on the stability and instability of n dimensional discrete systems n 1 the applicability of sufficient conditions for stability and for instability of multidimensional discrete systems is extended the approach is based on interpreting in the transform domain an extension which has been previously proposed only for one dimensional systems and had been based on time domain considerations

n dimensional stability margins computation and a variable transformation stability margins for n dimensional n geq 2 linear discrete causal systems are defined following a definition suggested recently in the literature for n 2 these can serve as a measure in some sense for the tendency of a stable n d system to become unstable also presented is a new procedure for the computation of these stability margins which is explicitly formulated the computational complexity is equivalent to that of solving for one indeterminate a set of n 1 real equations in n 1 real indeterminates also an n dimensional expansion of a known variable transformation which preserves the core condition of stability is presented and used to considerably simplify n dimensional stability tests and stability margins computations for a class of special cases numerical examples are also provided

simulation based finite and large sample tests in multivariate regressions abstract in the context of multivariate linear regression mlr models it is well known that commonly employed asymptotic test criteria are seriously biased towards overrejection in this paper we propose a general method for constructing exact tests of possibly nonlinear hypotheses on the coefficients of mlr systems for the case of uniform linear hypotheses we present exact distributional invariance results concerning several standard test criteria these include wilks likelihood ratio lr criterion as well as trace and maximum root criteria the normality assumption is not necessary for most of the results to hold implications for inference are two fold first invariance to nuisance parameters entails that the technique of monte carlo tests can be applied on all these statistics to obtain exact tests of uniform linear hypotheses second the invariance property of the latter statistic is exploited to derive general nuisance parameter free bounds on the distribution of the lr statistic for arbitrary hypotheses even though it may be difficult to compute these bounds analytically they can easily be simulated hence yielding exact bounds monte carlo tests illustrative simulation experiments show that the bounds perform well our findings illustrate the value of the bounds as a tool to be used in conjunction with more traditional simulation based test methods e g the parametric bootstrap which may be applied when the bounds are not conclusive

a size correction to the lagrange multiplier test for heteroskedasticity abstract making use by the recent work by harris this paper provides the formula for size correction to the lagrange multiplier test for heteroskedasticity monte carlo experiments indicate that our size correction is effective in improving the accuracy of the size of the test since the lagrange multiplier test tends to have a true size less than the nominal size in our experiments the application of the test at a higher true significance level tends to increase the power of the test as well reasonable results in our numerical experiments also give a partial check on the validity of the derived formula

exact tests for contemporaneous correlation of disturbances in seemingly unrelated regressions this paper proposes finite sample procedures for testing the sure specification in multi equation regression models i e whether the disturbances in different equations are contemporaneously uncorrelated or not we apply the technique of monte carlo mc tests see dwass and barnard respectively ann math statist 28 1957 181 j r statist soc ser b 25 1963 294 to obtain exact tests based on standard lr and lm zero correlation tests we also suggest a mc quasi lr qlr test based on feasible generalized least squares fgls we show that the latter statistics are pivotal under the null which provides the justification for applying mc tests furthermore we extend the exact independence test proposed by harvey and phillips bull econ res 34 2 1982 79 to the multi equation framework specifically we introduce several induced tests based on a set of simultaneous harvey phillips type tests and suggest a simulation based solution to the associated combination problem the properties of the proposed tests are studied in a monte carlo experiment which shows that standard asymptotic tests exhibit important size distortions while mc tests achieve complete size control and display good power moreover mc qlr tests performed best in terms of power a result of interest from the point of view of simulation based tests the power of the mc induced tests improves appreciably in comparison to standard bonferroni tests and in certain cases outperform the likelihood based mc tests the tests are applied to data used by fischer j monetary econ 32 485 1993 to analyze the macroeconomic determinants of growth

