root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

extinction properties of solutions for a class of fast diffusive p laplacian equations abstract we consider the extinction properties of solutions for the homogeneous dirichlet boundary value problem for the p laplacian equation u t div u p 2 u u q u r with 1 p 2 q 1 and r 0 for 0 it is known that r p 1 is the critical extinction exponent for the weak solution for 0 we show that r p 1 is still the critical extinction exponent when q 1 moreover the precise decay estimates of solutions before the occurrence of the extinction are derived however extinction can always occur when 0 q r 1

model selection in under specified equations facing breaks although a general unrestricted model may under specify the data generation process especially when breaks occur model selection can still improve over estimating a prior specification impulseindicator saturation iis can correct non constant int ercepts induced by location shifts in omitted variables which surprisingly leave slope parameters unaltered even when correlated with included variables however location shifts in included variables do induce changes in slopes when there are correlated omitted variables iis acts as a robust meth od when models are mis specified and helps mitigate the adverse impacts of induced location shifts on non constant intercepts and equation standard errors

tests for changes in models with a polynomial trend abstract in this paper we propose a class of tests for changes in models with a polynomial trend based on the generalized fluctuation testing principle of kuan and hornik 1995 we derive the asymptotic null distributions of the proposed tests and tabulate their asymptotic critical values we also show that these tests are consistent and have non trivial local power against a wide class of alternatives the simulation results suggest that the proposed tests can complement the existing tests in different time trend models

blow up phenomena for a doubly degenerate equation with positive initial energy abstract in this paper an initial boundary value problem related to the equation u t div u m p 2 u m f u is studied under suitable conditions on f we establish a blow up result for certain solution with positive initial energy and blow up time will be also considered by using the differential inequality technique the upper estimate of the blow up solution near the single blow up point is also obtained

the role of critical exponents in blow up theorems the sequel abstract in 27 fujita showed that for positive solutions the initial value problem in r n for u t u u p with p 1 exhibited the following behavior if p p c 1 2 n then the initial value problem does not have any nontrivial non negative solution existing on r n 0 a global solution whereas if p p c there exist global small data positive solutions as well as solutions which are non global we call such a result a blow up theorem of fujita type in 50 levine discussed the various theorems of this type that had appeared in the literature prior to 1990 in this paper we revisit the literature since 1990

a trend resistant test for structural change based on ols residuals abstract we discuss the null distribution and local power of an ols based version of the cusum test and show that this contrary to other tests for structural change like e g the ploberger kontrus kramer fluctuation test can also be applied to trending data

non extinction and critical exponent for a polytropic filtration equation abstract this paper is concerned with the homogeneous dirichlet boundary value problem of a polytropic filtration equation with reaction sources we will show the non extinction property of non trivial solutions and determine the critical fujita exponent for the problem

analytical three dimensional elasticity solutions to some plate problems and some observations on mindlin s plate theory abstract solutions are obtained using the exact three dimensional theory of elasticity to i the eigenvalue problem or buckling under biaxial compression or the free lateral vibration of a simply supported rectangular plate with orthotropic stress strain properties and ii the static response of the same plate to a lateral load that varies sinusoidally in two directions the eigenvalue in problem i and the lateral deflections of both the surface and middle plane of the plate as well as the bending strains in problem ii are obtained in the form of series expansions in even powers of the plate thickness exact algebraic expressions are presented for the first two coefficients in the case of orthotropic plates additional coefficients can be obtained if required and are given for the much simpler case of isotropic plates in all cases the first term agrees with classical plate theory the solutions are compared with those obtained from mindlin s plate theory in neither problem is it found to be possible in general to choose values for mindlin s effective shear moduli to make the mindlin solution agree with the first two terms of the exact solution there are however two exceptions to this namely a restricted class of orthotropic materials embracing all isotropic ones in which the elastic constants satisfy a certain condition and the case of cylindrical bending when the mindlin plate reduces to a timoshenko beam of wide rectangular cross section in both these exceptional cases appropriate values for the effective shear moduli are obtained

a class of nonlinear parabolic equations with anisotropic nonstandard growth conditions in this paper a doubly nonlinear parabolic problem involving nonstandard growth conditions under homogeneous dirichlet boundary conditions is studied to be a little precise first some energy estimates and inequalities are exploited to obtain energy decay estimates of the solution then it is proved that the rest field u x t 0 is asymptotically stable in terms of natural energy associated with the solution second we give two new blow up criteria that one of them is obtained to remove the exponent restriction by using an extended form of the concavity method and the other one is a blow up result of weak solutions with arbitrarily high initial energy moreover an extinction result is also showed by establishing a new auxiliary lemma the present results of this paper complement and improve a recent paper investigated by liu et al j math phys 59 121504 2018

