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

pitfalls of testing non nested hypotheses by the lagrange multiplier method abstract in applied research in econometrics a general model determined from the current knowledge of economic theory often establishes a natural method of embedding a number of otherwise non nested hypotheses under these circumstances significant tests of various hypotheses can be carried out within the classical framework and tests of non nested or separate families of hypotheses do not require development of new statistical methods the application of some suitable variant of likelihood ratio testing procedure will be quite appropriate there are however many ocassions in applied econometrics where the hypotheses under consideration are intended to provide genuine rival explanations of the same given phenomenon and the state of economic theory is not such as to furnish us with a general model that contains both of the rival hypotheses in a natural and theoretically consistent manner a number of investigators have advocated that even when a natural comprehensive model containing both of the hypotheses under consideration cannot be obtained from theoretical considerations it is still appropriate to base significant tests of non nested hypotheses upon a combined model artificially constructed from the rival alternatives moreover in a recent paper on the application of lagrange multiplier lm tests to model specification t s breusch and a r pagan 1980 have claimed that cox s test statistic is connected to an lm or score statistic derived from the application of the lm method to an exponentially combined model earlier employed by a c atkinson 1970 although the use of artificially constructed comprehensive models fortesting separate families of hypotheses is analytically tempting nevertheless it is subject to two major difficulties firstly in many cases of interest in econometrics the structural parameters under the combined hypothesis are not identified secondly the log likelihood function of the artificially constructed model has singularities under both the null and alternative hypotheses the paper firstly examines the derivation of lm statistics in the case of non nested hypotheses and shows that atkinson s general test statistic or breusch and pagan s result can be regarded as an lm test if the parameters of the alternative hypothesis are known the paper also shows that unless all the parameters of the combined models are identified no meaningful test of the separate families of the hypotheses by the artificial embedding procedure is possible and in the identified case an expression for the lm statistic which avoids the problem of the singularity of the information matrix under the null and the alternative hypotheses is obtained the paper concludes that none of the artificially embedding procedures are satisfactory for testing non nested models and should be abandoned it however emphasizes that despite these difficulties associated with the use of artificial embedding procedures cox s original statistic which is not derived as an lm statistic and does not depend on any arbitrary synthetic combination of hypotheses can still be employed as a useful procedure for testing the rival hypotheses often encountered in applied econometrics

velocity inversion using a stratified reference we present an inversion algorithm for backscattered stacked seismic data which will reconstruct the velocity profile in realistic earth conditions the basic approach follows that of the original constant reference speed cohen and bleistein paper 1979a in that hig hfrequency asymptotics and perturbation methods are used however we use a reference speed which may vary with depth and this greatly enhances the validity of the perturbation assumption and hence the inversion results the new algorithm enjoys the same economies and stability properties of the original algorithm making it very competitive with current migration schemes four major assumptions are made 1 the acoustic wave equation is an adequate model 2 stacked data have amplitude information worth preserving fairly accurately 3 the actual reflectivity coefficients can be adequately modeled as perturbations from a continuous reference velocity which depends only on the depth variable and 4 the subsurface can be adequately

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

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

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

a test of separate families of distributions based on the empirical moment generating function summary in testing an hypothesis that a population has a specified distribution against the alternative that its distribution belongs to a separate family it is well known that the likelihood ratio test does not apply we propose a test based on the difference between the sample moment generating function and its theoretical counterpart under ho the argument of the moment generating function is chosen to maximize the test s largesample power small sample properties of the test in two applications are studied by simulation

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

a general class of distributions on the simplex summary the dirichlet class of distributions on the simplex is overstructured for practical work because of its many strong independence properties a persistent problem of distribution theory has thus been to extend this class to include members free of these independence properties an alternative approach has been the recent introduction of the logistic normal class which contains members with and without the independence properties unfortunately this class is separate from the dirichlet class and so cannot sustain discussion of some strong forms of independence these difficulties are overcome in this paper by the introduction of a more general class which includes as special cases the dirichlet and logistic normal classes the role of this new class in relation to the analysis of compositional data in particular the investigation of independence hypotheses is discussed and illustrated

accommodating lateral velocity changes in kirchhoff migration by means of fermat s principle when velocity varies laterally as well as with depth an exact kirchhoff depth migration requires that rays be traced from each depth point in the section to each source receiver location because such a procedure is prohibitively expensive kirchhoff migration is usually carried out by using a velocity function that depends only on depth this paper introduces a new method based on fermat s principle which is a compromise between these two extremes the slowness reciprocal velocity function is written as the sum of two functions the first of which is large and depends only on depth while the other is small and varies both with depth and position along the line raypaths are traced for the first slowness function and are used to calculate migration curves for each depth point these same raypaths are used to calculate traveltime perturbations due to the laterally varying part of the slowness the traveltime perturbations are added to the migration curve to obtain an approximation to the exact migrat

