straightforward manner

sticky particles and scalar conservation laws one dimensional scalar conservation laws with nondecreasing initial conditions and general fluxes are shown to be the appropriate equations to describe large systems of free particles on the real line which stick under collision with conservation of mass and momentum

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

wald criteria for jointly testing equality and inequality restrictions on montre comment le test de wald s applique a des ensembles de restrictions d egalite et d inegalite et on presente la distribution pour de grands echantillons du test sous l hypothese nulle

the local nature of hypothesis tests involving inequality constraints in nonlinear models this paper derives several properties unique to nonlinear model hypothesis testing problems involving linear or nonlinear inequality constraints in the null or alternative hypothesis the paper is organized around a lemma which characterizes the set containing the least favorable parameter value for a nonlinear model inequality constraints hypothesis test we then present two examples which illustrate several implications of this lemma we also discuss the impact of these properties on the empirical implementation and interpretation of these test procedures

confidence sets for partially identified parameters that satisfy a finite number of moment inequalities this paper proposes a computationally simple way to construct confidence sets for a parameter of interest in models comprised of moment inequalities building on results from the literature on multivariate one sided tests i show how to test the hypothesis that any particular parameter value is logically consistent with the maintained moment inequalities the associated test statistic has an asymptotic chi bar square distribution and can be inverted to construct an asymptotic confidence set for the parameter of interest even if that parameter is only partially identified critical values for the test are easily computed and a monte carlo study demonstrates implementation and finite sample performance

a score test against one sided alternatives abstract a score type statistic t s is introduced for testing h 0 against k 0 and more general one sided hypotheses when nuisance parameters may be present is a vector parameter the main advantages of t s are that it requires estimation of the model only under the null hypothesis and that it is asymptotically equivalent to the likelihood ratio statistic these are precisely the reasons for the popularity of the score tests for testing against two sided alternatives in this sense t s preserves the main attractive features of the classical two sided score test the theoretical results are presented in a general framework where the likelihood based score function is replaced by an estimating function so that the test is applicable even if the exact population distribution is unknown computation of t s is simplified by the fact that it can be computed easily once the corresponding two sided statistic has been computed the relevance and simplicity of t s are illustrated by discussing

qualitative interactions in multifactor studies in clinical trials qualitative interaction or crossover interaction is said to occur when one treatment is superior for some sets of patients and the alternative treatment is superior for other subsets here we propose a definition of no qualitative interaction with respect to a single continuous covariate which implies that one treatment is superior to the other treatment over a prespecified range of the covariate further in studies involving patients cross classified by two or more prognostic factors we define a marginal qualitative interaction with respect to a treatment factor and a prognostic factor by averaging in some sense over the remaining prognostic factors in some situations the methodology of gail and simon 1985 biometrics 41 361 372 is shown to be appropriate their procedure assumes independent estimates of treatment effect for each subset of patients and this may not be appropriate for the generalizations we propose therefore we generalize the procedure of gail and simon to the case of two correlated estimates of treatment effect providing a table of critical values results for one sided tests for the case of j correlated estimates are also obtained we also present an example illustrating our procedure

sampling performance of some joint one sided preliminary test estimators under squared error loss in many areas of science when drawing conclusions concerning a set of phenomena individual or linear combinations of parameters are assumed to be nonnegative nonpositive or to lie between upper and lower bounds likewise many functions are assumed to be monotonic convex or quasiconvex consequently questions naturally arise as to the correctness of the assumptions and within the context of statistical inference how to evaluate the evidence against these assumptions and to use the data at hand to seek the appropriate statistical model and the corresponding method of estimation within the context of the general linear statistical model multivariate analogues of one sided inequality hypotheses tests have been explored by bartholomew 1959 kudo 1963 osterhoff 1969 barlow et al 1972 yancey judge and bock 1981 yancey bohrer and judge 1982 gourieroux holly and montfort ghm 1982 judge and yancey 1986 wolak 1987 and shapiro 1988 in general the likelihood ratio framework has been used in developing a test statistic and determining acceptance and rejection regions in order to facilitate the interpretation of these test results in econometric practice in this paper we evaluate under a squared error loss sel measure the risk characteristics of the preliminary test pt estimators that evolve when based on the data at hand an estimation decision is taken as a result of the outcomes of two one sided multivariate hypothesis tests

stability criteria for two partial difference equations abstract this paper is concerned with two classes of linear partial difference equations with constant coefficients explicit conditions are derived which are sufficient and or necessary for these equations to have stable solutions

