projected score methods for approximating conditional scores summary this paper extends the projected score methods of small mcleish 1989 it is shown that the conditional score function may be approximated with arbitrarily small stochastic error in terms of a natural basis for the space of centred likelihood ratios the utility of using this basis is established by identifying a u statistic representation theorem and a class of expectation identities for the basis elements making higher order asymptotics more tractable the results are applied to a canonical exponential family model where it is shown that the projected scores with estimated nuisance parameters can provide an accurate approximation to the conditional score function

exact closed form solution for the vibration modes of the euler bernoulli beam with multiple open cracks abstract in this study exact closed form expressions for the vibration modes of the euler bernoulli beam in the presence of multiple concentrated cracks are presented the proposed expressions are provided explicitly as functions of four integration constants only to be determined by the standard boundary conditions the enforcement of the boundary conditions leads to explicit expressions of the natural frequency equations besides the evaluation of the natural frequencies neither computational work nor recurrence expressions for the vibration modes are required the cracks that are not subjected to the closing phenomenon are modelled as a sequence of dirac s delta generalised functions in the flexural stiffness the eigen mode governing equation is formulated over the entire domain of the beam without enforcement of any continuity conditions which are already accounted for in the adopted flexural stiffness model the vibration modes of beams with different numbers of cracks under different boundary conditions have been analysed by means of the proposed closed form expressions in order to show their efficiency

exact solution for the transverse vibration of a beam a part of which is a taper beam and other part is a uniform beam abstract in this paper the free vibration frequencies of tapered beams in the most general possible boundary conditions are determined by means of direct method the study is extended to beams made up of two sections with different cross sectional variations the equations of motion can be solved by means of the well known bessel function the natural frequencies were determined using the false position method and symbolic program as roots of the corresponding characteristic equations finally an extensive number of structural system previously studied both exactly and approximately by other authors mentioned in the bibliography confirms the exactness of the results obtained 1997 elsevier science ltd

orthogonal locally ancillary estimating functions for matched pair studies and errors in covariates summary we propose an estimating function method for two related applications matched pair studies and studies with errors in covariates under a functional model where a mismeasured unknown scalar covariate is treated as a fixed nuisance parameter our method addresses the severe inferential problem that is posed by an abundance of nuisance parameters in these two applications we propose orthogonal locally ancillary estimating functions for these two applications that depend on merely the mean model and partial modelling of the variances of the observations and observed mismeasured covariate if applicable and we achieve first order bias correction of inferences under a small dispersion and large sample size asymptotic simulation results confirm that the estimator proposed is largely improved over that using a regular profile estimating function we apply the approach proposed to a length of hospital stay study with a mismeasured covariate

the hu washizu variational principle for the identification of imperfections in beams this paper presents a procedure for the identification of imperfections of structural parameters based on displacement measurements by static tests the proposed procedure is based on the well known hu washizu variational principle suitably modified to account for the response measurements which is able to provide closed form solutions to some inverse problems for the identification of structural parameter imperfections in beams copyright 2008 john wiley sons ltd

a simple and accurate method for approximate conditional inference applied to exponential family models summary a simple method for approximate conditional inference is described the methodology is applied to natural exponential family models where it is shown to provide accurate approximations to fully conditional estimates the approximation technique can be applied much more generally than in this particular class of models the technique depends only on the construction of certain projected scores derived from higher order likelihood derivatives and their covariances and so can be used in many problems where it is relevant to control for the estimation of nuisance parameters