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

three dimensional elasticity solutions to some orthotropic plate problems abstract this paper presents a three dimensional analysis of rectangular orthotropic plates by employing the differential quadrature dq method the derivation of the governing equations from the governing equations and the stress strain relationship of the three dimensional elasticity model is detailed the constrained conditions of the orthotropic plate edges are given the governing equations and boundary conditions are first normalized and discretized according to the dq procedure example problems pertaining to the bending buckling and free vibration of orthotropic plates with generic boundary conditions are selected to illustrate the simplicity and applicability of the dq method the convergence characteristics of the dq method are first obtained based on numerical studies after which the dq solutions are compared where possible with exact solutions it is found that the dq method yields accurate results for the plate problems under investigation

modeling and testing smooth structural changes with endogenous regressors abstract modeling and detecting parameter stability of econometric models is a long standing problem most existing estimation and testing methods are designed for models without endogeneity little attention has been paid to models with endogeneous regressors which may arise in many scenarios in economics in this paper we first consider a time varying coefficient time series model with potential time varying endogeneity a local linear two stage least squared estimation is developed to estimate coefficient functions the consistency and asymptotic normality of the estimator are derived furthermore a nonparametric test is proposed to check smooth structural changes as well as abrupt structural breaks with possibly unknown change points in regression models with potential endogeneity the idea is to compare the fitted values of the unrestricted nonparametric time varying coefficient model and the restricted constant parameter model the test has an asymptotic n 0 1 distribution and does not require any prior information about the alternatives a simulation study highlights the merits of the proposed estimator and test in an application we estimate the new keynesian phillips curve for the us nonparametrically and find strong evidence against its stability

a quasilinear reaction diffusion system coupled via nonlocal sources in this paper we establish the critical exponent and the blow up rate for a quasilinear reaction diffusion system with nonlocal nonlinear sources and inner absorptions subject to homogeneous dirichlet conditions and nonnegative initial data it is found that the critical exponent is determined by the interaction among all the six nonlinear exponents from all the three kinds of the nonlinearities while the blow up rate is independent of the nonlinear diffusion exponents due to the effects of the coupled nonlocal sources two kinds of characteristic algebraic systems are introduced to get simple descriptions for the critical exponent and the blow up rate respectively we prove moreover that the blow up could be global due to the nonlocality of the nonlinear sources

hierarchical statistical models and a generalized likelihood ratio test this paper deals with statistical inference for statistical models which have a nested structure the emphasis here is on the use of a classical test of significance and on a confidence set construction approach for model identification and the paper proposes a generalized likelihood ratio test with equal marginal error rate as a basic tool the power performance of this test is characterized and some applications are illustrated

inference for non stationary time series regression with or without inequality constraints summary we consider statistical inference for time series linear regression where the response and predictor processes may experience general forms of abrupt and smooth non stationary behaviours over time meanwhile the regression parameters may be subject to linear inequality constraints a simple and unified procedure for structural stability checks and parameter inference is proposed in the case where the regression parameters are constrained the methodology proposed is shown to be consistent whether or not the true regression parameters are on the boundary of the restricted parameter space via utilizing an asymptotically invariant geometric property of polyhedral cones

powerful tests for structural changes in volatility abstract detecting structural changes in volatility is important for understanding volatility dynamics and stylized facts observed for financial returns such as volatility persistence we propose modified cusum and lm tests that are built on a robust estimator of the long run variance of squared series we establish conditions under which the new tests have standard null distributions and diverge faster than standard tests under the alternative the theory allows smooth and abrupt structural changes that can be small the smoothing parameter is automatically selected such that the proposed test has good finite sample size and meanwhile achieves decent power gain

extinction and positivity for the evolution p laplacian equation in rn abstract the aim of this paper is to discuss extinction and positivity for the solution of the initial boundary value problem of evolution p laplacian equation it is proved that the weak solution will be extincted for 1 p 2 and will be positive for p 2 for large t

