bootstrap validity for the score test when instruments may be weak it is well known that size adjustments based on bootstrapping the t statistic perform poorly when instruments are weakly correlated with the endogenous explanatory variable in this paper we provide a theoretical proof that guarantees the validity of the bootstrap for the score statistic this theory does not follow from standard results since the score statistic is not a smooth function of sample means and some parameters are not consistently estimable when the instruments are uncorrelated with the explanatory variable

the non linear equations of motion of pipes conveying fluid abstract the non linear equations of motion of pipes conveying fluid are derived in simple and accessible terms by energy and newtonian methods different derivations are made for cantilevered pipes where the centreline is assumed inextensible and for pipes with both ends fixed it is shown that the derivations the origin of the various terms and the structure of the equations are distinctly different in these two cases the equations of motion are then compared with those already in existence e g by holmes rousselet and herrmann and lundgren sethna and bajaj at the same time clarifying the derivations and assumptions made and discussing the validity and completeness of the final equations some of the equations are found to be fully correct indeed superior to those derived here while others are found to be deficient because of assumptions made or inconsistencies in the derivations for pipes with both ends fixed the equations given in this paper are considered to be the most complete and correct

higher order approximations for frequency domain time series regression second order expansions and mean squared error approximations are given for efficient frequency domain regression estimators while bandwidth choices do not figure in first order asymptotics for these estimators they do influence second order terms and it is shown how suitable choices will enhance second order efficiency data based bandwidth selection rules are given for practical implementation of these procedures two commonly used and asymptotically equivalent spectral regression estimators are studied and shown to differ in their second order asymptotic behavior some monte carlo evidence is reported

range kernel orthogonality of derivations abstract let h be a separable infinite dimensional complex hilbert space and let b h denote the algebra of operators on h into itself the generalised derivation a b b h b h is defined by a b x ax xb let a b b h b h be defined by a b x axb x and let d a b denote a b or a b let s c p the schatten p class 1 given that the pair a b of operators satisfies the property kerd a b c p kerd a b c p we prove a necessary and sufficient condition for d a b x s p s p to hold for all x c p

approximate power functions for some robust tests of regression coefficients approximate power functions for some robust tests of regression coefficients thomas j rothenberg department o f economics u n i v e r s i t y o f c a l i f o r n i a berkeley research papers i n economics no 84 1 summary edgeworth expansions are developed f o r the d i s t r i b u t i o n functions o f some t e s t s t a t i s t i c s i n the normal l i n e a r regression model where the e r r o r covariance matrix i s unknown tests based on generalized l e a s t squares estimates and also on ordinary l e a s t squares estimates are considered in both cases adjustments t o the asymptotic c r i t i c a l the approxi values are found and approximate l o c a l power c a l c u l a t e d and a u t o c o r r e l a t i o n mations are applied to a number o f examples i n c l u d i n g h e t e r o s c e d a s t i c i t y

exact finite sample relative efficiency of suboptimally weighted least squares estimators in models with ordered heteroscedasticity this paper is concerned with regression models having heteroscedastic errors whose variances are not precisely known but can be ordered by size the object is to use this limited information to devise regression coefficient estimators which are more efficient in finite samples than the ordinary least squares ols estimator three common relative efficiency measures determinant trace and extreme eigenvalue are considered a class of weighted least squares wls estimators is proved to be efficient relative to the ols estimator on the determinant generalized variance measure only a partial result can be obtained for the trace measure a counterexample shows that no similar results are possible for the eigenvalue measure under the weak conditions of this paper the efficiency value of additional prior information on variance is also investigated

generalized least squares f test in regression analysis with two stage cluster samples abstract when data are obtained by two stage cluster sampling serious problems can arise if conventional methods that ignore the intracluster correlations are used wu holt and holmes showed that the standard f statistic in regression analysis leads to inflated type i error rate or size due to correlated errors in the regression model appropriate for clustered data they proposed a simple correction to the standard f statistic that takes into account common intracluster correlation p and showed through simulation that the corrected f test performs much better than the standard f test in controlling the size for a scalar hypothesis it also performed almost as well as an iterative generalized least squares igls f statistic for large values of and better than the igls for small in controlling the size this article considers a two step generalized least squares gls f statistic by first estimating using the well known method of fitting constants due to henderson and then substituting the