invariance nonlinear models and asymptotic tests the invariance properties of some well known asymptotic tests are studied three types of invariance are considered invariance to the representation of the null hypothesis invariance to one to one transformations of the parameter space reparameterizations and invariance to one to one transformations of the model variables such as changes in measurement units tests that are not invariant include the wald test and generalized versions of it a widely used variant of the lagrange multiplier test neyman s c a test and a generalized version of the latter for all these tests we show that simply changing measurement units can lead to vastly different answers even when equivalent null hypotheses are tested this problem is illustrated by considering regression models with box cox transformations on the variables we observe in particular that various consistent estimators of the information matrix lead to test procedures with different invariance properties general sufficient conditions are then established under which the generalized c a test becomes invariant to reformulations of the null hypothesis and or to one to one transformations of the parameter space as well as to transformations of the variables in many practical cases where wald type tests lack invariance we find that special formulations of the generalized c a test are invariant and hardly more costly to compute than wald tests this computational simplicity stands in contrast with other invariant tests such as the likelihood ratio test we conclude that noninvariant asymptotic tests should be avoided or used with great care further in many situations the suggested implementation of the generalized c a test often yields an attractive substitute to the wald test which is not invariant and to other invariant tests which are more costly to perform

power and robustness of jackknife and likelihood ratio tests for grouped heteroscedasticity abstract the jackknife technique is used to develop robust tests for heteroscedasticity in regression analysis consistent with time series cross sectional studies the variance is assumed constant within subgroups of observations but may vary from group to group we also consider the likelihood ratio lr test and develop a number of modified lr statistics similar to those of bartlett each test is developed in the context of regression where the vector of coefficients may be constant for all groups or may vary between groups a number of sampling experiments reveal that if the disturbance terms are normally distributed bartlett s test is slightly more powerful than either of the jackknife tests however in nonnormal situations jack2 the test based on jackknifing the regression is very robust under h 0 and has substantial power against a number of alternative hypotheses

probabilistic analysis on the splitting shooting method for image transformations abstract this paper explores a new topic in image processing where accuracy of images even in details is crucial and adopts a new methodology dealing with discrete topics by continuous mathematics and numerical approximation the key idea is that a pixel of images at different levels can be quantified by a greyness value which can then be regarded as the mean of an integral of continuous functions over a small pixel region and evaluated by numerical integration approximately hence new treatments of approximate integration and new discrete algorithms of images have been developed this paper also integrates different mathematics disciplines numerical analysis geometry probability and statistics to discrete images that can be applied to many areas in computer sciences image processing computer graphics computer vision geometric added designs and pattern recognition in this paper new error analysis in terms of probability theory is explored for the popular splitting shooting method ssm and the combination csim of the splitting shooting integrating methods proposed in 35 37 and convergence rates in probability of image greyness are proven to be o p 1 n 1 5 higher than o 1 n reported in 45 by strict error analysis moreover a new partial refinement technique of pixel partition is also proposed in this paper to achieve the convergence rate o p 1 n 2 in probability for ssm by the new study of this paper the ssm can be applied to real images with 256 greyness levels the numerical and graphical experiments are also provided to confirm the theoretical analysis made both the strict error bounds and the probabilistic error bounds with explicit constants are also derived for general norms as 1 and the countable probability inequalities for several sums of random variables are developed from probability theory which are more suited to numerical computations

the statistical foundations of a class of parametric tests for heteroscedasticity abstract in this paper we examine the statistical foundations of the five tests for heteroscedasticity considered by griffiths and surekha 1986 we identify the precise specification of the alternative hypothesis as an important determinant of the power of the tests

on the quartic curve of han the quartic curve of han x han piecewise quartic polynomial curves with shape parameter journal of computational and applied mathematics 195 2006 34 45 can be considered as the generalization of the cubic b spline curve incorporating shape parameters into the polynomial basis functions we show that this curve can be considered as the linear blending of the original cubic b spline curve and a fixed quartic curve moreover we present the bezier form of the curve which is useful in terms of incorporating the curve into existing cad systems geometric effects of the alteration of shape parameters is also discussed including design oriented computational methods for constrained shape control of the curve

