testing for non nested conditional moment restrictions using unconditional empirical likelihood we propose non nested tests for competing conditional moment resctriction models using a method of empirical likelihood our tests are based on the method of conditional empirical likelihood developed by kitamura tripathi and ahn 2004 and zhang and gijbels 2003 by using the conditional implied probabilities we develop three non nested tests the moment encompassing cox type and effcient score encompassing tests compared to the existing non nested tests which mainly focus on testing unconditional moment restrictions our approach directly tests conditional moment restrictions which imply the infinite number of unconditional moment restrictions we derive the null distributions and power properties of the proposed tests simulation experiments show that our tests have reasonable finite sample properties

tilting objects in the stable category of vector bundles on a weighted projective line of type national natural science foundation of china 11201386 10931006 11071040 11201388 natural science foundation of fujian province of china 2012j05009

tests for two separate regressions abstract several recently proposed tests for separate regressions in econometrics are re examined in the light of recommendations by cox 1961 this re examination points to simplified criteria and emphasizes the unity underlying the tests the exact distributions of some of the tests are developed under the tested hypothesis these are given a geometrical characterization which is helpful in exploring relations with the classical f test an orthogonal decomposition is proposed which provides a direct link between the f test and tests based upon artificial nesting

bootstrap j tests of nonnested linear regression models the j test for nonnested regression models often overrejects very severely as an asymptotic test we provide a theoretical analysis which explains why and when it performs badly this analysis implies that except in certain extreme cases the j test will perform very well when bootstrapped using several methods to speed up the simulations we obtain extremely accurate monte carlo results on the finite sample performance of the bootstrapped j test these results fully support the predictions of our theoretical analysis even in contexts where the analysis is not strictly applicable

a simple test for regression specification with non nested alternatives abstract in this paper i introduce a simple test for the presence of the data generating process among several non nested alternatives the test is an extension of the classical j test for non nested regression models i also provide a bootstrap version of the test that avoids possible size distortions inherited from the j test

comparison of local power of alternative tests of non nested regression models the paper derives and compares the local power of three different methods of testing non nested regression models that are available in the literature it shows that the asymptotic power of the orthodox f test against local alternatives is strictly less than that of cox s non nested test or the j test recently proposed by davidson and mackinnon 5 unless the number of non overlapping variables of the alternative hypothesis over the null hypothesis is unity in which case all three tests are shown to be asymptotically equivalent the final section of the paper gives results of monte carlo experiments designed to check the validity of the theoretical findings of the paper and also to shed light on the small sample properties of the cox test and the orthodox test

non regular maximum likelihood problems four non regular estimation problems are reviewed and discussed one the unbounded likelihood problem involves distributions with infinite spikes for which maximum likelihood can fail to give consistent estimators a comparison is made with modified likelihood and spacings methods which do give efficient estimators in this case an application to the box cox shifted power transform is given the other three problems occur when the true parameter lies in some special subregion in one the constrained parameter problem the subregion is a boundary the other two the embedded model and the indeterminate parameters problems occur when the model takes on a special form in the subregion these last two problems have previously been investigated separately we show that they are equivalent in some situations both often arise in non linear models and we give a directed graph approach which allows for their occurrence in nested model building it is argued that many non regular problems can be handled systematically without having to resort to elaborate technical assumptions relatively uncomplicated methods may be used provided that the underlying nature of the non regularity is understood

alternative nonnested specification tests of time series investment models abstract this paper develops and compares non nested hypothesis tests for linear regression models with first order serially correlated errors it extends the non nested testing procedures of pesaran fisher and mcaleer and davidson and mackinnon and compares their performance on four conventional models of aggregate investment demand using quarterly u s investment data from 1951 i to 1983 iv the data and the non nested hypothesis tests initially indicate that none of the models are correctly specified the tests are also intransitive in their assessments before rejecting these conventional models of investment demand we investigate the small sample properties of these different non nested test procedures through a series of monte carlo studies we find that these non nested tests can have significant finite sample size and power biases