random group effects and the precision of regression estimates abstract when explanatory variable data in a regression model are drawn from a population with grouped structure the regression errors are often correlated within groups error component and random coefficient regression models are considered as models of the intraclass correlation this paper analyzes several empirical examples to investigate the applicability of random effects models and the consequences of inappropriately using ordinary least squares ols estimation in the presence of random group effects the principal findings are that the assumption of independent errors is usually incorrect and the unadjusted ols standard errors often have a substantial downward bias suggesting a considerable danger of spurious regression

predicting phase shift effects for vibrating fluid conveying pipes due to coriolis forces and fluid pulsation abstract knowing the influence of fluid flow perturbations on the dynamic behavior of fluid conveying pipes is of relevance e g when exploiting flow induced oscillations of pipes to determine the fluids mass flow or density as done with coriolis flow meters cfm this could be used in the attempts to improve accuracy precision and robustness of cfms a simple mathematical model of a fluid conveying pipe is formulated and the effect of pulsating fluid flow is analyzed using a multiple time scaling perturbation analysis the results are simple analytical predictions for the transverse pipe displacement and approximate axial shift in vibration phase the analytical predictions are tested against pure numerical solution using representative examples showing good agreement fluid pulsations are predicted not to influence cfm accuracy since proper signal filtering is seen to allow the determination of the correct mean phase shift large amplitude motions which could influence cfm robustness do not appear to be induced by the investigated fluid pulsation pulsating fluid of the combination resonance type could however influence cfms robustness if induced pipe motions go unnoticed and uncontrolled during cfm operation by feedback control the analytical predictions offer an immediate insight into how fluid pulsation affects phase shift which is a quantity measured by cfms to estimate the mass flow and lead to hypotheses for more complex geometries i e industrial cfms the validity of these hypotheses is suggested to be tested using laboratory experiments or detailed computational models taking fluid structure interaction into account

bootstrap bartlett adjustment in seemingly unrelated regression abstract seemingly unrelated regression sur is a method introduced by zellner 1962 for estimating several regression equations simultaneously a common and important problem in econometrics this article considers hypothesis testing in sur using the log likelihood ratio llr test although the asymptotic distribution of this statistic is well known substantial departures occur in samples of the size commonly employed by economists significance levels given by the use of this asymptotic distribution are too low sometimes by an order of magnitude leading to the rejection of too many true null hypotheses a common approach to this problem is to use a bartlett 1937 adjustment to the llr statistic in which the test statistic is multiplied by a factor derived from second order asymptotics before it is referred to the asymptotic 2 q distribution this article proposes that the bartlett adjustment factor be computed using efron s bootstrap 1979 1982 in the cases examined this leads to more accu

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

a note on vibrations of generally restrained beams exact frequency and normal mode shape expressions are derived in this note for generally restrained bernoulli euler beams with unsymmetrical translations and rotations at either end the eigenfrequencies and mode shape parameters are presented for a wide range of restraint parameters several degenerate cases have been studied and some of these have been compared with those available in the published literature it is believed that the results presented in this paper will be of use in design of beams shafts and piping under dynamic considerations

nonlinear dynamics of a pipe conveying pulsating fluid with combination principal parametric and internal resonances abstract nonlinear dynamics of a hinged hinged pipe conveying pulsatile fluid subjected to combination and principal parametric resonance in the presence of internal resonance is investigated the system has geometric cubic nonlinearity due to stretching effect out of immovable support conditions at both ends the pipe conveys fluid at a velocity with a harmonically varying component over a constant mean velocity for appropriate choice of system parameters the natural frequency of the second mode is approximately three times that of the first mode for a range of mean flow velocity activating a three to one internal resonance the analysis is carried out using the method of multiple scales by directly attacking the governing nonlinear integro partial differential equations and the associated boundary conditions the set of first order ordinary differential equations governing the modulation of amplitude and phase is analyzed numerically for combination parametric resonance and principal parametric resonance stability bifurcation and response behavior of the pipe are investigated the amplitude and frequency detuning of the harmonic velocity perturbation are taken as the control parameters the system exhibits response in the directly excited and indirectly excited modes due to modal interaction dynamic response of the system is presented in the form of phase plane trajectories poincare maps and time histories a wide array of dynamical behavior is observed illustrating the influence of internal resonance