on tests against one sided hypotheses in some generalized linear models one sided hypotheses arise naturally in many situations when testing against such hypotheses it is desirable to take the available one sided information into account rather than simply applying a two sided test what we expect to gain by applying a one sided test instead of a two sided test is an increase in the power of the test we consider various tests of one sided hypotheses in a class of models that includes generalized linear and cox regression models the tests are likelihood ratio wald score generalized distance and a pearson chi square it is shown that these test statistics are asymptomatically equivalent in terms of local power this is a generalization of the well known corresponding result for two sided alternatives two examples are also discussed they are on 1 testing for interaction in binomial response models and 2 comparison of treatments with ordinal categorical responses

duality in testing multivariate hypotheses summary this paper derives a duality result for a general class of hypothesis testing problems in multivariate analysis utilizing the relationship between convex cones and their polar cones together with the properties of minimum norm problems between points and cones in euclidian space special cases of this result yield generalizations of a well known duality relation in multivariate equality constraints testing for example any multivariate inequality constraints test on the parameters of a multivariate normal random vector has an equivalent multivariate one sided test in terms of the vector of dual variables associated with the constraints also any combination multivariate inequality and equality constraints test has an equivalent combination multivariate one sided and two sided test in terms of the vector of dual variables associated with both sets of constraints

admissibility of the lidelihood ratio test when the parameter space is restricted under the alternative this paper considers hypothesis tests when the parameter space is restricted under the alternative hypothesis multivariate one sided tests are a leading example the likelihood ratio lr test is shown to be admissible and to maximize power against alternatives that are arbitrarily distant from the null hypothesis exact results are established first for gaussian linear regression models with known variance asymptotic analogues are then established for dynamic nonlinear models

order restricted inferences in linear regression abstract regression analysis constitutes a large portion of the statistical repertoire in applications in cases where such analysis is used for exploratory purposes with no previous knowledge of the structure one would not wish to impose any constraints on the problem but in many applications we are interested in curve fitting with a simple parametric model to describe the structure of a system with some prior knowledge about the structure an important example of this occurs when the experimenter has a strong belief that the regression function changes monotonically with some or all of the predictor variables in a region of interest the analyses needed for statistical inferences under such constraints are nonstandard considering the present body of knowledge developed for unconstrained regression it will be an enormous task to derive the analogs of even a small fraction of this for the restricted case in this article we initiate the study with simple linear regression on a single variable the est

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

imposing curvature restrictions on flexible functional forms abstract a general computational method for estimating the parameters of a flexible functional form subject to convexity quasi convexity concavity or quasi concavity at a point at several points or over a region is set forth and illustrated with an example

inference on inequality from household survey data abstract i develop a theory of asymptotic inference for the lorenz curve and the gini coefficient for testing economic inequality when the data come from stratified and clustered household surveys with large number of clusters per stratum using the asymptotic framework of bhattacharya asymptotic inference from multi stage surveys journal of econometrics 126 1 145 171 i derive a weak convergence result for the continuously indexed lorenz process even when the underlying density is not uniformly bounded away from zero i provide analytical formulae for the asymptotic covariance functions that are corrected for both stratification and clustering and develop consistent tests for lorenz dominance inference on the gini coefficient follows as a corollary the methods are applied to per capita household expenditure data from the complexly designed indian national sample survey to test for changes in inequality before and after the reforms of the early 1990s ignoring the survey design is seen to produce qualitatively different results especially in the urban sector where the population sorts more completely into rich and poor neighborhoods

bounds for solutions of a six point partial difference scheme abstract this paper is concerned with a class of partial difference equations which arise from discretising the one dimensional heat and the first order wave equations explicit bounds are found for their solutions and subexponential solutions are considered using the green s function we derive a stability criteria for arbitrary solutions of this equation

adaptive critical value for constrained likelihood ratio testing summary we present a new general method for constrained likelihood ratio testing which when few constraints are violated improves upon the existing approach in the literature that compares the likelihood ratio with the quantile of a mixture of chi squared distributions the improvement is in terms of both simplicity and power the proposed method compares the constrained likelihood ratio statistic against the quantile of only one chi squared random variable with data dependent degrees of freedom the new test is shown to have a valid exact significance level alpha it also has more power than the classical approach against alternatives for which the number of violations is not large we provide more details for testing a simple order mu 1 leqslant cdots leqslant mu p against all alternatives using the proposed approach and give clear guidelines as to when the new method would be advantageous a simulation study suggests that for testing a simple order the new approach is more powerful in many scenarios than the existing method that uses a mixture of chi squared variables we illustrate the results of our adaptive procedure using real data on the liquidity preference hypothesis