non nested tests for competing models estimated by generalized method of moments non nested tests are proposed for competing models estimated by generalized method of moments results are presented for non nested linear regression models with het eroskedasticity and serial correlation of unknown form and differing instrument validity assumptions regression forms of the statistics are also presented this paper is concerned with providing a procedure whereby non nested models estimated by generalized method of moments gmm hansen 1982 may be com pared in particular cox type cox 1961 1962 and encompassing tests mizon and richard 1986 are proposed implicit in such tests is a degree of arbitrariness in the way the statistics are constructed as typically the assumptions underlying gmm estima tion techniques are minimal and do not fully specify the data generation process dgp underlying the observable random variables in contradistinction to the method of maximum likelihood our procedures allow the population moment conditions on which gmm estimation of the competing models is based to differ in the conditioning sets under which conditional expectation is taken such differences may reflect different a priori assumptions concerning the exogeneity status of random variables in the models these tests may be regarded as generalizations of singleton 1985 more recent work includes ghysels and hall 1990 which requires the specification of the dgp under the null hypothesis and wooldridge 1990b which proposes heteroskedasticity robust tests for non nested non linear regression models our results are specialized to provide non nested tests for competing regression models estimated by instrumental variables where we allow a degree of heteroskedastic ity and serial correlation in the process generating the disturbance terms by assuming appropriate mixing conditions white 1984 and the instrument validity assumptions to differ across the models cf godfrey 1983 1984 which assume a scalar covariance matrix for the disturbances and that the set of instruments is valid in both models thus our framework includes models which may be both simultaneous and dynamic section 2 describes procedures for obtaining cox type and encompassing tests for competing models estimated by gmm section 3 specializes these results to competing linear regression models estimated by instrumental variables regression forms for the statistics are presented the paper is concluded by section 4 in our presentation we eschew detailed regularity assumptions

tests for model specification in the presence of alternative hypotheses some further results abstract in davidson and mackinnon 1981 two of the present authors proposed a novel and very simple procedure for testing the specification of a nonlinear regression model against the evidence provided by a non nested alternative in this paper we extend their results in several directions first we relax a number of the assumptions of the previous paper we admit the possibility that the nonlinear regression functions may depend on lagged dependent variables and we do not require that the error terms be normally distributed second we show how the earlier procedure may straightforwardly be generalized to the case where the two non nested models involve different transformations of the dependent variable finally we propose a simple procedure for testing non nested linear regression models which have endogenous variables on the right hand side and have therefore been estimated by two stage least squares

on the comprehensive method of testing non nested regression models abstract the paper derives the specific form of the exponentially combined likelihood function of two competing multivariate non linear regression models and shows that the application of the comprehensive approach to testing non nested regression models will in general be indeterminate it establishes that in the univariate case there exists a large number of tests of non nested regression models which are consistent in addition to having the same asymptotic distribution under the null hypothesis the paper then derives a set of conditions under which all these consistent tests are asymptotically equivalent not only under the null hypothesis but also under local alternatives as an application of this latter result the paper establishes the asymptotic equivalence of the tests recently proposed by davidson and mackinnon and fisher and mcaleer under local alternatives and shows that within the class of tests considered in the paper these proposed tests possess maximum local power the latter test has this property only when the number of explanatory variables of the true model is not more than that of the false model

bootstrapping regression models the regression and correlation models are considered it is shown that the bootstrap approximation to the distribution of the least squares estimates is valid and some error bounds are given

a laplace approximation to the moments of a ratio of quadratic forms summary the laplace method for approximating integrals is applied to give a general approximation for the kth moment of a ratio of quadratic forms in random variables the technique utilises the existence of a dominating peak at the boundary point on the range of integration as closed form and tractable formulae do not exist in general this simple approximation which only entails basic algebraic operations has evident practical appeal we exploit the approximation to provide an approximate mean bias function for the least squares estimator of the coefficient of the lag dependent variable in a first order stochastic difference equation