vibration of a flexible pipe conveying viscous pulsating fluid flow abstract the non linear equations of motion of a flexible pipe conveying unsteadily flowing fluid are derived from the continuity and momentum equations of unsteady flow these partial differential equations are fully coupled through equilibrium of contact forces the normal compatibility of velocity at the fluid pipe interfaces and the conservation of mass and momentum of the transient fluid poisson coupling between the pipe wall and fluid is also incorporated in the model a combination of the finite difference method and the method of characteristics is employed to extract displacements hydrodynamic pressure and flow velocities from the equations a numerical example of a pipeline conveying fluid with a pulsating flow is given and discussed

free vibration of a beam supported on a stepped elastic foundation abstract the problem of free lateral vibration of a bernoulli euler beam supported on a step like varying winkler elastic foundation is considered four types of boundary conditions are investigated the frequency equation is obtained by dividing the beam into segments each with a constant foundation this equation is then solved numerically

power in econometric applications this paper is concerned with the use of power properties of tests in econometric applications inverse power functions are defined these functions are designed to yield summary measures of power that facilitate the interpretation of test results in practice simple approximations are introduced for the inverse power functions of wald likelihood ratio lagrange multiplier and hausman tests these approximations readily convey the general qualitative features of the power of a test examples are provided to illustrate their usefulness in interpreting test results a common problem faced in applied econometrics is that of interpreting the results of a hypothesis test when the test fails to reject the null hypothesis most practitioners realize that just because a test fails to reject a hypothesis one cannot claim to accept it nevertheless it is common for this to be ignored since the practitioner is often in a position where he would like the outcome of the test to provide useful inferences whether or not the test rejects the purpose of this paper is to introduce inverse power ip summary measures that enable the practitioner to avoid such errors and make valid inferences when a test fails to reject the null hypothesis these summary measures are widely applicable easy to use especially in the common case of a test concerning a single restriction and simple to compute when a test rejects the null hypothesis the implication is that the data are inconsistent with each parameter point in the null in the sense that the probabil ity of type i error for each point is small viz a or less correspondingly when a test fails to reject the null hypothesis an analogous statement is needed regarding the error probabilities for points in the alternative hypothesis it is not the case that all points in the alternative are inconsistent with the data in the sense that their probability of type ii error is small a or less it is possible however to determine the region s in the alternative parameter space that is inconsistent with the data in this sense the ip function introduced below evaluated at

analytical predictions for vibration phase shifts along fluid conveying pipes due to coriolis forces and imperfections abstract resonant vibrations of a fluid conveying pipe are investigated with special consideration to axial shifts in vibration phase accompanying fluid flow and various imperfections this is relevant for understanding elastic wave propagation in general and for the design and trouble shooting of phase shift measuring devices such as coriolis mass flowmeters in particular small imperfections related to elastic and dissipative support conditions are specifically addressed but the suggested approach is readily applicable to other kinds of imperfection e g non uniform stiffness or mass non proportional damping weak nonlinearity and flow pulsation a multiple time scaling perturbation analysis is employed for a simple model of an imperfect fluid conveying pipe this leads to simple analytical expressions for the approximate prediction of phase shift providing direct insight into which imperfections affect phase shift and in which manner the analytical predictions are tested against results obtained by pure numerical analysis using a galerkin expansion showing very good agreement for small imperfections the analytical predictions are thus comparable in accuracy to numerical simulation but provide much more insight this may aid in creating practically useful hypotheses that hold more generally for real systems of complex geometry e g that asymmetry or non proportionality in axial distribution of damping will induce phase shifts in a manner similar to that of fluid flow while the symmetric part of damping as well as non uniformity in mass or stiffness do not affect phase shift the validity of such hypotheses can be tested using detailed fluid structure interaction computer models or laboratory experiments

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

higher order approximations for wald statistics in time series regressions with integrated processes asymptotic expansions are developed for wald test statistics in time series regressions with integrated processes these expansions provide an opportunity to reduce size distortion in testing by suitable bandwidth selection and automated rules for doing so are calculated a band spectral regression and the associated wald test are also considered both the first order and second order properties of the estimator are studied

on the converse of anderson s theorem abstract we investigate the converse of anderson s theorem on the range kernel orthogonality of a derivation in particular we show that a pair of bounded linear operators on a hilbert space satisfies the fuglede putnam theorem relative to the ideal of compact operators if and only if it satisfies anderson s inequality relative to the same ideal