exact tests and confidence sets in linear regressions with autocorrelated errors this article proposes a general method to build exact tests and confidence sets in linear regressions with first order autoregressive gaussian disturbances because of a nuisance parameter problem we argue that generalized bounds tests and conservative confidence sets provide natural inference procedures in such a context given an exact confidence set for the autocorrelation coefficient we describe how to obtain a similar simultaneous confidence set for the autocorrelation coefficient and any subvector of regression coefficient conservative confidence sets for the regression coefficients are then deduced by a projection method for any hypothesis that specifies jointly the value of the autocorrelation coefficient and any set of linear restrictions on the regression coefficients we get exact similar tests for tesing linear hypotheses about the regression coefficients only we suggest bounds type procedures exact confidence sets for the autocorrelation coefficient are built by inverting autocorrelation tests the method is illustrated with two examples copyright 1990 by the econometric society

finite sample properties and asymptotic efficiency of monte carlo tests on donne une approche unifiee qui couvre le cas d une distribution nulle arbitraire afin d etudier les proprietes statistiques des tests de monte carlo

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

some heteroskedasticity consistent covariance matrix estimators with improved finite sample properties abstract we examine several modified versions of the heteroskedasticity consistent covariance matrix estimator of hinkley 1977 and white 1980 on the basis of sampling experiments which compare the performance of quasi t statistics we find that one estimator based on the jackknife performs better in small samples than the rest we also examine the finite sample properties of using modified critical values based on edgeworth approximations as proposed by rothenberg 1984 in addition we compare the power of several tests for heteroskedasticity and find that it may be wise to employ the jackknife heteroskedasticity consistent covariance matrix even in the absence of detected heteroskedasticity

properties of sufficiency and statistical tests 1 in a previous paper dealing with the importance of properties of sufficiency in the statistical theory of small samples attention was mainly confined to the theory of estimation in the present paper the structure of small sample tests whether these are related to problems of estimation and fiducial distributions or are of the nature of tests of goodness of fit is considered further

a monte carlo evaluation of the power of some tests for heteroscedasticity abstract szroeter s asymptotically normal test outperforms the goldfeld qu2ndt test the breusch pagan lagrange multiplier test and bamset when it is possible to order the observations according to increasing variance with no prior information on variance ordering bamset is best some observations concerning degree of heteroscedasticity and model specification are made

tests for parameter instability and structural change with unknown change point this paper considers tests for parameter instability and structural change with unknown change point the results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures the asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null the tests considered here are shown to have nontrivial asymptotic local power against all alternatives for which the parameters are nonconstant the tests are found to perform quite well in a monte carlo experiment reported elsewhere copyright 1993 by the econometric society

interpolation with slackness and continuity control and convexity preservation using singular blending this paper presents a new interpolation method that enables the construction of c2 cubic polynomial spline curves without solving a global system of equations while providing slackness continuity control and convexity preserving ability the basic idea is to blend a cubic b spline curve with a singularly parametrized sequence of connected line segments a global slackness parameter controls the tautness specifically the distance between the interpolating curve and the linear interpolant the order of continuity at each knot is controlled via multiple knot insertions so that cusps and straight line segments can be conveniently prescribed in addition a method for selecting local slackness values to produce g1 convexity preserving curve is presented with the low degree polynomials and direct computation of control vertices this local method is computationally simple and is useful for interactive shape design and computer graphics applications

inference when a nuisance parameter is not identified under the null hypothesis many econometric testing problems involve nuisance parameters which are not identified under the null hypotheses this paper studies the asymptotic distribution theory for such tests the asymptotic distributions of standard test statistics are described as functionals of chi square processes in general the distributions depend upon a large number of unknown parameters we show that a transformation based upon a conditional probability measure yields an asymptotic distribution free of nuisance parameters and we show that this transformation can be easily approximated via simulation the theory is applied to threshold models with special attention given to the so called self exciting threshold autoregressive model monte carlo methods are used to assess the finite sample distributions the tests are applied to u s gnp growth rates and we find that potter s 1995 threshold effect in this series can be possibly explained by sampling variation