some aspects of testing non nested hypotheses abstract this paper examines some aspects of testing non nested hypotheses an inequality between the cox and atkinson statistics is noted and the necessary and sufficient condition for the atkinson test to be consistent is derived a new test procedure is also outlined the rest of the paper illustrates the various test statistics their properties and relationships for competing linear regression models

monte carlo methodology and the finite sample properties of instrumental variables statistics for testing nested and non nested hypotheses using monte carlo methodology this paper investigates the effect of dynamics and simultaneity on the finite sample properties of instrumental variables statistics for testing nested and nonnested hypotheses simple numerical analytical formulae response surfaces are obtained which closely approximate the statistics unknown size and power functions for a dynamic simultaneous equations model the analysis illustrates the value and limitations of asymptotic theory in interpreting finite sample properties two practical results arise the f form and the wald statistic is favored over its chi squared form and large sigma and small effective sample size strongly affect the test of over identifying restrictions and the cox type test copyright 1991 by the econometric society

a comparison of nonnested tests for misspecified models using the method of approximate slopes abstract comparisons of the cox wald and j tests are conducted under a standard framework and in a misspecified setting the data generation process includes a regressor that is not in either model most power comparisons have been carried out for local alternatives but comparisons under a nonlocal alternatives framework using the method of approximate slopes developed by bahadur 1960 1967 are made in this paper monte carlo experiments are conducted and the cox test is shown to have the highest small sample power and approximate slope for most of the cases considered the results from response surface regressions provide strong evidence that the approximate slope is a good predictor of the small power of nonnested tests it is also useful for directly comparing the small sample power of one degree of freedom tests of nonnested hypotheses

goodness of fit statistics for age specific reference intervals the age specific reference interval is a commonly used screening tool in medicine it involves estimation of extreme quantile curves such as the 5th and 95th centiles of a reference distribution of clinically normal individuals it is crucial that models used to estimate such intervals fit the data extremely well however few procedures to assess goodness of fit have been proposed in the literature and even fewer have been evaluated systematically here we consider procedures based on the distribution of the z scores standardized residuals from a model and on pearson chi 2 statistics for observed and expected counts in groups defined by age and the estimated reference centile curves two of the procedures q and grid tests are mainly inferential whereas the third permutation bands and b tests is essentially graphical we obtain approximations to the null distributions of several relevant test statistics and examine their size and power for a range of models based on real data sets we recommend q tests in all situations where z scores are available since they are general simple to calculate and usually have the highest power among the three classes of test considered for the cases considered the grid tests are always inferior to the q and b tests

regularity conditions for cox s test of non nested hypotheses abstract in this article we provide for the first time general regularity conditions and a rigorous proof of the asymptotic normality of cox s statistic for testing separate families of hypotheses the cox test for choosing between competing linear regression models is discussed as an example

statistical inference in non nested econometric models the purpose of this paper is to discuss some procedures that are available for testing non nested or separate hypotheses in the statistics and econometrics literature since many of these techniques may also be exploited in other disciplines it is hoped that an elaboration of the principal theoretical findings may make them more readily accessible to researchers in other disciplines several simple examples are used to illustrate the concepts of nested and non nested hypotheses and within the latter category global and partial non nested hypotheses two alternative methods of testing non nested hypotheses are discussed and contrasted the first of these is cox s modification of the likelihood ratio statistic and the second is atkinson s comprehensive model approach a major emphasis is placed on the role of the cox principle of hypothesis testing which enables a broad range of hypotheses to be tested within the same framework the problem associated with the application of the comprehensive model approach to composite non nested hypotheses is also highlighted roy s union intersection principle is presented as a viable method of dealing with this problem simulation results concerning the finite sample properties of various tests are discussed together with an analysis of some attempts to correct the poor size of the cox and related tests