the small sample properties of some preliminary test estimators in a linear model with autocorrelated errors abstract a monte carlo study is used to examine the finite sample relative efficiency of a number of estimators including pre test estimators and the accuracy of asymptotic confidence intervals derived from them for a linear model with ar 1 or ma 1 errors the bias of the ml estimator of the ar 1 parameter and the frequency of ml estimates equal to 1 for the ma 1 parameter have a large bearing on the properties of the estimators of the regression coefficient the traditional ols ar pre test estimator compares relatively favorably even under an ma error specification however the confidence intervals associated with positive autoregressive errors and a trended explanatory variable can be quite inaccurate

alternative size corrections for some gls test statistics the case of the ar 1 model abstract alternative size corrections are developed for the t and f tests in the ar 1 normal linear model edgeworth corrected critical values are obtained from normal student t chi square and f distributions alternatively we may use cornish fisher corrected test statistics to avoid the problem of negative tail probabilities of an edgeworth distribution the use of the exact distributions student t f results in approximations that are locally exact i e they reduce to the exact formulae for a sufficient simplification of the model monte carlo findings support the theoretical considerations in favour of the locally exact cornish fisher corrections

a small sample correction for tests of hypotheses on the cointegrating vectors abstract the main purpose of the analysis of the cointegrated var model is conducting inference on the cointegrating relations asymptotic inference is 2 but the asymptotic results are not accurate enough for small samples therefore we derive here a correction factor depending on sample size and parameters for the likelihood ratio test of some linear hypotheses on the cointegrating space in a vector autoregressive model we have to assume that the adjustment coefficients are known the main idea is to condition on the common trends when calculating the correction factor some simulation experiments illustrate the findings

missing observations and the use of the durbin watson statistic summary this paper recommends the use of the usual durbin watson test for the serial independence of errors on a classical regression equation in the presence of occasional gaps in the data

an edgeworth test size correction for the linear model with ar 1 errors rothenberg s edgeworth size correction is applied to tests of linear hypotheses in the linear regression model with ar 1 errors previous simulation findings on the effect of autocorrelation in the regressors on over rejection are supported when the correction is examined analytically in a special case a simulation study shows that the correction adjusts the size in the right direction but still leaves substantial over rejection when the sample size is small and the original amount of over rejection is large

estimation of a linear regression model with stationary arma p q errors abstract it is well known that consistent estimation of a linear regression model with a stationary gaussian arma process in the errors can be carried out by maximum likelihood or alternatively by two stage procedures involving estimation of the nuisance parameters followed by feasible generalized least squares for the model parameters we show that the estimators coincide up to o p t 3 2 and derive the variance to o t 2 which up to terms of this order is the same for both estimators considering the form of the error covariance matrix for an arma p q process allows us to examine a computationally convenient algorithm for estimation of the parameters of the regression model finally we provide a monte carlo comparison of the small sample properties of ols and two versions of the proposed estimator

the sensitivity of ols when the variance matrix is partially unknown we consider the standard linear regression model y xb u with all standard assumptions except that the variance matrix is assumed to be p2x h where x depends on m unknown parameters h 1 2 h m our interest lies exclusively in the mean parameters b or xb we introduce a new sensitivity statistic b1 which is designed to decide whether yl or bk is sensitive to covariance misspeci cation we show that the durbin watson test is inappropriate in this context because it measures the sensitivity of pl 2 to covariance misspeci cation our results demonstrate that the estimator bk and the predictor yl are not very sensitive to covariance misspeci cation the statistic is easy to use and performs well even in cases where it is not strictly applicable 1999 elsevier science s a all rights reserved

finite sample power of linear regression autocorrelation tests abstract we consider autocorrelation tests in the linear regression model which can be expressed as ratios of quadratic forms in the true disturbances given a particular such test as e g the durbin watson test and many others we show that there exist design matrices such that the power of the test drops to zero as autocorrelation among the disturbances increases we also show how to compute this limiting power for arbitrary design matrices

the power of the durbin watson test for regressions without an intercept abstract in the linear regression model without an intercept the limiting power of the durbin watson test as correlation among errors increases is shown to take only one of two values this is either one or zero depending on the underlying regressor matrix some examples and a simple rule to decide from a given regressor matrix which of these cases applies are also given