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

critical fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux we establish the critical fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux and then determine the blow up rates and the blow up sets for the nonglobal solutions

does modeling a structural break improve forecast accuracy mean square forecast error loss implies a bias variance trade off that suggests that structural breaks of small magnitude should be ignored in this paper we provide a test to determine whether modeling a structural break improves forecast accuracy the test is near optimal even when the date of a local to zero break is not consistently estimable the results extend to forecast combinations that weight the post break sample and the full sample forecasts by our test statistic in a large number of macroeconomic time series we find that structural breaks that are relevant for forecasting occur much less frequently than existing tests indicate

change point analysis of imprecise time series abstract in this paper we describe how to conduct a change point analysis when dealing with time series imprecisely or vaguely observed i e time ordered observations whose values are not known exactly such as interval or ordinal time series imprecise time series in order to treat such time series we propose to employ a fuzzy approach i e data are parameterized in the form of fuzzy variables then to detect the number and location of change points we employ a deviation measure for fuzzy variables in the framework of atheoretical regression trees art we present simulation results pertaining to the behavior of the proposed approach as well as two empirical applications to real imprecise time series

numerical solution of a fast diffusion equation in this paper the authors consider the first boundary value problem for the nonlinear reaction diffusion equation u t u m u p 1 in a smooth bounded domain in r d d 1 with the zero lateral boundary condition and with a positive initial condition m e 0 1 fast diffusion problem 0 and p1 m sufficient conditions on the initial data are obtained for the solution to vanish or become infinite in a finite time a scheme for the discretization in time of this problem is proposed the numerical scheme preserves the essential properties of the initial problem namely existence of an extinction or a blow up time for which estimates have been obtained the convergence of the method is also proved

on the three dimensional vibrations of the cantilevered rectangular parallelepiped a solution is presented for the three dimensional problem of determining the free vibration frequencies and mode shapes for a rectangular parallelepiped which is completely fixed on one face and free on the other five faces this problem apparently is previously unsolved in the published literature the ritz method is used with displacements assumed in the form of algebraic polynomials convergence is studied numerical results are given for the first five frequencies of each of the four symmetry classes of vibration for five thick parallelepiped configurations including the cube contour plots are exhibited for the modal displacements of the cube the effects of varying poisson s ratio are also observed

three dimensional vibration of rectangular plates variance of simple support conditions and influence of in plane inertia plate models developed on the basis of the three dimensional elasticity theory are crucial to the correct solutions in dynamics problems in a three dimensional setting there exist numerous possible definitions of boundary conditions this paper attempts to identify the variance of three dimensional simple support conditions existing in practice the hard simple support condition assumes vanishing normal stresses at the edges and zero transverse and tangential displacement at the peripheries the soft simple support on the other hand imposes zero transverse displacement with vanishing normal and shear stresses at the boundaries to quantify the relative effects of each boundary condition on the vibratory responses of thick plates a global three dimensional ritz formulation is employed for analysis this technique uses sets of finite polynomial series in cartesian co ordinates to approximate the global normal mode variations of the plate these separable one dimensional polynomials are orthogonally generated within the plate domain such that all the essential edge conditions are identically satisfied the accuracy of the proposed three dimensional ritz method is assured from the convergence and comparison studies numerical experiments have been conducted to study firstly the effects of geometric parameters on the overall normal mode characteristics of simply supported plates and secondly the effects of in plane inertia on the vibration frequencies of plates with different thicknesses the three dimensional deformed mode shapes for selected cases have also been computed these have served to describe more vividly the normal mode characteristics of different types of simply supported rectangular plates

estimating structural changes in regression quantiles this paper considers the estimation of multiple structural changes occurring at unknown dates in one or multiple conditional quantile functions the analysis covers time series models as well as models with repeated cross sections we estimate the break dates and other parameters jointly by minimizing the check function over all permissible break dates the limiting distribution of the estimator is derived and the coverage property of the resulting confidence interval is assessed via simulations a procedure to determine the number of breaks is also discussed empirical applications to the quarterly us real gdp growth rate and the underage drunk driving data suggest that the method can deliver more informative results than the analysis of the conditional mean function alone

trend function hypothesis testing in the presence of serial correlation in this paper test statistics are proposed that can be used to test hypotheses about the parameters of the deterministic trend function of a univariate time series the tests are valid in the presence of general forms of serial correlation in the errors and can be used without having to estimate the serial correlation parameters either parametrically or nonparametrically the tests are valid for i 0 and i 1 errors trend functions that are permitted include general linear polynomial trend functions that may have breaks at either known or unknown locations asymptotic distributions are derived and consistency of the tests is established the general results are applied to a model with a simple linear trend a local asymptotic analysis is used to compute asymptotic size and power of the tests for this example size is well controlled and is relatively unaffected by the variance of the initial condition asymptotic power curves are computed for the simple linear trend model and are compared to existing tests it is shown that the new tests have nontrivial asymptotic power a simulation study shows that the asymptotic approximations are adequate for sample sizes typically used in economics the tests are used to construct confidence intervals for average gnp growth rates for eight industrialized countries using post war data