a simulation approach to the problem of computing cox s statistic for testing nonnested models abstract this paper proposes a new procedure for computing the cox statistic for tests of nonnested hypotheses using the method of stochastic simulation the procedure is applicable to a wide class of probability distributions is relatively simple to implement and does not require an analytic derivation of the pseudo true estimators that enter the cox test statistic the paper also contains an application of the proposed method to the test of probit versus logistic formulations of the univariate binary choice models the empirical results show that the simulation method works reasonably well even for a moderate number of replications

the likelihood dominance criterion a new approach to model selection abstract the dominance ordering and the ldc provide a new approach to model selection the dominance ordering is described in terms of a fictive experiment in which the two competing hypotheses are nested in a composite if estimating the composite would lead to accepting one hypothesis and rejecting the other then which would be accepted and which rejected is determined by the two adjusted likelihood values and does not require estimating the composite although it does require specifying its parametric size the ldc generalizes the dominance ordering by considering a range of admissible composite parametric sizes this range will usually include all sizes of practical interest

exactly distribution free inference in instrumental variables regression with possibly weak instruments abstract this paper introduces a rank based test for the instrumental variables regression model that dominates the anderson rubin test in terms of finite sample size and asymptotic power in certain circumstances the test has correct size for any distribution of the errors with weak or strong instruments the test has noticeably higher power than the anderson rubin test when the error distribution has thick tails and comparable power otherwise like the anderson rubin test the rank tests considered here perform best relative to other available tests in exactly identified models

some robust exact results on sample autocorrelations and tests of randomness abstract several exact results on the second moments of sample autocorrelations for both gaussian and non gaussian series are presented general formulae for the means variances and covariances of sample autocorrelations are given for the case where the variables in a sequence are exchangeable bounds for the variances and covariances of sample autocorrelations from an arbitrary random sequence are derived exact and explicit formulae for the variances and covariances of sample autocorrelations from a gaussian white noise are given it is observed that the latter results hold for all spherically symmetric distributions a simulation experiment with gaussian series indicates that normalizing each sample autocorrelation with its exact mean and variance instead of the usual approximate moments can improve considerably the accuracy of the asymptotic n 0 1 distribution to obtain critical values for tests of randomness the exact second moments of rank autocorrelations are also studied

a nonlinear hyperbolic maxwell system using measure valued functions abstract we consider a modified antenna s problem with power type constitutive laws this consists in a new nonlinear hyperbolic system that extends a duvaut lions model using the galerkin approximation properties of the natural functional spaces and exploring the l p l p duality we prove the existence of solutions in a generalized sense passing to the limit in a family of approximated problems and using measure valued functions in this process the difficulties in obtaining the necessary a priori estimates for the solutions of the finite dimensional problems are overcome through the use of bases with special properties related to the model

mutation of tilting bundles of tubular type abstract let x be a weighted projective line of tubular type and coh x the category of coherent sheaves on x the main purpose of this note is to show that the subgraph of the tilting graph consisting of all basic tilting bundles in coh x is connected this yields an alternative proof for the connectedness of the tilting graph of coh x our approach leads to the investigation of the change of slopes of a tilting sheaf in coh x under co apr mutations which may be of independent interest

the rank version of von neumann s ratio test for randomness abstract although rank tests for randomness were proposed in the literature as early as 1943 no such test has gained wide acceptance comparable to say spearman s rho test this may be due to the lack of small sample theory and of tables of critical values to enable such a test to be carried out on small samples in this article we consider the rank version of the von neumann ratio statistic and we obtain the critical values of this statistic under the randomization hypothesis in a monte carlo experiment we then show that the resulting nonparametric test for randomness has far greater power than the test based on the number of runs up and down moreover under normality its power vis a vis the normal theory von neumann ratio test is also very good it is therefore suggested that with the tables presented in this article the rank von neumann ratio test for randomness provides an easy and powerful alternative to nonparametric tests now in common use