asymptotically efficient estimation of a nonlinear model of the heteroscedasticity and the calibration of measurement systems the measurement system calibration includes the estimation of the sensor error models in order to get an optimal estimation of the measured parameters the paper is devoted to the estimation of a nonlinear parametric model of the heteroscedasticity and its application to the calibration of measurement systems the heteroscedasticity occurs in regression when the measurement noise variance is nonconstant the maximum likelihood ml estimation of variance function parameters leads to a system of nonlinear equations the iterative solution of these nonlinear equations is based entirely on a successful choice of initial conditions which is intractable in practice to overcome this difficulty another linear quasi ml estimator is proposed it is strongly consistent asymptotically gaussian and only slightly less efficient than the cramer rao lower bound by using this estimator as an initial condition an asymptotically efficient estimation is obtained by using one step noniterative newton method the theoretical findings have been applied to the calibration of the egnos gps positioning algorithm in the sub urban environments

variance function estimation abstract heteroscedastic regression models are used in fields including economics engineering and the biological and physical sciences often the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters standard asymptotic theory implies that how one estimates the variance function in particular the structural parameters has no effect on the first order properties of the regression parameter estimates there is evidence however both in practice and higher order theory to suggest that how one estimates the variance function does matter further in some settings estimation of the variance function is of independent interest or plays an important role in estimation of other quantities in this article we study variance function estimation in a unified way focusing on common methods proposed in the statistical and other literature to make both general observations and compare different estimation schemes we show that there are significant di

efficiency of iterative estimators in the regression model with ar 1 disturbances abstract the mean square error approximation method of nagar is applied to the iterated prais winsten and iterated maximum likelihood estimators of regression coefficients in the model with ar 1 disturbances their mean square errors are found to equal that of the two stage prais winsten estimator at the second order level of approximation

generalized least squares inference in panel and multilevel models with serial correlation and fixed effects in this paper i consider generalized least squares gls estimation in fixed effects panel and multilevel models with autocorrelation the presence of fixed effects complicates implementation of gls as estimating the fixed effects will typically render standard estimators of the covariance parameters necessary for obtaining feasible gls estimates inconsistent i focus on the case where the disturbances follow an ar p process and offer a simple to implement bias correction for the ar coefficients the usefulness of gls and the derived bias correction for the parameters of the autoregressive process is illustrated through a simulation study which uses data from the current population survey

divergence instability of pipes conveying fluid with uncertain flow velocity abstract this article deals with investigation of probabilistic stability of pipes conveying fluid with stochastic flow velocity in time domain as a matter of fact this study has focused on the randomness effects of flow velocity on stability of pipes conveying fluid while most of research efforts have only focused on the influences of deterministic parameters on the system stability the euler bernoulli beam and plug flow theory are employed to model pipe structure and internal flow respectively in addition flow velocity is considered as a stationary random process with gaussian distribution afterwards the stochastic averaging method and routh s stability criterion are used so as to investigate the stability conditions of system consequently the effects of boundary conditions viscoelastic damping mass ratio and elastic foundation on the stability regions are discussed results delineate that the critical mean flow velocity decreases by increasing power spectral density psd of the random velocity moreover by increasing psd from zero the type effects of boundary condition and presence of elastic foundation are diminished while the influences of viscoelastic damping and mass ratio could increase finally to have a more applicable study regression analysis is utilized to develop design equations and facilitate further analyses for design purposes

free vibrations of beams with general boundary conditions a simple and unified approach is presented for the vibration analysis of a generally supported beam the flexural displacement of the beam is sought as the linear combination of a fourier series and an auxiliary polynomial function the polynomial function is introduced to take all the relevant discontinuities with the original displacement and its derivatives at the boundaries and the fourier series now simply represents a residual or conditioned displacement that has at least three continuous derivatives as a result not only is it always possible to expand the displacement in a fourier series for beams with any boundary conditions but also the solution converges at a much faster speed the reliability and robustness of the proposed technique are demonstrated through numerical examples

the exact powers of some autocorrelation tests when the disturbances are heteroscedastic abstract this paper considers the exact finite sample powers of some popular tests for ar 1 disturbances when heteroscedasticity is also present although test sizes are found to be robust severe reductions in power are found particularly under strong positive autocorrelation factors influencing these power reductions are identified analytically