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

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

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

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

a method for discriminating between models describing compositional data summary until recently only the dirichlet class of distributions was available to describe compositional data but now there is an alternative more flexible class of logistic normal distributions to choose between these two classes requires methods for testing separate families of distributions but application of the methods described in the literature involves extremely tedious calculation in this paper a conceptually straightforward and computationally simpler method is introduced and illustrated

robust properties of likelihood ratio tests summary the usual asymptotic chi squared distribution for the likelihood ratio test statistic is based on the assumptions that the data come from the parametric model under consideration and that the parameter satisfies the null hypothesis in this paper we examine the distribution of the likelihood ratio statistic when the data do not come from the parametric model but when the nearest member of the parametric family still satisfies the null hypothesis in general the likelihood ratio statistic no longer follows an asymptotic chi squared distribution and an alternative statistic based on the unionintersection approach is proposed

stability of semilinear stochastic evolution equations stability of moments of the mild solution of a semilinear stochastic evolution equation is studied and sufficient conditions are given for the exponential stability of the pth moment in terms of liapunov function sufficient conditions for sample continuity of the solution are also obtained and the exponential stability of sample paths is proved three examples are given to illustrate the theory

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

identification of rational expectations models abstract this paper deals with the problem of the identification of simultaneous rational expectations re models in the case of re models with current expectations of the endogenous variables the necessary and sufficient conditions for the global identification are derived explicitly in terms of the structural parameters and the linear homogenous identifying restrictions it is shown that in the absence of a priori restrictions on the processes generating the exogenous variables and the disturbances re models and general distributed lag models are observationally equivalent in the case of re models with future expectations of the endogenous variables a general solution that highlights the non uniqueness problem and from which other solutions such as forward or backward solutions can be obtained is derived it is shown that untestable and often quite arbitrary restrictions are needed if re models with future expectations are to be identifiable certain order conditions similar to those obtained for the identification of re models with current expectations are also derived for this case

ray kirchhoff migration in inhomogeneous media a kirchhoff method that avoids possible singularities on the surface of integration and is more accurate than previous kirchhoff methods has been developed for seismic migration in laterally inhomogeneous media it is based on a newly derived integral solution to the acoustic wave equation this solution indicates that wave fields in an inhomogeneous medium can be expressed as a summation of ray solutions determined by the transport and extended eikonal equations the extended eikonal equation is in turn solved by an asymptotic series for implementation a perturbation scheme is developed for solving the ray and transport equations in addition to computing higher order terms of the asymptotic series this scheme can be used to avoid most of the ray tracing required for wave extrapolation in a medium where vertical variations may be large but lateral variations are small compared to velocity itself where an analytic ray solution for the reference velocity used in the perturbation scheme exists ray kirchhoff migration in such a medium can be carried out without numerical ray tracing

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

active impedance control of linear one dimensional wave equations active impedance control of linear one dimensional wave equations is investigated the proposed control algorithms are based on the concepts of wave propagation and impedance matching two control objectives are considered the first objective is to obtain total reflection and the second objective is to achieve total absorption e g matched impedance both control laws utilize some interesting properties of the wave type partial differential equation and do not require information about the disturbance and boundary conditions the resulting controllers although boundary independent contain an infinite number of poles on the imaginary axis and the closed loop systems are not internally stable a simple modification is added to the control laws and the stability is analysed an example of active sound cancellation in ducts with a moving medium is given to demonstrate one of the control algorithms

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

stabilization of some distributed parameter systems the question of stabilization of perturbed or uncertain infinite dimensional systems is considered one class of perturbations for which the system remains stabilizable by the same feedback law as for the nominal system is identified sufficient conditions are presented that generate strong stabilizability of the perturbed system given that the unperturbed system has similar properties it is also shown that for deterministic as well as stochastic systems exponential stability can be achieved by choice of a suitable feedback controller the theoretical results are illustrated by some numerical examples

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

structural stabilization of uncertain systems necessity of the matching condition this paper investigates one aspect of the problem of stabilizing an uncertain linear system that is the systems under consideration contain uncertain parameters which are unknown but bounded the question arises as to whether such a system can be stabilized via feedback control in some of the previous papers in this area the system is assumed to satisfy a so called matching condition this type of assumption is used to assure that the uncertain system can be stabilized it is known however that the matching condition is not a necessary condition for stabilizability this paper introduces a strengthened notion of stabilizability referred to as structural stabilizability via a nominally determined quadratic lyapunov function it is then shown that if a system is to have this stronger property the matching condition must necessarily be satisfied

extended local rytov fourier migration method we develop a novel depth migration method termed the extended local rytov fourier elrf migration method it is based on the scalar wave equation and a local application of the rytov approximation within each extrapolation interval wavefields are fourier transformed back and forth between the frequency space and frequency wavenumber domains during wavefield extrapolation the lateral slowness variations are taken into account in the frequency space domain the method is efficient due to the use of a fast fourier transform algorithm under the small angle approximation the elrf method leads to the split step fourier ssf method that is unconditionally stable the elrf method and the extended local born fourier elbf method that we previously developed can handle wider propagation angles than the ssf method and account for the phase and amplitude changes due to the lateral variations of slowness whereas the ssf method only accounts for the phase changes the stability of the elrf method is controlled