testing separate regression models subject to specification error within the framework of linear regression errors arising from artificial inclusion or exclusion of variables are considered with augmentations or restrictions on a given maintained hypothesis this permits exploitation of relations between tests based on wald and lagrange multiplier principles it is demonstrated that the standard f test though based on biased estimators is nevertheless valid the traditional analysis of misspecification is applied to the linear specialization of tests for separate families of hypotheses an empirical example is provided examining the effect of labour legislation on the growth of canadian trade union membership using annual data for 1925 72 this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item

exact permutation tests for non nested non linear regression models abstract this paper proposes exact distribution free permutation tests for the specification of a non linear regression model against one or more possibly non nested alternatives the new tests may be validly applied to a wide class of models including models with endogenous regressors and lag structures these tests build on the well known j test developed by davidson and mackinnon 1981 several tests for model specification in the presence of alternative hypotheses econometrica 49 781 793 and their exactness holds under broader assumptions than those underlying the conventional j test the j type test statistics are used with a randomization or monte carlo resampling technique which yields an exact and computationally inexpensive inference procedure a simulation experiment confirms the theoretical results and also shows the performance of the new procedure under violations of the maintained assumptions the test procedure developed is illustrated by an application to inflation dynamics

econometric modelling with non normal disturbances abstract this paper analyzes a general class of non normal density functions dubbed sargan densities in the context of the ordinary regression model and the simple one market disequilibrium model use of the normal density in disequilibrium models is unwieldy especially for multimarket models since the application of maximum likelihood methods requires numerical evaluation of multiple integrals these difficulties are avoided with the sargan densities and based on both asymptotic results and limited sampling experiments these densities appear to offer a promising alternative to the normal in disequilibrium models

on tests applied to residuals abstract the null distribution of a test statistic computed on residuals can be affected by the dependence among the residuals it might be expected however that the dependence decreases as the sample size increases so that the limiting null distribution is the same as if the test were based on independent observations the author investigates whether this large sample equivalence holds for tests of correlation scale difference regression and location difference particular emphasis is placed on showing when rank tests based on residuals have a strongly asymptotically distribution free property u statistic theorems are used to investigate these issues

a note on studentizing a test for heteroscedasticity abstract breusch and pagan 1979 have recently proposed a convenient test for heteroscedasticity in general linear models this note derives the asymptotic distribution of their test under sequences of contiguous alternatives to the null hypothesis of homoscedasticity the test is shown to possess asymptotically incorrect size nominal significance level except in the case of strictly gaussian disturbances a slight modification of the test is proposed which corrects this defect

the effect of simulation order on level accuracy and power of monte carlo tests we discuss the effect of simulation order on level accuracy and power of monte carlo tests in a very general setting both parametric problems with or without nuisance parameters and nonparametric problems are treated by a single unifying argument it is shown that if the level of a monte carlo test is known only nominally not precisely then the level error of a monte carlo test is an order of magnitude less than that of the corresponding asymptotic test this result is available whenever the test statistic is asymptotically pivotal even if the number of simulations is held fixed as the sample size n increases it implies that monte carlo methods are a real alternative to asymptotic methods we also show that even if the number of simulations is held fixed a monte carlo test is able to distinguish between the null hypothesis and alternative hypotheses distant n 12 from the null

bootstrap based critical values for the information matrix test abstract in finite samples the true size of white s information matrix test often differs greatly from its nominal size based on asymptotic critical values this paper shows how the bootstrap can be used to obtain improved finite sample critical values the results of monte carlo experiments show that for the cases investigated the bootstrap largely eliminates the problem of incorrect finite sample size moreover when size corrected critical values are used forms of the test that have small size distortions with asymptotic critical values can have much lower power than forms that have large size distortions with asymptotic critical values