difference in difference meets generalized least squares higher order properties of hypotheses tests we investigate the estimation and inference in difference in difference econometric models used in the analysis of treatment effects when the innovations in such models display serial correlation commonly used ordinary least squares ols procedures are inefficient and may lead to tests with incorrect size implementation of feasible generalized least squares fgls procedures is often hindered by too few observations in the cross section to allow for unrestricted estimation of the weight matrix without leading to tests with similar size distortions as conventional ols based procedures we analyze the small sample properties of fgls based tests with a formal higher order edgeworth expansion that allows us to construct a size corrected version of the test we also address the question of optimal temporal aggregation as a method to reduce the dimension of the weight matrix we apply our procedure to data on regulation of mobile telephone service prices we find that a size corrected fgls based test outperforms tests based on ols

joint one sided tests of linear regression coefficients abstract the main example of the class of problems considered below is that of testing whether a subset of regression coefficients are jointly zero assuming knowledge of the coefficients signs if this knowledge is ignored the likelihood ratio wald and lagrange multiplier tests are each equivalent to the f test we propose a new test which can be applied as a one sided t test and which is umpi in a subspace of the parameter space empirical power comparisons with the power envelope the f test and the exact one sided likelihood ratio test show that the new test can have exceptionally good power over a wide range of the parameter space

range kernel orthogonality of the elementary operator x i 1naixbi x abstract let h be a separable infinite dimensional complex hilbert space and let b h denote the algebra of operators on h into itself let a a 1 a 2 a n and b b 1 b 2 b n be n tuples in b h define the elementary operators ab and ab b h b h by ab x i 1 n a i xb i x and ab x i 1 n a i xb i x this note considers the range kernel orthogonality of the restrictions of ab and ab to schatten p classes c p it is proved that a if 1 p s c p and i 1 n a i a i i 1 n a i a i i 1 n b i b i and i 1 n b i b i are all 1 then min ab x s p ab x s p s p for all x c p if and only if ab s 0 ab s b if p 2 and s c 2 then ab x s 2 2 ab x 2 2 s 2 2 and ab x s 2 2 ab x 2 2 s 2 2 if and only if ab s 0 ab s and c if a and b are the n tuples of a such that bb s 0 bb s for some injective s c 1 then the inequality of a holds with p 1 and for all x c 1 if and only if ab s 0 ab s

the transition conditions in the dynamics of elastically restrained beams abstract this paper deals with the free transverse vibration of a non homogeneous tapered beam subjected to general axial forces with arbitrarily located internal hinge and elastics supports and ends elastically restrained against rotation and translation a rigorous and complete development is presented first a brief description of several papers previously published is included second the hamilton principle is rigorously stated by defining the domain d of the action integral and the space d a of admissible directions the differential equations boundary conditions and particularly the transitions conditions are obtained third the transition conditions are analysed for several sets of restraints conditions fourth the existence and uniqueness of the weak solutions of the boundary value problem and the eigenvalue problem which respectively govern the statical and dynamical behaviour of the mentioned beam is treated finally the method of separation of variables is used for the determination of the exact frequencies and mode shapes and a modern application of the ritz method to obtain approximate eigenvalues in order to obtain an indication of the accuracy of the developed mathematical model some cases available in the literature have been considered new results are presented for different boundary conditions and restraint conditions in the internal hinge

vibration of beams with generally restrained boundary conditions using fourier series this work presents a method to find accurate vibration frequencies of beams with generally restrained boundary conditions using fourier series the suggested method is very convenient to find an accurate frequency parameter for beams with not only classical boundary conditions but also non classical boundary conditions restrained by rotational and translational springs numerical results for various degenerate cases are compared with existing results for natural frequency obtained by conventional analysis the results indicate that the present method can be used very effectively in the design of beams with various supporting conditions

on the sensitivity of the usual t and f tests to covariance misspecification we consider the standard linear regression model with all standard assumptions except that the disturbances are not white noise but distributed n 0 p2x h where x 0 i n our interest lies in testing linear restrictions using the usual f statistic based on ols residuals we are not interested in nding out whether h 0 or not instead we want to nd out what the e ect is of possibly nonzero h on the f statistic itself we propose a sensitivity statistic for this purpose discuss its distribution and obtain a practical and easy to use decision rule to decide whether the f test is sensitive or not to covariance misspeci cation when h is close to zero some nite and asymptotic properties of u are studied as well as its behaviour in the special case of an ar 1 process near the unit root 2000 elsevier science s a all rights reserved jel classixcation c12 c22 c51 c52