semi analytical analysis for multi directional functionally graded plates 3 d elasticity solutions semi analytical 3 d elasticity solutions are presented for orthotropic multi directional functionally graded plates using the differential quadrature method dqm based on the state space formalism material properties are assumed to vary not only through the thickness but also in the in plane directions following an exponential law the graded in plane domain is solved numerically via the dqm while exact solutions are sought for the thickness domain using the state space method convergence studies are performed and the present hybrid semi analytical method is validated by comparing numerical results with the exact solutions for a conventional unidirectional functionally graded plate finally effects of material gradient indices on the displacement and stress fields of the plates are investigated and discussed copyright 2009 john wiley sons ltd

detecting gradual changes in locally stationary processes in a wide range of applications the stochastic properties of the observed time series change over time the changes often occur gradually rather than abruptly the properties are approximately constant for some time and then slowly start to change in such situations it is frequently of interest to locate the time point where the properties start to vary in contrast to the analysis of abrupt changes methods for detecting smooth or gradual change points are less developed and often require strong parametric assumptions in this paper we develop a fully nonparametric method to estimate a smooth change point in a locally stationary framework we set up a general procedure which allows to deal with a wide variety of stochastic properties including the mean auto covariances and higher order moments the theoretical part of the paper establishes the convergence rate of the new estimator in addition we examine its finite sample performance by means of a simulation study and illustrate the methodology by applications to temperature and financial return data

blow up versus extinction in a nonlocal p laplace equation with neumann boundary conditions abstract this paper studies a fast diffusive p laplace equation with the nonlocal source u q u q d x in a bounded domain subject to homogeneous neumann boundary value condition a critical criterion is determined that the changing sign solutions blow up in finite time with q 1 and non positive initial energy associated and must be global for any initial energy if q 1 in particular the conditions are obtained under which the changing sign solutions vanish in finite time

asymptotic theory for time series with changing mean and variance abstract the paper develops point estimation and asymptotic theory with respect to a semiparametric model for time series with moving mean and unconditional heteroscedasticity these two features are modelled nonparametrically whereas autocorrelations are described by a short memory stationary parametric time series model we first study the usual least squares estimate of the coefficient of the first order autoregressive model based on constant but unknown mean and variance allowing for both the latter to vary over time in a general way we establish its probability limit and a central limit theorem for a suitably normed and centred statistic giving explicit bias and variance formulae as expected mean variation is the main source of inconsistency and heteroscedasticity the main source of inefficiency though we discuss circumstances in which the estimate is consistent for and asymptotically normal about the autoregressive coefficient albeit inefficient we then consider standard implicitly defined whittle estimates of a more general class of short memory parametric time series model under otherwise more restrictive conditions when the mean is correctly assumed to be constant estimates that ignore the heteroscedasticity are again found to be asymptotically normal but inefficient allowing a slowly time varying mean we resort to trimming out of low frequencies to achieve the same outcome returning to finite order autoregression nonparametric estimates of the varying mean and variance are given asymptotic justification and forecasting formulae developed finite sample properties are studied by a small monte carlo simulation and an empirical example is also included

a nonparametric test for changing trends many tests of parameter change in dynamic models exhibit nonmonotonic power an important source of the nonmonotonic power comes from the bias in estimating parameters when there is a change in the deterministic component to avoid this bias we propose a nonparametric test for changing trends based on nonparametrically detrended data the tests are similar in spirit to nonparametric conditional moment tests such as fan and li j nonparametr stat 10 1999a 245 11 1999b 251 and zheng j econometrics 75 1996 263 the resulting statistics have a standard normal distribution a monte carlo experiment suggests that the tests have good power against changes in the deterministic component

three dimensional vibration of rectangular plates effects of thickness and edge constraints abstract a continuum three dimensional ritz formulation is presented for the free vibration analysis of homogeneous isotropic thick rectangular plates the method is applied specifically to investigate the effects of boundary constraints and thickness ratios on the vibration responses of these plates a general switching of transverse vibratory motions to surface parallel modes at the higher thickness ratio is manifested vividly through three dimensional deformed mode shape plots the present formulation is based on the linear three dimensional small strain elasticity energy principle in the solution process sets of self generating polynomial shape functions are used to derive the governing eigenvalue equation in essence these functions comprise a class of orthogonal polynomial functions and a basic function which is chosen to satisfy the essential geometric boundary conditions at the outset they are found very suitable for the computationally intensive task of 3 d modelling due to the ease of generation and numerical implementation several numerical examples have been computed to demonstrate the accuracy and efficiency of the method the influences of plate thickness and boundary constraints on the overall vibratory characteristics of thick plates are also discussed in detail