tests of non nested regression models small sample adjustments and monte carlo evidence abstract it is known that the small sample significance levels of cox type tests of non nested regression models can be much greater than the nominal level adjustments designed to overcome this problem are discussed and two tests are proposed monte carlo evidence on the performance of the tests derived in this paper the davidson mackinnon j test and the fisher mcaleer test is presented the f test applied to the comprehensive model is also included in the simulation experiments

misspecification tests in econometrics based on ranks abstract this paper introduces a class of rank statistics for use in testing econometric models for misspecification these statistics are ideally suited to survey data since endogenous and exogenous variables in econometric models may therefore be considered exchangeable thus residuals from a wide class of models e g linear regression non linear regression simultaneous equations etc are also exchangeable since rank statistics are distribution free when based on exchangeable data it follows the rank statistics based on these residuals are also distribution free simulation studies in the linear regression case suggest that they have good power characteristics and are distributionally robust in comparison to the usual classical procedures

robustness of size of tests of autocorrelation and heteroscedasticity to nonnormality abstract a comprehensive empirical examination is made of the sensitivity of tests of disturbance covariance in the linear regression model to nonnormal disturbance behaviour tests of autocorrelation appear to be quite robust except for extreme nonnormality but tests for heteroscedasticity are highly susceptible to kurtosis

the encompassing principle and its application to testing nonnested hypotheses the encompassing principle is used to develop a testing framework which unifies the literature on non nested testing allowing analysis of the relationship between alternative tests and in particular enabling asymptotic and finite sample equivalences and identities to be established easily when they exist as well as embracing nested hypothesis testing the concept of the implicit null hypothesis of a test is introduced to show that the effective acceptance region for some tests extends beyond the acceptance region corresponding to the null of interest and so such tests can be inconsistent against fixed alternatives closely related to the nominal null and alternative the analysis is illustrated by an application to two non nested linear regression models and it is shown that the conventional f test as well as all the one degree of freedom non nested tests has an encompassing interpretation and that the f test is a complete parametric encompassing test

testing nested or non nested hypotheses this paper presents a test procedure for nested or non nested hypotheses the test statistic is based on the difference between two estimators of the pseudo true value as defined for instance by sawa this statistic is similar to the usual wald statistic in the case of nested hypotheses and it can be replaced by an asymptotically equivalent one deduced from the score function

encompassing tests when no model is encompassing this paper considers regression based tests for encompassing when none of the models under consideration encompasses all the other models for both in and out of sample applications i derive asymptotic distributions and propose feasible procedures to construct confidence intervals and test statistics procedures that are asymptotically valid under the null of encompassing e g davidson and mackinnon econometrica 49 1981 781 can have large asymptotic and finite sample distortions simulations indicate that the proposed procedures can work well in samples of size typically available though the divergence between actual and nominal confidence interval coverage sometimes is large

tests of non nested regression models some results on small sample behaviour and the bootstrap the most popular procedures for testing a regression model against a single non nested alternative can be substantially oversized in small samples also when a regression model is to be tested in the presence of several non nested alternatives the null model is sometimes accepted only if testing against each alternative in turn produces no significant outcomes this approach leads to an implicit overall test with a significance level that is not known even asymptotically it is shown that the bootstrap can be used to control significance levels in both types of situation power estimates for various tests using bootstrap critical values are also obtained and compared

a robust test for non nested hypotheses we propose a robust version of cox type test statistics for the choice between two non nested hypotheses we first show that the influence of small amounts of contamination in the data on the test decision can be very large secondly we build a robust test statistic by using the results on robust parametric tests that are available in the literature and show that the level of the robust test is stable finally we show numerically not only the robustness of this new test statistic but also that its asymptotic distribution is a good approximation of its sample distribution unlike for the classical test statistic we apply our results to the choice between a pareto and an exponential distribution as well as between two competing regressors in the simple linear regression model without intercept