bootstrapping cointegrating regressions abstract in this paper we consider bootstrapping cointegrating regressions it is shown that the method of bootstrap if properly implemented generally yields consistent estimators and test statistics for cointegrating regressions for the cointegrating regression models driven by general linear processes we employ the sieve bootstrap based on the approximated finite order vector autoregressions for the regression errors and the first differences of the regressors in particular we establish the bootstrap consistency for ols method the bootstrap method can thus be used to correct for the finite sample bias of the ols estimator and to approximate the asymptotic critical values of the ols based test statistics in general cointegrating regressions the bootstrap ols procedure however is not efficient for the efficient estimation and hypothesis testing we consider the procedure proposed by saikkonen 1991 asymptotically efficient estimation of cointegration regressions econometric theory 7 1 21 and stock and watson 1993 a simple estimator of cointegrating vectors in higher order integrating systems econometrica 61 783 820 relying on the regression augmented with the leads and lags of differenced regressors the bootstrap versions of their procedures are shown to be consistent and can be used to do asymptotically valid inferences a monte carlo study is conducted to investigate the finite sample performances of the proposed bootstrap methods

the finite sample distributions of heteroskedasticity robust wald statistics the imhof procedure is used to calculate the exact finite sample distributions of alternative heteroskedasticity robust wald type tests of scalar linear hypothesis in the normal linear model the tests are distinguished by the variance estimator that they use these include the white eicker and jackknife estimators the calculations demonstrate the importance of regression design in determining the quality of conventional first order asymptotic approximations to the null distributions of the tests

an approximate method for one dimensional structures with strong nonlinear and nonhomogenous boundary conditions abstract there is a lack of analytic methods for vibration analysis of structures with strong nonlinear and non homogenous boundary conditions this paper proposes such a method a distinct feature of the method is to introduce the generalized coordinates for nonlinear and nonhomogeneous boundary conditions the total solution of the structure consists of a sum of a spatial particular solution for the boundary conditions and a field solution satisfying linear and homogeneous boundary conditions the field solution can be obtained in terms of the modal expansion the modal coefficients together with the generalized coordinates for the boundary conditions satisfy a set of nonlinear ordinary differential equations which are solved with the harmonic balance method two examples are presented to study the convergence and accuracy of the solution the first example is the longitudinal vibration of a bar subject to a base excitation on the left and restrained by a damper on the right the wave method and the differential quadrature method dqm are compared with the proposed method and are found in good agreement the second example is a beam with nonlinear torsional boundary absorbers the method shows a good accuracy to deal with the complex boundary conditions as compared with the differential quadrature element method dqem the proposed method is also compared with the multi scale method msm and shows an advantage to deal with strong nonlinearities the proposed method is highly promising for vibration analysis of complex structures with nonlinear and nonhomogeneous boundary conditions

the optimal size of a preliminary test of linear restrictions in a misspecified regression model abstract when the choice of estimator for the coefficients in a linear regression model is determined by the outcome of a prior test of the validity of restrictions on the model it is well known that a minimax risk regret criterion leads to the simple rule that the optimal critical value for the preliminary test is approximately two in value regardless of the degrees of freedom we show that this result no longer holds in the likely event that relevant regressors are excluded from the model at the outset

a point optimal test for autoregressive disturbances abstract this paper is concerned with testing for first order autoregressive disturbances in the linear regression model and recommends an alternative test to the durbin watson test the new test is most powerful invariant in a given neighbourhood of the alternative hypothesis parameter space an empirical power comparison indicates that the test is generally more powerful than the durbin watson test the comparison also suggests that for many economic applications the difference in power will be small although circumstances do exist in which the power advantage of the new test is very real selected bounds for the test s significance points are tabulated

operators that are orthogonal to the range of a derivation the gateaux differentiability of the schatten p norms and the usual operator norm is used to characterize those operators that are orthogonal to the range of a derivation with respect to these norms