nonlinear hypotheses inequality restrictions and non nested hypotheses exact simultaneous tests in linear regressions in the context of the classical linear model the problem of comparing two arbitrary hypotheses on the regression coefficients is considered problems involving nonlinear hypotheses inequality restrictions or non nested hypotheses are included as special cases exact bounds on the null distribution of likelihood ratio statistics are derived the bounds are based on the central fisher distribution and are very easy to use in an important special case a bounds test similar to the durbin watson test is proposed multiple testing problems are also studied the bounds obtained for a single pair of hypotheses are shown to enjoy a simultaneity property that allows one to combine any number of tests this result extends to nonlinear hypotheses a well known result given by scheffe for linear hypotheses a method of building bounds induced tests is also suggested

admissibility of the likelihood ratio test when a nuisance parameter is present only under the alternative this paper establishes the asymptotic admissibility of the likelihood ratio lr test for a general class of testing problems in which a nuisance parameter is present only under the alternative hypothesis the paper also establishes the finite sample admissibility of the lr test for testing problems of this sort that arise in gaussian linear regression models with known variance

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

bartlett s cochran s and hartley s tests on variances are liberal when the underlying distribution is long tailed abstract for samples of equal size the p values of bartlett s cochran s and hartley s tests for the equality of several variances obtained under the normality assumption are shown to underestimate the true p values when the parent distribution is a normal or a x 2 1 scale mixture or when there is within sample dependence the proof uses elements of majorization theory when the sample sizes are not equal a partial extension is obtained for the two sample case

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

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

finite sample multivariate structural change tests with application to energy demand models abstract this paper considers finite sample motivated structural change tests in the multivariate linear regression model with application to energy demand models in which case commonly used structural change tests remain asymptotic as in dufour and kiviet 1996 exact tests for structural change in first order dynamic models journal of econometrics 70 39 68 we account for intervening nuisance parameters through a two stage maximized monte carlo test procedure our contributions can be classified into five categories i we extend tests for which a finite sample theory has been supplied for gaussian distributions to the non gaussian context ii we show that bai et al 1998 testing and dating common breaks in multi variate time series the review of economic studies 65 3 395 432 test severely over rejects and propose exact variants of this test iii we consider predictive break test approaches which generalize tests in dufour 1980 dummy variables and predictive tests for structural change economics letters 6 241 247 and dufour and kiviet 1996 exact tests for structural change in first order dynamic models journal of econometrics 70 39 68 iv we propose exact non bonferonni based extensions of the multivariate outliers test from wilks 1963 multivariate statistical outliers sankhya series a 25 407 426 to models with covariates v we apply these tests to the energy demand system analyzed by arsenault et al 1995 a total energy demand model of quebec forecasting properties energy economics 17 2 163 171 for two out of the six industrial sectors analyzed over the 1962 2000 period break and further goodness of fit and diagnostic tests allow to identify and correct specification problems arising from historical regulatory changes or possibly random industry specific effects the procedures we propose have potential useful applications in statistics econometrics and finance e g event studies