some results on the glejser and koenker tests for heteroskedasticity abstract the glejser and koenker studentized lagrange multiplier tests for heteroskedasticity are considered asymptotic theory and monte carlo experiments are used to investigate the effects of nonnormality under null and alternative hypotheses and also the consequences of using an incorrect alternative a method for using test outcomes to select models of heteroskedasticity is critically examined glejser s test is not in general asymptotically valid under asymmetric disturbances koenker s test is asymptotically valid under asymmetric and other nonnormal disturbances but has estimated finite sample significance levels that are sometimes sensitive to skewness an adjusted version of koenker s statistic is discussed

monte carlo tests with nuisance parameters a general approach to finite sample inference and nonstandard asymptotics abstract the technique of monte carlo mc tests dwass 1957 annals of mathematical statistics 28 181 187 barnard 1963 journal of the royal statistical society series b 25 294 provides a simple method for building exact tests from statistics whose finite sample distribution is intractable but can be simulated when no nuisance parameter is involved we extend this method in two ways first by allowing for mc tests based on exchangeable possibly discrete test statistics second by generalizing it to statistics whose null distribution involves nuisance parameters maximized mc mmc tests simplified asymptotically justified versions of the mmc method are also proposed these provide a simple way of improving standard asymptotics and dealing with nonstandard asymptotics

the pseudo true score encompassing test for non nested hypotheses abstract well known encompassing tests are usually difficult to implement because it is difficult to compute the pseudo true value of the quasi maximum likelihood estimator in this paper we propose a more operational encompassing test that does not involve such pseudo true value and is asymptotically equivalent to the wald and score encompassing tests instead the proposed test relies on the pseudo true score which is relatively easy to evaluate this test is not restricted to testing conditional mean specifications and hence extends the applicability of the conditional mean encompassing test of wooldridge j econom 45 1990b 331 the proposed test is particularly useful when data characteristics can be fully incorporated into the likelihood function our simulations confirm that this test compares favorably with the j and ja tests in testing conditional mean specifications and outperforms the cox test in testing conditional variance specifications

asymptotic power comparisons of tests of separate parametric families by bahadur s approach summary the paper investigates asymptotic power comparisons of tests of separate parametric families when the size of the test is allowed to tend to zero as the sample size tends to infinity it shows that bahadur s method of asymptotic comparison by means of the approximate slope of the tests can be extended to the case of separate parametric families the paper contains a number of applications

exact tests in single equation autoregressive distributed lag models abstract for hypotheses on the coefficient values of the lagged dependent variables in the arx class of dynamic regression models test procedures are developed which yield exact inference for given up to an unknown scale factor distribution of the innovation errors they include exact tests on the maximum lag length for structural change and on the presence of seasonal or multiple unit roots i e they cover situations where usually asymptotic and non exact t f aoc adf or hegy tests are employed the various procedures are demonstrated and compared in illustrative empirical models and the approach is critically discussed

well posedness theory for electromagnetic obstacle problems abstract this paper develops a well posedness theory for hyperbolic maxwell obstacle problems generalizing the result by duvaut and lions 1976 5 building on the recently developed result by yousept 2020 30 we prove an existence result and study the uniqueness through a local h curl regularity analysis with respect to the constraint set more precisely every solution is shown to locally satisfy the maxwell ampere equation resp faraday equation in the region where no obstacle is applied to the electric field resp magnetic field by this property along with a structural assumption on the feasible set we are able to localize the obstacle problem to the underlying constraint regions in particular the resulting localized problem does not employ the electric test function resp magnetic test function in the area where the l 2 regularity of the rotation of the electric field resp magnetic field is not a priori guaranteed this localization strategy is the main ingredient for our uniqueness proof after establishing the well posedness we consider the case where the electric permittivity is negligibly small in the electric constraint region and investigate the corresponding eddy current obstacle problem invoking the localization strategy we derive an existence result under an l 2 boundedness assumption for the electric constraint region along with a compatibility assumption on the initial data the developed theoretical results find applications in electromagnetic shielding