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

a new class of stabilizing controllers for uncertain dynamical systems this paper is concerned with the problem of designing a stabilizing controller for a class of uncertain dynamical systems the vector of uncertain parameters q cdot is time varying and its values q t lie within a prespecified bounding set q in r p furthermore no statistical description of q cdot is assumed and the controller is shown to render the closed loop system practically stable in a so called guaranteed sense that is the desired stability properties are assured no matter what admissible uncertainty q cdot is realized within the perspective of previous research in this area this paper contains one salient feature the class of stabilizing controllers which we characterize is shown to include linear controllers when the nominal system happens to be linear and time invariant in contrast in much of the previous literature see for example 1 2 7 and 9 a linear system is stabilized via nonlinear control another feature of this paper is the fact that the

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

another look at the identification of current rational expectations models abstract this paper provides a complete treatment of the identification of the current rational expectations model with generated forecasts of exogenous variables as introduced by pesaran 1981 it separates the question of the identifiability of the parameters of an re model from that of the model s distinguishability from a non re model it shows how some models classified as unidentified are identified the paper offers a treatment of the surprise model and shows how contrary to popular opinion covariance restrictions are not needed to identify it conditions are developed that are easy to interpret and to check it is shown how standard identification results for models without expectations can be applied to re models that have been appropriately augmented

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

the effects of transformations and preliminary tests for non linearity in regression non linear relationships between two variables are often detected as a result of a preliminary statistical test for linearity common approaches to dealing with non linearity are to a make a linearizing transformation in the independent variable or b fit a relationship that is non linear in the independent variable such as including a quadratic term with either approach the resulting test for association between the two variables can have an inflated type i error we consider testing the significance of the quadratic term in a quadratic model as a preliminary test for non linearity using simulation experiments and asymptotic arguments we quantify the type i error inflation and suggest simple modifications of standard practice to protect the size of the type i error in the case of quadratic regression the type i error will be increased by roughly 50 per cent the simple strategy of appropriately correcting the alpha level is shown to have minimal loss of power if the relationship is truly linear in the case of a linearizing transformation the impact on the type i error will depend on the values of the independent variable and on the set of potential linearizing transformations considered simulation results suggest that a procedure which adjusts the test statistic according to the results of the preliminary test may offer adequate protection

bounded feedback stabilization and global separation principle of distributed parameter systems we show that the infinite dimensional system spl sigma x spl dot t ax t bu t x sub 0 spl epsiv h is globally strongly asymptotically stabilizable by an arbitrarily small smooth feedback here the operator a is the infinitesimal generator of a c sub 0 semigroup of contractions e sup ta on real hilbert space h and b is a bounded linear operator mapping a hilbert space of controls u into h an explicit smooth feedback control law is given further we identify the class of perturbations for which the system is still stabilizable by the same feedback law as for the nominal system based on these results and some differential lyapunov operator equations we then establish a global separation principle for the system spl sigma with a kalman like observer finally these results are illustrated via an example dealing with the wave equation

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

testing strategies for model specification a crucial element in the development of econometric methodology during the past decade has been the concern with testing as opposed to estimating econometric models in this paper we discuss especially for the econometric analysis of time series the main types of test procedures and we also investigate the opportunities to uphold the neyman pearson theory in the context of thorough model specification testing in applied work it is quite usual to carry out several tests on the same set of sample data we consider an extension of the neyman pearson framework to the case of such repeated testing and examine situations where the various hypotheses under test have a particular nesting structure for the case where a sequence of superposed alternatives is tested by so called marginal tests we prove that the various test statistics are asymptotically independent under a common null hypothesis if the statistics are based on either the likelihood ratio or the wald or the lagrange multiplier approach testing a particular null hypothesis against a series of juxtaposed alternatives appears to lead to independent test statistics only in specific circumstances it is shown how independence of test statistics enables the control over the overall type i error probability which is an essential element in the neyman pearson theory using the notions of constructive hypotheses and auxiliary hypotheses we can draw a clear distinction between specification tests and misspecification tests next an overview is given of approaches to and examples of specification and misspecification testing with respect to the former attention is paid to the problem determining the order of dynamics and discriminating between system dynamics and error dynamics the misspecification testing is reviewed for specification error nonconstancy of coefficients heteroscedasticity serial dependence and nonnormality of disturbances also the problem of testing for several misspecifications jointly or sequentially is considered finally we discuss the options and associated difficulties in implementing the various tests in an overall testing strategy