the asymptotic behavior of the solutions of a discrete reaction diffusion equation abstract by means of bihari type inequalities we derive sufficient conditions for solutions of a discrete reaction diffusion equation to be bounded or to converge to zero asymptotic representation of solutions are also derived our results yield estimates and explicit attractive regions for the solutions

testing multivariate economic restrictions using quantiles the example of slutsky negative semidefiniteness abstract this paper is concerned with testing a core economic restriction negative semidefiniteness of the slutsky matrix we consider a system of nonseparable structural equations with infinite dimensional unobservables and employ quantile regression methods because they allow us to utilize the entire distribution of the data difficulties arise because the restriction involves several equations while the quantile is a univariate concept we establish that we may use quantiles of linear combinations of the dependent variable develop a new empirical process based test that applies kernel quantile estimators and investigate its finite and large sample behavior finally we apply all concepts to canadian microdata

testing the rank and definiteness of estimated matrices with applications to factor state space and arma models abstract consider any consistent asymptotically normal estimate of an arbitrary rectangular or square matrix a this article derives an explicit test for the rank of a and a related test of semi definiteness of a potential applications include testing for identification of structural models testing for the number of state variables in state space models including tests for the order of autoregressive moving average arma processes consumer demand analysis applications and testing for the number of factors in factor analysis and related procedures the test is based on the gaussian elimination lower diagonal upper triangular ldu decomposition the test is illustrated with an empirical application to testing the order of arma processes

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

an algorithm for restricted least squares regression abstract a commonly occurring problem in statistics is that of minimizing a least squares expression subject to side constraints here a simple iterative algorithm is presented and shown to converge to the desired solution several examples are presented including finding the closest concave convex function to a set of points and other general quadratic programming problems the dual problem to the basic problem is also discussed and a solution for it is given in terms of the algorithm finally extensions to expressions other than least squares are given

a test in the presence of nuisance parameters abstract we are interested in testing 0 against an alternative in the presence of some nuisance parameter the usual procedure for such problems is to use a test statistic that is a function of the data only let q denote the p value at a given value if q does not depend on then in principle we can apply this procedure however a major difficulty that arises in many situations is that q depends on and therefore cannot be used as a p value in such cases the usual approach is to define the p value as the supremum of q over the nuisance parameter space because this approach ignores sample information about it may be unnecessarily conservative this is a serious problem in order restricted inference to overcome this i propose the following obtain say a 99 confidence region for under the null hypothesis now for a given let t be a test statistic and r be the p value the test procedure is to reject the null hypothesis if 0 01 supremum of r over the 99 c

marginal regression models for the analysis of positive association of ordinal response variables given a set of discrete response variables some of which are ordinal and an arbitrary set of discrete explanatory variables we propose a simple matrix formulation for parameterising the saturated model as in glonek 1996 this is such that within a hierarchical structure marginal logits and log odds ratios of various possible types together with the remaining log linear interactions of high order may be modelled by equality and inequality constraints inequality constraints are particularly relevant for specifying models of positive association efficient algorithms are provided for computing maximum likelihood estimates under such constraints the asymptotic distribution of the likelihood ratio test is derived and an extension of the usual analysis of deviance is outlined which incorporates inequality constraints

riemann problems for a class of coupled hyperbolic systems of conservation laws abstract we study a class of coupled hyperbolic systems of conservation laws which contain the one dimensional zero pressure gas dynamics as a prototypical example the riemann problems are solved constructively the riemann solutions exactly include two kinds delta shock wave solutions and vacuum solutions under the generalized rankine hugoniot relation and entropy condition all of the existence uniqueness and stability of solutions to viscous perturbations are proved two typical examples are presented finally

boundary conditions for nonlinear hyperbolic systems of conservation laws we propose two formulations of the boundary conditions for nonlinear hyperbolic systems of conservation laws a first approach is based on the vanishing viscosity method and a second one is related to the riemann problem the equivalence between these two conditions is studied the latter formulation is extended to treat numerically physically relevant boundary conditions monodimensional experiments are presented