alternative procedures and associated tests of significance for non nested hypotheses this paper attempts to synthesize various procedures for testing non nested hypotheses within the framework of artificial nesting and establishes the result that different tests correspond to different treatments of its identification problem numerical and a priori identification methods are distinguished we derive two modified likelihood ratio tests that are asymptotically equivalent to the cox test and explain the relationship between them the tests are consistent this abstract was borrowed from another version of this item

comparing non nested regression models a method for comparing the fits of two non nested models based on a suggestion of davidson and mackinnon 1981 is developed in the context of linear and nonlinear regression with normal errors each model is regarded as a special case of an artificial supermodel and is obtained by restricting the value of a mixing parameter gamma to 0 or 1 to enable estimation and hypothesis testing for gamma an approximate supermodel is used in which the fitted values from the individual models appear in place of the original parametrization in the case of nested linear models the proposed test essentially reproduces the standard f test the calculations required are for the most part straight forward basically linear regression through the origin the test is extended to cover situations in which serious bias in the maximum likelihood estimate of gamma occurs simple approximate bounds for the bias being given two real datasets are used illustratively throughout

the distributions of the j and cox non nested tests in regression models with weakly correlated regressors abstract this paper examines the asymptotic null distributions of the j and cox non nested tests in the framework of two linear regression models with nearly orthogonal non nested regressors the analysis is based on the concept of near population orthogonality npo according to which the non nested regressors in the two models are nearly uncorrelated in the population distribution from which they are drawn new distributional results emerge under npo the j and cox tests tend to two different random variables asymptotically each of which is expressible as a function of a nuisance parameter c a n 0 1 variate and a 2 q variate where q is the number of non nested regressors in the alternative model the monte carlo method is used to show the relevance of the new results in finite samples and to compute alternative critical values for the two tests under npo by plugging consistent estimates of c into the relevant asymptotic expressions an empirical example illustrates the plug in procedure

prepivoting test statistics a bootstrap view of asymptotic refinements abstract approximate tests for a composite null hypothesis about a parameter may be obtained by referring a test statistic to an estimated critical value either asymptotic theory or bootstrap methods can be used to estimate the desired quantile the simple asymptotic test a refers the test statistic to a quantile of its asymptotic null distribution after unknown parameters have been estimated the bootstrap approach used here is based on the concept of prepivoting prepivoting is the transformation of a test statistic by the cdf of its bootstrap null distribution the simple bootstrap test b refers the prepivoted test statistic to a quantile of the uniform 0 1 distribution under regularity conditions the bootstrap test b has a smaller asymptotic order of error in level than does the asymptotic test a provided that the asymptotic null distribution of the test statistic does not depend on unknown parameters in the contrary case both a and b have the same order of level error certain class

robustness to nonnormality of the durbin watson test for autocorrelation abstract this study investigates the robustness to nonnormality of the null distribution of the durbin watson test for autocorrelation in regression errors the first four moments of the null distribution are derived to the order o 1 n 3 when the regression errors are nonnormal with n the sample size it is found that nonnormality has an insignificant effect on the mean and the fourth central moment of the distribution the variance tends to be deflated inflated if the error distribution is long tailed short tailed the third central moment is reduced if the error distribution is skewed left or right both skewness and kurtosis of the distribution are affected by nonnormality but these effects are negligible in large samples it seems the test is relatively robust for moderate nonnormality and moderately large sample size these effects are also found to have insignificant influence from the regressors

well posedness for bean s critical state model with displacement current this paper deals with bean s critical state model for superconductors with displacement current and field dependent critical current density the main goal is to prove the existence and uniqueness of solutions

exact tests of a model against nonnested alternatives the results of milliken graybill 1970 are used to develop a general procedure for obtaining exact tests of a linear model against several nonnested and nonlinear alternatives simultaneously the procedure may be extended to test a null model against alternatives in which the dependent variable is subjected to different data transformations arguments are presented in favour of multiple tests