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

estimation and inference in unstable nonlinear least squares models there is compelling evidence that many macroeconomic and financial variables are not generated by linear models this evidence is based on testing linearity against either smooth nonlinearity or piece wise linearity but there is no framework that encompasses both this paper provides an econometric framework that allows for both breaks and smooth nonlinearity in between breaks we estimate the unknown break dates simultaneously with other parameters via nonlinear least squares using new central limit results for nonlinear processes we provide inference methods on break dates and parameter estimates and several instability tests we illustrate our methods via simulated and empirical smooth transition models with breaks

accurate and robust tests for indirect inference in this paper we propose accurate parameter and over identification tests for indirect inference under the null hypothesis the new tests are asymptotically 2 distributed with a relative error of order n 1 they exhibit better finite sample accuracy than classical tests for indirect inference which have the same asymptotic distribution but an absolute error of order n 1 2 robust versions of the tests are also provided we illustrate their accuracy in nonlinear regression poisson regression with overdispersion and diffusion models

computing distributions for exact logistic regression abstract logistic regression is a commonly used technique for the analysis of retrospective and prospective epidemiological and clinical studies with binary response variables usually this analysis is performed using large sample approximations when the sample size is small or the data structure sparse the accuracy of the asymptotic approximations is in question on other occasions singularity of the covariance matrix of parameter estimates precludes asymptotic analysis under these circumstances use of exact inferential procedures would seem to be a prudent alternative cox 1970 showed that exact inference on the parameters of a logistic model with binary response requires consideration of the distribution of sufficient statistics for these parameters to date however resorting to the exact method has not been computationally feasible except in a few special situations this article presents an efficient recursive algorithm that generates the joint and conditional distributions of the sufficient

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

identification of multiple cracks in a beam using vibration amplitudes abstract a simple method to identify multiple cracks in a beam using the vibration amplitudes is presented the cracks are modeled as massless rotational springs and the forward problem is solved using the finite element method the inverse problem is solved iteratively for the crack locations and sizes using the newton raphson method and the singular value decomposition method a two dimensional finite element model is built to simulate the experimental results and to provide vibration amplitude measurements the difficulty of identifying multiple cracks without a priori knowledge of the number of cracks is overcome by comparing the residual sum of squares of each solution with assumed number of cracks the crack locations are estimated accurately and the accuracy of the crack size estimations are to be enhanced greatly by an improved torsional stiffness model

a simple method for the adjustment of profile likelihoods summary we propose a simple adjustment for profile likelihoods the aim of the adjustment is to alleviate some of the problems inherent in the use of profile likelihoods such as bias inconsistency and overoptimistic variance estimates the adjustment is applied to the profile loglikelihood score function at each parameter value so that its mean is zero and its variance is the negative expected derivative matrix of the adjusted score function for cases in which explicit calculation of the adjustments is difficult we give two methods to simplify their computation an automatic simulation method that requires as input only the profile loglikelihood and its first few derivatives first order asymptotic expressions some examples are provided and a comparison is made with the conditional profile log likelihood of cox and reid

likelihood ratio tests for multiple structural changes abstract this paper proposes a likelihood ratio type test for multiple structural changes in regression models the model allows for lagged dependent variables and trending regressors the limiting distribution of the test is derived we show that asymptotic critical values can be obtained analytically in addition the number and the locations of change points can be consistently determined via the test procedure the method is straightforward to implement

semiparametric estimation in the rasch model and related exponential response models including a simple latent class model for item analysis abstract the rasch model for item analysis is an important member of the class of exponential response models in which the number of nuisance parameters increases with the number of subjects leading to the failure of the usual likelihood methodology both conditional likelihood methods and mixture model techniques have been used to circumvent these problems in this article we show that these seemingly unrelated analyses are in fact closely linked to each other despite dramatic structural differences between the classes of models implied by each approach we show that the finite mixture model for j dichotomous items having t latent classes gives the same estimates of item parameters as conditional likelihood on a set whose probability approaches one if t j 1 2 unconditional maximum likelihood estimators for the finite mixture model can be viewed as keifer wolfowitz estimators for the random effects version of the rasch model latent class versions of the model are especially attractive when t is