nonparametric specification tests for conditional duration models this paper deals with the testing of autoregressive conditional duration acd models by gauging the distance between the parametric density and hazard rate functions implied by the duration process and their non parametric estimates we derive the asymptotic justification using the functional delta method for fixed and gamma kernels and then investigate the finite sample properties through monte carlo simulations although our tests display some size distortion bootstrapping suffices to correct the size without compromising their excellent power we show the practical usefulness of such testing procedures for the estimation of intraday volatility patterns

the aw rascle traffic model with chaplygin pressure abstract in this paper we introduce the chaplygin pressure function to the aw rascle ar traffic model the solutions to the riemann problem of the ar model with chaplygin pressure are obtained constructively in particular the existence and uniqueness of delta shock solutions are established under the generalized rankine hugoniot relation and entropy conditions the delta shock may be useful for the description of the serious traffic jam more importantly it is proved that the limits of the riemann solutions of the ar traffic model with chaplygin pressure are exactly those of the pressureless gas dynamics model as the traffic pressure vanishes furthermore we study the initial boundary value problem of the ar model with chaplygin pressure a boundary entropy condition is derived thanks to the results of dubois and le floch f dubois p le floch boundary conditions of nonlinear hyperbolic systems of conservation laws journal of differential equations 71 1988 93 122 the application of our results in real traffic problem is also given

nonparametric maximum likelihood estimation of survival functions with a general stochastic ordering and its dual summary this paper discusses estimation of survival functions under an arbitrary partial stochas tic ordering of the underlying populations this technique is especially useful when data are not easily acquired from one or more of the populations but data from the other populations are available estimation of the ordered survival functions entails use of a fenchel duality theorem that results in an algorithm to identify and resolve violations of the underlying ordering the algorithm produces estimates which converge to the maximum likelihood estimates of the survival functions given the underlying ordering the method is illustrated by an example in life testing of components and in clinical trials estimation of a survival function p t is often of prime interest if the functional form of the survival function is unknown nonparametric methods such as the product limit estimator kaplan meier 1958 are needed johansen 1978 showed that the product limit estimator is a maximum likelihood estimator in the class of all distributions under a generalized maximum likelihood framework kiefer wolfowitz 1956 since the generalized maximum likelihood esti mates for continuous survival functions place probability only on those time points at which observations occur suppose however that one desires to estimate a number of survival functions when a partial stochastic ordering exists among them and under censoring for example in a clinical trial of two treatments for a rare debilitating disease let pi p2 and p3 be the survival functions respectively for the disease free group and for the disease groups under the two treatments the well documented survival function p1 can be used to generate better estimates for p2 and p3 by using the order restrictions pi t p2 t and pi t p3 t brunk et al 1966 developed the maximum likelihood estimators for two stochastically ordered distributions for uncensored independent random samples dykstra

bounds on mixtures of distributions arising in order restricted inference in testing hypotheses involving order restrictions on a collection of parameters distributions arise which are mixtures of standard distributions since tractable expressions for the mixing proportions generally do not exist even for parameter collections of moderate size the implementation of these tests may be difficult stochastic upper and lower bounds are obtained for such test statistics in a variety of these kinds of problems these bounds are also shown to be tight the tightness results point out some situations in which the bounds could be used to obtain approximate methods these results can also be applied to obtain the least favorable configutiation when testing the equality of two multinomial populations versus a stochastic ordering alternative

joint tests for zero restrictions on nonnegative regression coefficients summary three tests for zero restrictions on regression coefficients that are known to be nonnegative are considered the classical f test the likelihood ratio test and a one sided t test in a particular direction critical values for the likelihood ratio test are given for the cases of two and three restrictions and the power function is calculated for the case of two restrictions the analysis is conducted in terms of a characterization of the clas all similar tests for the problem of which each of the above tests is a member the likelihood ratio test emerges as the preferred test

hypothesis testing with a restricted parameter space abstract this paper considers hypothesis tests when the parameter space is restricted under the alternative hypothesis multivariate one sided tests are a leading example optimal tests called directed tests are derived using a weighted average power criterion exact results are established first for gaussian linear regression models with known variance asymptotic analogues are then established for dynamic nonlinear models simulation is used to compare the tests discussed in the paper the d w directed test is found to perform best in an overall sense for multivariate one sided alternatives with the likelihood ratio test being a close second the d w and likelihood ratio tests are found to perform best for mixed one and two sided alternatives