hypothesis testing in linear models when the error covariance matrix is nonscalar a well developed exact statistical theory exists for hypothesis testing in the normal linear regression model when the errors are independent and homoscedastic in the more general case where the error covariance matrix is nonscalar and depends on a set of unknown parameters exact analysis is difficult and reliance is usually placed on asymptotic approximations for large sample size n in this paper higher order asymptotic expansions are developed for comparing the size and power of some common procedures for testing linear hypotheses on the regression coefficients in a class of generalized normal linear models the class investigated is essentially the same as in breusch 4 and magnus 6 and includes many of the examples of heteroscedasticity and autocorrelation discussed in the literature we assume simply that the regressors are nonrandom and that the error covariance matrix is a smooth function of a few parameters that can be efficiently estimated by maximum likelihood tests based on the wald likelihood ratio and lagrange multiplier principles are considered these principles lead to three tests which though distinct in finite samples are locally asymptotically equivalent and share certain asymptotic optimality properties of course there are infinitely many other tests that are asymptotically equivalent to the ones examined here although the techniques of this paper can be applied to any of them our results concern only the tests arising from the three traditional principles we show that to a second order of approximation under local alternatives the likelihood ratio test statistic is a simple average of the wald statistic and the lagrange multiplier statistic when the null hypothesis is one dimensional the three tests are to second order equally powerful that is after the critical regions are adjusted so that the tests have to order n i the same size the local power functions differ by terms of smaller order than n when the null hypothesis contains more than one

autocorrelation pre testing in the linear model estimation testing and prediction abstract this paper explores by means of a monte carlo experiment the consequences of autocorrelation pre testing on estimation hypothesis testing and prediction in the linear regression model with first order autoregressive disturbances we find that overall pre testing is preferable to pure ols regression techniques and generally compares favourably with the strategy of always correcting for possible autocorrelation more surprising findings include the degree to which the regression matrix affects the relative performance of the various strategies and the degree to which the familiar ols based t test can lose power in the presence of autocorrelation

on estimating and testing in a linear regression model with autocorrelated errors abstract in this paper we examine the small sample properties of feasible gls estimators and tests of individual regression coefficients bayesian and non bayesian estimators for an autocorrelation coefficient denoted by are examined by monte carlo experiments it is shown that when the value of is large the bayesian estimator for performs better than non bayesian estimators for when the value of is large and the sample size is 20 none of the feasible gls estimators performs well in hypothesis testing however when the sample size is 40 the feasible bayesian gls estimator performs much better that the feasible non bayesian gls estimators in hypothesis testing

on the power function of the durbin watson test abstract recent papers have drawn attention to the fact that the power function of the durbin watson dw test against the alternative of a stationary first order autoregression is not necessarily monotonic as p departs from the null hypothesis that p 0 indeed for some data sets the power tends to 0 as p 1 making inferences based on the dw test meaningless the purpose of the present study is twofold first the paper provides new insight into the factors underlying this worrisome aspect of the dw power function and shows that it is not restricted to stationary processes second the paper presents a fairly easily calculated boundary power function which for any given data set gives some guidance as to whether or not the dw test will have poor power properties

a note on the efficiency of sandwich covariance matrix estimation the sandwich estimator also known as robust covariance matrix estimator heteroscedasticity consistent covariance matrix estimate or empirical covariance matrix estimator has achieved increasing use in the econometric literature as well as with the growing popularity of generalized estimating equations its virtue is that it provides consistent estimates of the covariance matrix for parameter estimates even when the fitted parametric model fails to hold or is not even specified surprisingly though there has been little discussion of properties of the sandwich method other than consistency we investigate the sandwich estimator in quasi likelihood models asymptotically and in the linear case analytically we show that under certain circumstances when the quasi likelihood model is correct the sandwich estimate is often far more variable than the usual parametric variance estimate the increased variance is a fixed feature of the method and the price that one pays to obtain consistency even when the p

the effect of estimating weights in weighted least squares abstract in weighted least squares it is typical that the weights are unknown and must be estimated most packages provide standard errors assuming that the weights are known this is fine for sufficiently large sample sizes but what about for small to moderate sample sizes the investigation of this article into the effect of estimating weights proceeds under the assumption typical in practice that one has a parametric model for the variance function in this context generalized least squares consists of a an initial estimate of the regression parameter b a method for estimating the variance function and c the number of iterations in reweighted least squares by means of expansions for the covariance it is shown that each of a c can matter in problems of small to moderate size a few conclusions may be of practical interest first estimated standard errors assuming that the weights are known can be too small in practice the investigation indicates that a simple bootstrap operation resul

fighting the teflon factor comparing classical and bayesian estimators for autocorrelated errors abstract this paper claims on the basis of a monte carlo study that current estimators employed in the context of first order autocorrelated errors should be abandoned in favor of a bayesian alternative frequentists are confronted on their own playing field the bayesian estimator employs an ignorance prior and the criterion adopted is the mean square error of the competing estimators with the predictable exception of the ols estimator when the autocorrelation parameter is close to zero the bayesian estimator dominates the competition by a substantive margin