vibration analysis of multiple cracked non uniform beams this paper presents the energy based method for the vibration identification of non uniform euler bernoulli beams having multiple open cracks the method includes significant modifications for the energy based method presented by yang et al crack identification in vibrating beams using the energy method journal of sound and vibration 244 2 2001 339 357 the distribution of the energy consumed is determined by taking into account not only the strain change at the cracked beam surface as in general but also the considerable effect of the stress field caused by the angular displacement of the beam due to bending the rayleigh ritz approximation method is used in the analysis the method is adapted to the cases of multiple cracks with an approach based on the definition of strain disturbance variation along the beam examples are presented on cantilever beams having different truncation factors when the results are compared with a commercial finite element program and with the results of zheng and fan natural frequencies of a non uniform beam with multiple cracks via modified fourier series journal of sound and vibration 242 4 2001 701 717 good agreements are obtained the effects of truncation factors and positions of cracks on the natural frequency ratios are presented in graphics

optimal tests when a nuisance parameter is present only under the alternative this paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null for example the results apply to tests of structural change with unknown changepoint the testing problem considered is nonstandard and the classical asymptotic optimality results for the lagrange multiplier wald and likelihood ratio do not apply a weighted average power criterion is used here to generate optimal tests this criterion is similar to that used by a wald 1943 to obtain the classical asymptotic optimality properties of wald tests in regular testing problems copyright 1994 by the econometric society

smooth and accurate multivariate confidence regions this article describes multivariate approximate conditional confidence regions for canonical exponential families these confidence regions have actual coverage probabilities that are closer to their nominal levels than are the actual coverage probabilities of traditional normaltheory regions and have boundaries that are smoother than those obtained by inverting traditional exact tests our method is based on constructing one dimensional conditional tests combining p values and inverting more specifically consider a statistical model with three parameters of which two are of interest and one is not of interest we generate a confidence region for the two parameters of interest by first generating a confidence interval for one of the parameters conditional on sufficient statistics associated with the other interest parameter and the nuisance parameter for values of this bounded parameter inside the confidence interval we determine a confidence interval for the remaining interest parameter condition

bootstrapping general empirical measures it is proved that the bootstrapped central limit theorem for empirical processes indexed by a class of functions mathscr f and based on a probability measure p holds a s if and only if mathscr f in mathrm clt p and int f 2 dp infty where f sup f in mathscr f f and it holds in probability if and only if mathscr f in mathrm clt p thus for a large class of statistics no local uniformity of the clt about p is needed for the bootstrap to work consistency of the bootstrap the bootstrapped law of large numbers is also characterized these results are proved under certain weak measurability assumptions on mathscr f

projection as a method for increasing sensitivity and eliminating nuisance parameters l article analyse des methodes statistiques basees sur les fonctions d estimation qui sont des fonctions de parametres et de donnees a la fois destinees a permettre une inference sur un parametre inconnu une methode de projection peut etre utilisee pour la reduction de ces fonctions afin d accroitre la puissance d un test et l efficacite d un estimateur ponctuel ou bien de rendre une fonction d inference insensible a la valeur d un parametre de nuisance

a study of vibration of geometrically segmented beams with and without crack in this paper a method of modelling for transverse vibrations of a geometrically segmented slender beam with and without a crack normal to its axis has been proposed using the frobenius technique there are two segments one segment is uniform in depth and the other segment has a linearly variable depth the thickness is uniform along the whole length in the presence of a crack the crack section is represented by a rotational spring thereby it is possible to solve both the forward and inverse problems in the forward problem the frequencies can be determined by giving the rotational spring stiffness as an input in the inverse problem the method can be employed to detect the location and size of a crack by providing the natural frequencies as an input a number of numerical examples are presented to demonstrate the accuracy of the method wherever possible results have been compared with analytical solutions available in the literature in the remaining cases the results are found to be in very good agreement with finite element solutions in the inverse problems the error in prediction of crack location is less than 3 and that in size is around 25