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

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

testing the assumptions behind importance sampling importance sampling is used in many areas of modern econometrics to approximate unsolvable integrals its reliable use requires the sampler to possess a variance for this guarantees a square root speed of convergence and asymptotic normality of the estimator of the integral however this assumption is seldom checked in this paper we use extreme value theory to empirically assess the appropriateness of this assumption our main application is the stochastic volatility model where importance sampling is commonly used for maximum likelihood estimation of the parameters of the model

a multivariate extension of the dynamic logit model for longitudinal data based on a latent markov heterogeneity structure for the analysis of multivariate categorical longitudinal data we propose an extension of the dynamic logit model the resulting model is based on a marginal parameterization of the conditional distribution of each vector of response variables given the covariates the lagged response variables and a set of subject specific parameters for the unobserved heterogeneity the latter ones are assumed to follow a first order markov chain for the maximum likelihood estimation of the model parameters we outline an em algorithm the data analysis approach based on the proposed model is illustrated by a simulation study and an application to a dataset which derives from the panel study on income dynamics and concerns fertility and female participation to the labor market

inference for non stationary time series regression with or without inequality constraints summary we consider statistical inference for time series linear regression where the response and predictor processes may experience general forms of abrupt and smooth non stationary behaviours over time meanwhile the regression parameters may be subject to linear inequality constraints a simple and unified procedure for structural stability checks and parameter inference is proposed in the case where the regression parameters are constrained the methodology proposed is shown to be consistent whether or not the true regression parameters are on the boundary of the restricted parameter space via utilizing an asymptotically invariant geometric property of polyhedral cones

asymptotic inference for the constrained quantile regression process abstract i investigate the asymptotic distribution of linear quantile regression coefficient estimates when the parameter lies on the boundary of the parameter space in order to allow for inferences made across many conditional quantiles i provide a uniform characterization of constrained quantile regression estimates as a stochastic process over an interval of quantile levels to do this i pose the process of estimates as solutions to a parameterized family of constrained optimization problems parameterized by quantile level a uniform characterization of the dual solution to these problems the so called regression rankscore process is also derived which can be used for score type inference in quantile regression the asymptotic behavior of quasi likelihood ratio wald and regression rankscore processes for inference when the null hypothesis asserts that the parameters lie on a boundary follows from the features of the constrained solutions

a likelihood ratio test against stochastic ordering in several populations abstract the likelihood ratio test is often used to test hypotheses involving a stochastic ordering distribution theory for the likelihood ratio test has been developed only for two stochastically ordered distributions for testing equality of distributions against a stochastic ordering in several populations this paper derives the null asymptotic distribution of the likelihood ratio test statistic which is characterized by minimization problems and has no closed form a monte carlo simulation is conducted to study the limiting distribution because the limiting distribution depends on the specific values of the unknown distributions under the null hypothesis asymptotic and bootstrap approaches are proposed to overcome practical difficulties and implement tests based on the likelihood principle asymptotic validities for these tests are established and simulations are carried out to check their performances for finite sample sizes the tests are applied to an example involving data for survival time f

one sided tests in generalized linear models with parallel regression lines likelihood ratio tests for two general one sided hypotheses in generalized linear models with parallel regression lines are discussed in this paper this kind of model may be interpreted as a generalization of the finney s 1971 probit analysis cambridge cambridge university press model for simple similar action between two or more compounds in particular for some balanced studies it is shown that the asymptotic null distributions do not depend on the parameters and have the same size for a class of ordered hypotheses for the potencies the conventional distribution theory of the likelihood ratio test does not hold in these cases for the practical situations of simple order and simple tree order the asymptotic null distributions reduce to the 2 distribution a power study is also conducted in order to compare the likelihood ratio tests against ordered and different potencies finally we present an illustrative example where the direction of the antagonism between two insecticides is investigated by comparing the relative potencies of their mixtures

green s function and stability of a linear partial difference scheme abstract this paper is concerned with a linear partial difference equation which arises from discretizing a heat and a first order wave equations a green s function for this equation is derived various representation theorems monotonicity and oscillatory properties of the green s functions are obtained then by means of the representation theorems we derive several stability criteria for arbitrary solutions of this equation