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

exact and asymptotic tests for possibly non regular hypotheses on stochastic volatility models abstract we study the problem of testing hypotheses on the parameters of one and two factor stochastic volatility models sv allowing for the possible presence of non regularities such as singular moment conditions and unidentified parameters which can lead to non standard asymptotic distributions we focus on the development of simulation based exact procedures whose level can be controlled in finite samples as well as on large sample procedures which remain valid under non regular conditions we consider wald type score type and likelihood ratio type tests based on a simple moment estimator which can be easily simulated we also propose a c type test which is very easy to implement and exhibits relatively good size and power properties besides usual linear restrictions on the sv model coefficients the problems studied include testing homoskedasticity against a sv alternative which involves singular moment conditions under the null hypothesis and testing the null hypothesis of one factor driving the dynamics of the volatility process against two factors which raises identification difficulties three ways of implementing the tests based on alternative statistics are compared asymptotic critical values when available a local monte carlo or parametric bootstrap test procedure and a maximized monte carlo mmc procedure the size and power properties of the proposed tests are examined in a simulation experiment the results indicate that the c based tests built upon the simple moment estimator available in closed form have good size and power properties for regular hypotheses while monte carlo tests are much more reliable than those based on asymptotic critical values further in cases where the parametric bootstrap appears to fail for example in the presence of identification problems the mmc procedure easily controls the level of the tests moreover mmc based tests exhibit relatively good power performance despite the conservative feature of the procedure finally we present an application to a time series of returns on the standard and poor s composite price index

simulation based finite sample tests for heteroskedasticity and arch effects tests for heteroskedasticity in linear regressions are typically based on asymptotic approximations we show that the size of such tests can be perfectly controlledin nite samples through monte carlo test techniques with both gaussian and non gaussian heavy tailed disturbance distributions the procedures studied include standard heteroskedasticity tests e g glejser bartlett cochran hartley breusch pagan godfrey white szroeter as well as tests for arch type heterosked asticity sup type andcombinedtests are also proposedto allow for unknown breakpoints in the variance the fact that the proposedproced ures achieve size control andhave goodpower is demonstrated in a monte carlo simulation c 2003 elsevier b v all rights reserved

a class of algebraic trigonometric blended splines this paper presents a new kind of algebraic trigonometric blended spline curve called xyb curves generated over the space 1 t sint cost sin 2t sin 3t cos 3t the new curves not only inherit most properties of usual cubic b spline curves in polynomial space but also enjoy some other advantageous properties for modeling for given control points the shape of the new curves can be adjusted by using the parameters x and y when the control points and the parameters are chosen appropriately the new curves can represent some conics and transcendental curves in addition we present methods of constructing an interpolation xyb spline curve and an xyb spline curve which is tangent to the given control polygon the generation of tensor product surfaces by these new spline curves is straightforward many properties of the curves can be easily extended to the surfaces the new surfaces can exactly represent the rotation surfaces as well as the surfaces with elliptical or circular sections

combining p values to test for multiple structural breaks in cointegrated regressions we propose a multiple hypothesis testing approach to assess structural stability in cointegrating regressions underlying tests are constructed via a vector error correction model vecm and generalize the reduced rank regression procedures of hansen 2003 we generalize the likelihood ratio test proposed in hansen 2003 to accommodate unknown break dates through the specification of several scenarios regarding the number and the location of the breaks we define a combined p value adjustment which proceeds by simulating the entire dataset imposing the relevant null hypothesis this framework accounts for both correlation of underlying tests and the fact that empirically parameters of interest often pertain to a limited even though uncertain stylized fact based change points we prove asymptotic validity of the proposed procedure monte carlo simulations show that proposed tests perform well infinite samples an application to the s p 500 prices and dividends series suggests a breaking cointegration relation as long as a multiple simulation based adjustment is applied

markovian processes two sided autoregressions and finite sample inference for stationary and nonstationary autoregressive processes in this paper we develop finite sample inference procedures for stationary and non stationary autoregressive ar models the method is based on special properties of markov processes and a split sample technique the results on markovian processes intercalary independence and truncation only require the existence of conditional densities they are proved for possibly nonstationary and or non gaussian multivariate markov processes in the context of a linear regression model with ar 1 errors we show how these results can be used to simplify the distributional properties of the model by conditioning a subset of the data on the remaining observations this transformation leads to a new model which has the form of a two sided autoregression to which standard classical linear regression inference techniques can be applied we show how to derive tests and confidence sets for the mean and or autoregressive parameters of the model we also develop a test on the order of an autoregression we show that a combination of subsample based inferences can improve the performance of the procedure an application to u s domestic investment data illustrates the method