approximate monte carlo conditional inference in exponential families summary this article presents an algorithm for approximate frequentist conditional inference on two or more parameters for any regression model in the generalized linear model glim family we thereby extend highly accurate inference beyond the cases of logistic regression and contingency tables implimented in commercially available software the method makes use of the double saddlepoint approximations of skovgaard 1987 journal of applied probability24 875 887 and jensen 1992 biometrika79 693 703 to the conditional cumulative distribution function of a sufficient statistic given the remaining sufficient statistics this approximation is then used in conjunction with noniterative monte carlo methods to generate a sample from a distribution that approximates the joint distribution of the sufficient statistics associated with the parameters of interest conditional on the observed values of the sufficient statistics associated with the nuisance parameters this algorithm is an alternate approach to that presented by kolassa and tanner 1994 journal of the american statistical association89 697 702 in which a markov chain is generated whose equilibrium distribution under certain regularity conditions approximates the joint distribution of interest in kolassa and tanner 1994 the gibbs sampler was used in conjunction with these univariate conditional distribution function approximations the method of this paper does not require the construction and simulation of a markov chain thus avoiding the need to develop regularity conditions under which the algorithm converges and the need for the data analyst to check convergence of the particular chain examples involving logistic and truncated poisson regression are presented

approximate conditional inference in generalized linear models on developpe des approximations precises et facilement calculables pour les densites conditionnelles et les distributions des statistiques exhaustives dans les modeles lineaires generalises avec des fonctions de liaison canoniques

conditional score functions some optimality results summary the conditional score function has previously been shown to generate the optimal estimating equation for a parameter of interest when the conditioning statistic is complete and sufficient for the nuisance parameters godambe 1976 the present paper generalizes these results to partial likelihood factorizations and then examines the nature of the problem when the appropriate conditioning statistics depend on the parameter of interest in this case globally optimal estimating functions are impossible a weaker criterion of optimal weighting leads to a class of estimated conditional score functions which satisfy an information equality the purpose of this paper is to develop and justify an approach based on conditional likelihood to estimation in the presence of nuisance parameters the arguments focus on the case when there is a complete and sufficient statistic s 0 for the nuisance parameters when the parameter of interest 0 is fixed an extended notion of completeness will be presented in the context of partial likelihoods the problem takes on two separate natures depending on whether the statistic s 0 truly depends on 0 or not if s s 0 is free of 0 then the conditional likelihood of the data given s has been shown to generate optimal inferential procedures giving a best estimating equation godambe 1976 and a best asymptotically normal estimator in a mixture setting lindsay 1980 if s 0 depends on 0 then it will be shown that the best estimating equation also a conditional likelihood score will generally be only locally optimal leaving no single best strategy consideration of an optimal weighting strategy yields estimators which have second order properties similar to the conditional likelihoods of the first type

detection of crack location and size in structures using wavelet finite element methods abstract a methodology to detect crack location and size is presented which takes advantage of wavelet finite element methods wfem in the modal analysis for singularity problems like a cracked beam first the beam is discretized into a set of wavelet finite elements and then the natural frequencies of the beam with various crack locations and sizes are accurately obtained the frequency response functions function of crack location and size are approximated by means of surface fitting techniques measured natural frequencies are used in a crack detection process and the crack location and size can be identified by finding the point of intersection of three frequency contour lines the experimental data from a free free beam studied by silva are employed to verify the accuracy of the method the present method is general and can be easily extended to complex structures with multiple cracks

testing constancy in varying coefficient models abstract this article proposes a coefficients constancy test in semi varying coefficient models that only needs to estimate the restricted coefficients under the null hypothesis the test statistic resembles the union intersection test after ordering the data according to the varying coefficients explanatory variable this statistic depends on a trimming parameter that can be chosen by a data driven calibration method we propose a bootstrap test is justified under fairly general regularity conditions under more restrictive assumptions the critical values can be tabulated and trimming is unnecessary the finite sample performance is studied by means of monte carlo experiments and a real data application for modeling education returns