nonparametric analysis of random utility models abstract this paper considers two sided tests for the parameter of an endogenous variable in an instrumental variable iv model with heteroskedastic and autocorrelated errors we develop the finite sample theory of weighted average power wap tests with normal errors and a known long run variance a typical weight choice yields tests with power near zero for parts of the parameter space we propose two boundary conditions that yield two sided tests with hac errors the locally unbiased lu condition is related to the power around the null hypothesis and is a weaker requirement than unbiasedness the strongly unbiased su condition is more restrictive than lu but the associated wap tests are easier to implement the wap su tests can outperform several tests under the weak iv asymptotics as they make use of the data beyond the anderson rubin and score statistics

kuhn tucker likelihood ratio and wald tests for nonlinear models with inequality constraints on the parameters abstract this paper considers the problem of testing statistical hypothesis in nonlinear regression models with inequality constraints on the parameters first the kuhn tucker test procedure is defined next it is shown that the distribution of the kuhn tucker the likelihood ratio and the wald test statistics converges to the same mixture of chi square distributions under the null hypothesis to illustrate these results two examples are considered 1 the problem of testing that individual effects are missing in an error component model and 2 the problem of testing equilibrium for a model of markets in disequilibrium

nonparametric estimation of convex models via mixtures we present a general approach to estimating probability measures constrained to lie in a convex set we represent constrained measures as mixtures of simple known extreme measures and so the problem of estimating a constrained measure becomes one of estimating an unconstrained mixing measure convex constraints arise in many modeling situations such as estimation of the mean and estimation under stochastic ordering constraints we describe mixture representation techniques for these and other situations and discuss applications to maximum likelihood and bayesian estimation

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

testing multiple inequality hypotheses a smoothed indicator approach abstract this paper proposes a class of origin smooth approximators of indicators underlying the sum of negative part statistic for testing multiple inequalities the need for simulation or bootstrap to obtain test critical values is thereby obviated a simple procedure is enabled using fixed critical values the test is shown to have correct asymptotic size in the uniform sense that supremum finite sample rejection probability over null restricted data distributions tends asymptotically to nominal significance level this applies under weak assumptions allowing for estimator covariance singularity the test is unbiased for a wide class of local alternatives a new theorem establishes directions in which the test is locally most powerful the proposed procedure is compared with predominant existing tests in structure theory and simulation

toward an empirical analysis of polarization stochastic dominance conditions may be interpreted as a means of defining the degree and nature of separateness of two distributions by describing polarization states in terms of stochastic dominance conditions this paper presents a taxonomy of and tests for polarization both between and within population distributions four examples from the poverty growth and development wage distribution and assortative pairing literatures are used to illustrate how the techniques may be used in empirical applications

the generalized riemann problem for the aw rascle model with phase transitions abstract it is proved that the generalized riemann problem for the aw rascle vehicular traffic flow with phase transitions admits a unique local solution in the class of piecewise c 1 functions and in a neighborhood of the origin this solution possesses a structure similar to the solution of the corresponding riemann problem especially when the vacuum state is involved the riemann solution is also well posed which allows us to fit experimental data well

on testing monotone tendencies abstract in certain problems it may be expected that a regression function has a substantial overall tendency to be monotone and yet we may not be certain that all of the restrictions imposed by a simple order are satisfied distribution theory for liklihood ratio tests of homogeneity of a collection of normal means when the collection is decreasing on the average and for testing decreasing on the average as a null hypothesis is presented the restriction decreasing on the average is less restrictive than the usual monotone restriction and allows the data to give rise to reversals over short ranges of values of the parameter set it is closely related to the starshaped ordering restriction

identification of mixture models using support variations abstract we consider the issue of identifying nonparametrically continuous mixture models in these models all observed variables depend on a common and unobserved component but are mutually independent conditional on it such a structure applies for instance to measurement error matching and auction models traditional approaches rely on parametric assumptions or strong functional restrictions we show that these models are actually identified nonparametrically if the supports of the observed variables move with the value of the unobserved component moreover this assumption is testable nonparametrically using tools from extreme value theory we develop an appropriate test and derive its asymptotic properties

seminonparametric bayesian estimation of the asymptotically ideal production model abstract recently it has been shown that seminonparametric methods can be used to produced high quality approximations to a firm s technology unlike the local approximations provided by the conventional class of flexible functional forms seminonparametric methods generate global spans within large classes of functions however that approach usually spans a much larger space than the neoclassical function space relevant to most production modeling an exception is the asymptotically ideal model aim generated from the muntz szatz series expansion since every basis function in that expansion is within the neoclassical function space a straightforward method exists for imposing neoclassical regularity when all factors are substitutes since the relevant constraints are inequality restrictions we implement the approach using bayesian methods to avoid the problems of sampling distribution truncation that would occur from sampling theoretic methods we further discuss the relevant extensions that would permit complementary factors nonconstant returns to scale and technological change