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

exact inference methods for first order autoregressive distributed lag models methods are proposed to build exact tests and confidence sets in the linear first order autoregressive distributed lag model with i i d disturbances for general linear hypotheses on the regression coefficients inference procedures are obtained which have known level the tests proposed are either similar i e they have constant rejection probability for all data generating processes consistent with the null hypothesis or use bounds which are free of nuisance parameters correspondingly the confidence sets are either similar with known size i e they have constant coverage probability or conservative we also develop exact tests and confidence sets for various nonlinear transformations of model parameters such as long run multipliers and mean lags the practical usefulness of these exact methods which are also asymptotically valid under weak regularity conditions is illustrated by some power comparisons and with applications to a dynamic trend model of money velocity and a model of money demand

a study of several new and existing tests for heteroscedasticity in the general linear model abstract several optimum non parametric tests for heteroscedasticity are proposed and studied along with the tests introduced in the literature in terms of power and robustness properties it is found that all tests are reasonably robust to the ordinary least squares ols residual estimates number and character of the regressors only a few are robust to both the distributional and independence assumptions about the errors the power of tests can be improved with the ols residual estimates the increased sample size and the variability of the regressors it can be substantially reduced if the observations are not normally distributed and may increase or decrease if the errors are dependent each test is optimum to detect a specific form of heteroscedasticity and a serious power loss may occur if the underlying heteroscedasticity assumption in the data generation deviates from it

exact confidence sets and goodness of fit methods for stable distributions abstract usual inference methods for stable distributions are typically based on limit distributions but asymptotic approximations can easily be unreliable in such cases for standard regularity conditions may not apply or may hold only weakly this paper proposes finite sample tests and confidence sets for tail thickness and asymmetry parameters and of stable distributions the confidence sets are built by inverting exact goodness of fit tests for hypotheses which assign specific values to these parameters we propose extensions of the kolmogorov smirnov shapiro wilk and filliben criteria as well as the quantile based statistics proposed by mcculloch 1986 in order to better capture tail behavior the suggested criteria compare empirical goodness of fit or quantile based measures with their hypothesized values since the distributions involved are quite complex and non standard the relevant hypothetical measures are approximated by simulation and p values are obtained using monte carlo mc test techniques the properties of the proposed procedures are investigated by simulation in contrast with conventional wisdom we find reliable results with sample sizes as small as 25 the proposed methodology is applied to daily electricity price data in the us over the period 2001 2006 the results show clearly that heavy kurtosis and asymmetry are prevalent in these series

testing for structural change in conditional models in the past decade we have seen the development of a new set of tests for structural change of unknown timing in regression models most notably the supf statistic of andrews 1993 econometrica 61 825 856 the expf and avef statistics of andrewsploberger 1994 econometrica 62 1383 1414 and the statistic of nyblom 1989 journal of american statistical association 84 223 230 the distribution theory used for these tests is primarily asymptotic and has been derived under the maintained assumption that the regressors are stationary this excludes structural change in the marginal distribution of the regressors as a result these tests technically cannot discriminate between structural change in the conditional and marginal distributions this paper attempts to remedy this de ciency by deriving the large sample distributions of the test statistics allowing for structural change in the marginal distribution of the regressors we nd that the asymptotic distributions of the supf expf avef and statistics are not invariant to structural change in the regressors to solve the size problem we introduce a xed regressor bootstrap which achieves the rst order asymptotic distribution and appears to possess reasonable size properties in small samples our bootstrap theory allows for arbitrary structural change in the regressors including structural shifts polynomial trends and exogenous stochastic trends it allows for lagged dependent variables and heteroskedastic error processes 2000 elsevier science s a all rights reserved