the exact explicit dynamic stiffness matrix of multi cracked euler bernoulli beam and applications to damaged frame structures abstract in this paper the closed form expression of the exact dynamic stiffness matrix of an euler bernoulli beam in the presence of an arbitrary number of concentrated cracks is derived the procedure adopted for the evaluation of the dynamic stiffness matrix is based on the availability of the exact closed form solution of the vibration modes of the multi cracked beam derived by the same authors in a previous paper the knowledge of the exact explicit dynamic stiffness matrix of the multi cracked beam makes the direct evaluation of the exact global dynamic stiffness matrix of damaged frame structures possible furthermore it allows the exact evaluation of the frequencies and the corresponding vibration modes consistent with the distributed parameter model through the application of the well known wittrick williams algorithm some numerical applications relative to the evaluation of frequencies and the corresponding mode shapes of multi cracked framed structure are reported furthermore the closed form solution has been validated by comparing with some exact results available in the literature for a simple single cracked frame finally further new results for a multi cracked frame have been compared with those obtained by a finite element simulation

small sample confidence regions in exponential families this article presents an algorithm for small sample conditional confidence regions for two or more parameters for any discrete regression model in the generalized linear interactive model family regions are constructed by careful inversion of conditional hypothesis tests this method presupposes the use of approximate or exact techniques for enumerating the sample space for some components of the vector of sufficient statistics conditional on other components such enumeration may be performed exactly or by exact or approximate monte carlo including the algorithms of kolassa and tanner 1994 journal of the american statistical association 89 697 702 1999 biometrics 55 246 251 this method also assumes that one can compute certain conditional probabilities for a fixed value of the parameter vector because of a property of exponential families one can use this set of conditional probabilities to directly compute the conditional probabilities associated with any other value of the vector of the parameters of interest this observation dramatically reduces the computational effort required to invert the hypothesis test to obtain the confidence region to construct a region with confidence level 1 alpha the algorithm begins with a grid of values for the parameters of interest for each parameter vector on the grid corresponding to the current null hypothesis one transforms the initial set of conditional probabilities using exponential tilting and then calculates the p value for this current null hypothesis the confidence region is the set of parameter values for which the p value is at least alpha

identification of multiple cracks in a beam using natural frequencies abstract a simple method to identify multiple cracks in a beam is presented the cracks are modeled as rotational springs and the forward problem is solved using the finite element method the inverse problem is solved iteratively for the locations and sizes of the cracks using the newton raphson method numerical examples are provided for the identification of triple cracks in a cantilever beam as well as double cracks the detected crack locations and sizes are in excellent agreement with the actual ones

determination of crack location in beams using natural frequencies abstract in this paper we describe a numerical method for determining the location of a crack in a beam of varying depth when the lowest three natural frequencies of the cracked beam are known the crack is modelled as a rotational spring and graphs of spring stiffness versus crack location are plotted for each natural frequency the point of intersection of the three curves gives the location of the crack earlier work in this area involved the use of the frobenius technique for solving the governing differential equation analytically and then using a semi numerical approach to obtain the crack location in this work we use the finite element approach to solve the same problem the beam is modelled using beam elements and the inverse problem of finding the spring stiffness given the natural frequency is shown to be related to the problem of a rank one modification of an eigenvalue problem examples outlining the accuracy and ease of using this method are shown the results are compared with those from semi analytical approaches the biggest advantage of this method is the generality in the approach different boundary conditions and variations in the depth of the beam can be easily modelled

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

inference regarding multiple structural changes in linear models with endogenous regressors this paper considers the linear model with endogenous regressors and multiple changes in the parameters at unknown times it is shown that minimization of a generalized method of moments criterion yields inconsistent estimators of the break fractions but minimization of the two stage least squares 2sls criterion yields consistent estimators of these parameters we develop a methodology for estimation and inference of the parameters of the model based on 2sls the analysis covers the cases where the reduced form is either stable or unstable the methodology is illustrated via an application to the new keynesian phillips curve for the us

optimal tests for parameter instability in the generalized method of moments framework this paper presents optimal tests for parameter instability in the gmm framework the new tests include tests that are optimal for both one sided and two sided alternatives one of the optimal tests for two sided alternatives is the gmm generalization of the test presented in andrews and ploberger 1994 for the likelihood framework the new tests include a class of optimal tests that direct the test s power to specific locations in the sample one of these optimal tests has the attractive feature of a normal distribution under the null hypothesis