likelihood ration test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters likelihood ratio test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters this paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients the kuhn tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the wald test are examined it is shown in particular that these relationships are the same as in the equality constrained case it is emphasized however that their common asymptotic distribution is a mixture of chi square distributions under the null hypothesis

bounding quantile demand functions using revealed preference inequalities this paper develops a new technique for the estimation of consumer demand models with unobserved heterogeneity subject to revealed preference inequality restrictions particular attention is given to nonseparable heterogeneity the inequality restrictions are used to identify bounds on quantile demand functions a nonparametric estimator for these bounds is developed and asymptotic properties are derived an empirical application using data from the u k family expenditure survey illustrates the usefulness of the methods by deriving bounds and con dence sets for estimated quantile demand functions

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

riemann problem for the relativistic chaplygin euler equations abstract the relativistic euler equations for a chaplygin gas are studied the riemann problem is solved constructively there are five kinds of riemann solutions in which four only contain different contact discontinuities and the other involves delta shock waves under suitable generalized rankine hugoniot relation and entropy condition the existence and uniqueness of delta shock solutions are established

maximum likelihood estimation of the survival functions of stochastically ordered random variables abstract many times aspects of populations exist that must satisfy a stochastic ordering requirement nevertheless estimates may not bear out this stochastic ordering because of the inherent variability of the observations this article will consider the problem of finding maximum likelihood estimates of stochastically ordered survival functions for the cases a one survival function being fixed in advance and b estimating two survival functions when the data include censored observations a numerical example is discussed in detail to illustrate the solution to this problem

a family of autoregressive conditional duration models this paper develops a family of autoregressive conditional duration acd models that encompasses most specifications in the literature the nesting relies on a box cox transformation with shape parameter delta to the conditional duration process and a possibly asymmetric shocks impact curve we establish conditions for the existence of higher order moments strict stationarity geometric ergodicity and beta mixing property with exponential decay we next derive moment recursion relations and the autocovariance function of the power delta of the duration process finally we assess the practical usefulness of our family of acd models using nyse price duration data on the ibm stock while the in sample results warrant the extra flexibility provided either by the box cox transformation or by the asymmetric response to shocks we find no specification that entails satisfactory out of sample performance

testing for separable functional structure using temporary equilibrium models abstract the importance that functional structure plays in the analysis of producer behavior is well known and responsible for the empirical tests of input separability hypotheses found in the contemporary literature unfortunately to our knowledge all such tests have been conducted under the maintained assumption of full factor input equilibrium in this paper we propose and implement a method for testing functional structure hypotheses when the behavioral units are permitted to be in disequilibrium the results of this more general test provide less support for the existence of input separability in two digit manufacturing than previously reported by the authors using tests assuming full equilibrium

serial correlation in latent discrete variable models abstract we consider the problems of estimation and testing in models with serially correlated discrete latent variables a particular case of this is the time series regression model in which a discrete explanatory variable is measured with error test statistics are derived for detecting serial correlation in such a model we then show that the likelihood function can be evaluated by a recurrence relation and thus maximum likelihood estimation is computationally feasible an illustrative example of these methods is given followed by a brief discussion of their applicability to a markov model of switching regressions

restricted likelihood ratio lack of fit tests using mixed spline models penalized regression spline models afford a simple mixed model representation in which variance components control the degree of non linearity in the smooth function estimates this motivates the study of lack of fit tests based on the restricted maximum likelihood ratio statistic which tests whether variance components are 0 against the alternative of taking on positive values for this one sided testing problem a further complication is that the variance component belongs to the boundary of the parameter space under the null hypothesis conditions are obtained on the design of the regression spline models under which asymptotic distribution theory applies and finite sample approximations to the asymptotic distribution are provided test statistics are studied for simple as well as multiple regression models