a point optimal test for heteroscedastic disturbances abstract a new test for additive heteroscedasticity in the disturbances of the linear regression model is proposed power functions of various forms of the new test are compared empirically with those of currently favoured tests for a range of heteroscedastic models the results highlight the power advantage of a test which is mp1 at a central point in the alternative hypothesis parameter space the main conclusion is that the recommended version of the new test is generally more powerful than existing tests against medium and severe heteroscedasticity whereas the king and szroeter tests perform better against weak heteroscedasticity

asymmetric least squares estimation and testing this paper considers estimation and hypothesis tests for coefficients of linear regression models where the coefficient estimates are based on location measures defined by an asymmetric least squares criterion function these asymmetric least squares estimators have properties which are analogous to regression quantile estimators but are much simpler to calculate as are the corresponding test statistics the coefficient estimators can be used to construct test statistics for homoskedasticity and conditional symmetry of the error distribution and we find these tests compare quite favorably with other commonly used tests of these null hypotheses in terms of local relative efficiency consequently asymmetric least squares estimation provides a convenient and relatively efficient method of summarizing the conditional distribution of a dependent variable given the regressors and a means of testing whether a linear model is an adequate characterization of the typical value for this conditional distribution

boundary penalty finite element methods for blending surfaces iii superconvergence and stability and examples abstract this paper is part iii of the study on blending surfaces by partial differential equations pdes the blending surfaces in three dimensions 3d are taken into account by three parametric functions x r t y r t and z r t the boundary penalty techniques are well suited to the complicated tangent i e normal derivative boundary conditions in engineering blending by following the previous papers parts i and ii in li j comput math 16 1998 457 480 j comput appl math 110 1999 155 176 the corresponding theoretical analysis is made to discover that when the penalty power 2 3 or 3 5 and 0 1 5 in the boundary penalty finite element methods bp fems optimal convergence rates superconvergence and optimal numerical stability can be achieved respectively several interesting samples of 3d blending surfaces are provided to display the remarkable advantages of the proposed approaches in this paper unique solutions of blending surfaces optimal blending surfaces in minimum energy ease in handling the complicated boundary constraint conditions and less cpu time and computer storage needed this paper and li j comput math 16 1998 457 480 j comput appl math provide a foundation of blending surfaces by pde solutions a new trend of computer geometric design

an asymptotic expansion for the null distribution of the efficient score statistic summary an asymptotic expansion for the null distribution of the efficient score statistic for testing a composite hypothesis in the presence of nuisance parameters is derived and an interpretation of the terms occurring in the expansion is given the use of the expansion to modify the percentage points of the large sample reference x2 distribution is discussed the first three moments of the null distribution are obtained and are used as a check on the accuracy of the algebra via a comparison with the first three moments of the index of dispersion test for homogeneity of poisson parameters

exact tests for structural change in first order dynamic models abstract several finite sample tests of parameter constancy against the presence of structural change are proposed for a linear regression model with one lagged dependent variable and independent normal disturbances the procedures derived include analysis of covariance cusum cusum of squares and predictive tests the approach used to obtain the tests involves the application of three techniques derivation of an exact confidence set for the autoregressive parameter based on using an appropriately extended regression a union intersection technique and when required randomization the tests proposed are illustrated with some artificial data and applied to a dynamic trend model of gross private domestic investment in the u s

testing the nullity of garch coefficients correction of the standard tests and relative efficiency comparisons this article is concerned with testing the nullity of coefficients in generalized autoregressive conditionally heteroscedastic garch models the problem is nonstandard because the quasi maximum likelihood estimator is subject to positivity constraints this article establishes the asymptotic null and local alternative distributions of wald score and quasi likelihood ratio tests efficiency comparisons under fixed alternatives are considered two cases of special interest are tests of the null hypothesis of one coefficient equal to zero and tests of the null hypothesis of no conditional heteroscedasticity finally the proposed approach is used in the analysis of financial data and suggests reconsidering the preeminence of garch 1 1 among garch models