structural change tests for simulated method of moments simulation based estimation methods have become more widely used in recent years we propose a set of tests for structural change in models estimated via simulated method of moments see duffe and singleton econometrica 61 1993 929 these tests extend the work of andrews econometrica 61 1993 821 ghysels et al j econom 82 1997 209 and sowell econometrica 64 1996 1085 tests for violation of moment conditions manuscript graduate school of industrial administration carnegie mellon university which covered generalized method of moments estimators not involving simulation we derive the asymptotic distributions of various tests we show that the number of simulations does not affect the asymptotic distribution under the null but adversely influences local asymptotic power a monte carlo investigation of the finite sample size and power reveals that a relatively small number of simulations suffices to obtain tests with desirable small sample size and power properties

testing structural stability with endogenous breakpoint a size comparison of analytic and bootstrap procedures abstract we compare the performance of two alternative approximations to the finite sample distributions of test statistics for structural change one based on asymptotics and one based on the bootstrap we focus on tests acknowledging that the breakpoint is selected endogenously in particular the supremum tests of andrews 1993 we explore a variety of issues of interest in applied work focusing particularly on smaller samples and persistent dynamics the bootstrap approximation to the finite sample distribution appears consistently accurate in contrast to the asymptotic approximation the results are of interest not only from the perspective of testing for structural change but also from the broader perspective of compiling evidence on the adequacy of bootstrap approximations to finite sample distributions in econometrics

a direct solution for the transverse vibration of euler bernoulli wedge and cone beams abstract a number of publications have appeared on the transverse vibration of complete and truncated wedge and cone beams the mode shape equations are linear differential equations with regular singularity the natural frequencies of complete beams are found in several publications for truncated beams several numerical solutions have been proposed and the natural frequencies documented in most cases for cantilever wedge and cone beams clamped at the large end analytical solutions of the mode shape equations have been derived based on bessel functions only in one publication are the natural frequencies tabulated for nine combinations of clamped pinned and free boundary conditions but the accuracy of the frequencies is limited to two figures after the decimal point for the fundamental frequency and the higher mode frequencies are rounded to integers the results are not suitable for judging the quality of the various approximate methods in this paper a direct solution of the mode shape equation is presented the sliding boundary condition is also considered and the first three dimensionless natural frequencies computed for 16 combinations of the boundary conditions are tabulated for values of truncation factors from 0 05 to 0 7 the tabulated results are benchmarks and frequencies for truncation factors not in the tables may be interpolated to within 0 1 accuracy

efficiency of projected score methods in rectangular array asymptotics summary the paper considers a rectangular array asymptotic embedding for multistratum data sets in which both the number of strata and the number of within stratum replications increase and at the same rate it is shown that under this embedding the maximum likelihood estimator is consistent but not efficient owing to a non zero mean in its asymptotic normal distribution by using a projection operator on the score function an adjusted maximum likelihood estimator can be obtained that is asymptotically unbiased and has a variance that attains the cram6r rao lower bound the adjusted maximum likelihood estimator can be viewed as an approximation to the conditional maximum likelihood estimator

infereni on full or partial parameters based on the standardized signed log likelihood ratio on etudie des tests et des limites de confiance bases sur la statistique du rapport de log vraisemblance signee en ajustant cette statistique de telle sorte qu a un ordre superieur d approximation la distribution normale standard soit valable

regression analysis nonlinear or nonnormal simple and accurate p values from likelihood analysis we develop simple approximations for the p values to use with regression models having linear or nonlinear parameter structure and normal or nonnormal error distribution computer iteration then gives confidence intervals both frequentist and bayesian versions are given the approximations are derived from recent developments in likelihood analysis and have third order accuracy also for very small and medium sized samples the accuracy can typically be high the likelihood basis of the procedure seems to provide the grounds for this general accuracy examples are discussed and simulations record the distributional accuracy