an instrumental variable approach for tests of unit roots and seasonal unit roots in asymmetric time series models the unit root tests of caner and hansen econometrica 69 2001 1555 for asymmetric time series models based on the ordinary least squares estimator olse have asymptotic null distributions that depend on parameters of asymmetry we resolve this parameter dependency by adopting the instrumental variable estimation of shin and lee j business economic statist 19 2001 233 and the recursive mean adjustment of shin and so j time series anal 22 2001b 595 if the threshold parameter is known the limiting null distribution of the proposed wald test does not depend on any nuisance parameter and is chi squared if the threshold parameter is unknown and is estimated from data then under threshold effect the limiting null distributions of the proposed wald tests are chi squared as those for model with known threshold parameter whereas under no threshold effect they are chi squared only conditionally on the weak limit of the estimated threshold parameter our wald tests extend to seasonal models retaining the chi square asymptotics regardless of the parameter of seasonality which is not the case of the olse based tests moreover the proposed tests can be modified into one sided wald tests which are significantly more powerful than the tests of caner and hansen 2001 we apply our method to the monthly us unemployment rate and find some evidences of seasonal unit roots suggesting nonstationarity rather than the strong stationarity of caner and hansen 2001

semiparametric tests of conditional moment restrictions under weak or partial identification abstract we propose two new semiparametric specification tests which test whether a vector of conditional moment conditions is satisfied for any vector of parameter values 0 unlike most existing tests our tests are asymptotically valid under weak and or partial identification and can accommodate discontinuities in the conditional moment functions our tests are moreover consistent provided that identification is not too weak we do not require the availability of a consistent first step estimator like robinson robinson peter m 1987 asymptotically efficient estimation in the presence of heteroskedasticity of unknown form econometrica 55 875 891 and many others in similar problems subsequently we use k nearest neighbor knn weights instead of kernel weights the advantage of using knn weights is that local power is invariant to transformations of the instruments and that under strong point identification computation of the test statistic yields an efficient estimator of 0 as a byproduct

el inference for partially identified models large deviations optimality and bootstrap validity this paper addresses the issue of optimal inference for parameters that are partially identied in models with moment inequalities there currently exists a variety of inferential methods for use in this setting however the question of choosing optimally among contending procedures is unresolved in this paper i rst consider a canonical large deviations criterion for optimality and show that inference based on the empirical likelihood ratio statistic is optimal this nding is a direct analog to that in kitamura 2001 for moment equality models second i introduce a new empirical likelihood bootstrap that provides a valid resampling method for moment inequality models and overcomes the implementation challenges that arise as a result of non pivotal limit distributions lastly i analyze the nite sample properties of the proposed framework using monte carlo simulations the

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

general solutions of a three level partial difference equation abstract this paper is concerned with a linear partial difference equation which includes the well known dufort frankel multilevel difference scheme for the heat equation by introducing green s functions for this equation we obtain via a novel formal approach an explicit formula for all its solutions given exponential initial conditions separable solutions are also found as applications we derive several stability criteria for the solutions of this equation

statistical inference for uniform stochastic ordering in several populations tion for k population problems under uniform stochastic ordering restrictions we derive closed form estimates even with right censored data by a reparameterization which reduces the problem to a well known isotonic regression problem we also derive the asymptotic distribution of the likelihood ratio statistic for testing equality of the k populations against the uniform stochastic ordering restriction this asymptotic distribution is of the chi bar square type as discussed by robertson wright and dykstra these distributional results are obtained by appealing to elegant results from empirical process theory and showing that the proposed test is asymptotically distribution free recurrence formulas are derived for the weights of the chi bar square distribution for particular cases the theory developed in this paper is illustrated by an example involving data for survival times for carcinoma of the oropharynx

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

modified lagrange multiplier tests for problems with one sided alternatives abstract a modified lagrange multiplier test statistic is proposed which takes explicit account of the one sided nature of the alternative in problems where the null hypothesis specifies that the true value of the parameter vector lies on the boundary of the parameter space computation of this statistic requires only the constrained maximum likelihood estimator conditions for the consistency of tests based on this statistic are examined and it is shown that the distribution of the statistic is not affected of nuisance parameters are allowed to lie on the boundary of the parameter space

inference for likelihood ratio ordering in the two sample problem abstract we obtain the maximum likelihood estimators of two multinomial probability vectors under the constraint that they are likelihood ratio ordered we extend this estimation approach to the case of two univariate distributions and show strong consistency of the estimators we also derive and study the asymptotic distribution of the likelihood ratio statistic for testing the equality of two discrete probability distributions against the alternative that one distribution is greater than the other in the likelihood ratio ordering sense finally we examine a data set pertaining to average daily insulin dose from the boston collaborative drug surveillance program and compare our testing procedure to testing procedures for other stochastic orderings