a simple consistent bootstrap test for a parametric regression function abstract a simple consistent test is considered and a bootstrap method is proposed for testing a parametric regression functional form it is shown that the bootstrap method gives a more accurate approximation to the null distribution of the test than the asymptotic normal theory result we also propose a consistent test for testing a parametric partially linear model versus a semiparametric partially linear alternative monte carlo simulations suggest that the bootstrap test performs well based on wild bootstrap critical values

two new approximate methods for analyzing free vibration of structural components two approximate methods which have not previously been used for structural dynamics problems are applied to the free vibration analysis of various structural components the first method is a new version of the complementary energy method it is shown to be considerably more accurate than the conventional rayleigh and rayleigh schmidt methods when applied to spatially one dimensional free vibration problems prismatic and tapered bars prismatic beams and axisymmetric motion of circular membranes the second method is the differential quadrature method introduced by bellman and his associates it is applied successfully here to all of the problems mentioned plus square membranes and circular and square plates

estimating and testing linear models with multiple structural changes this paper develops the statistical theory for testing and estimating multiple change points in regression models the rate of convergence and limiting distribution for the estimated parameters are obtained several test statistics are proposed to determine the existence as well as the number of change points a partial structural change model is considered the authors study both fixed and shrinking magnitudes of shifts in addition the models allow for serially correlated disturbances mixingales an estimation strategy for which the location of the breaks need not be simultaneously determined is discussed instead the authors method successively estimates each break point

three dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method this paper presents accurate three dimensional elasticity solutions for free vibrations of six types of plates having free lateral surfaces two opposite sides simply supported and two other sides having combinations of simply supported clamped and free boundary conditions the solution methodology adopted in the present work first reduces the spatial variables in the governing elasticity equations to two by using displacement functions in the forms which satisfy the boundary conditions of the assumed simply supported sides the eigenvalue equations are then formulated from the reduced governing equations and the boundary conditions via the differential quadrature method the numerical results include the first nine natural frequencies of the six plate configurations for combinations of three aspect ratios and two thickness ratios these results are supported by appropriate convergence studies and comparisons with the results of other authors

testing for smooth structural changes in time series models via nonparametric regression checking parameter stability of econometric models is a long standing problem almost all existing structural change tests in econometrics are designed to detect abrupt breaks little attention has been paid to smooth structural changes which may be more realistic in economics we propose a consistent test for smooth structural changes as well as abrupt structural breaks with known or unknown change points the idea is to estimate smooth time varying parameters by local smoothing and compare the fitted values of the restricted constant parameter model and the unrestricted time varying parameter model the test is asymptotically pivotal and does not require prior information about the alternative a simulation study highlights the merits of the proposed test relative to a variety of popular tests for structural changes in an application we strongly reject the stability of univariate and multivariate stock return prediction models in the postwar and post oil shocks periods

a continuum three dimensional vibration analysis of thick rectangular plates abstract this paper presents a continuum three dimensional ritz formulation for the vibration analysis of homogeneous thick rectangular plates with arbitrary combinations of boundary constraints this model is formulated on the basis of the linear three dimensional small deformation elasticity theory to predict the vibratory responses of these thick rectangular plates the displacement fields in the transverse and in plane directions are expressed by sets of orthogonally generated polynomial functions these shape functions are intrinsically a product of a class of orthogonal polynomial functions and a basic function which are chosen to satisfy the essential geometric boundary conditions at the outset sets of frequency data for plates with various aspect ratios and thickness ratios have been presented these data are used to examine the merits and limitations of the classical plate theory and mindlin plate theory by direct comparisons finally using the three dimensional continuum approach sets of first known deformed mode shapes have been generated thus helping to understand the vibratory motion furthermore these results may also serve as the benchmark to further research into the refined plate theories

a complete characterization of nonlinear absorption for the evolution p laplacian equations to have positive or extinctive solutions this paper is concerned with long time behaviors of solutions to the initial boundary value problem of the evolution p laplacian equations with nonlinear absorption a long time behavior of solutions to these equations has been studied so far for particular types of nonlinear absorption term the purpose of this paper is to give a complete characterization of the nonlinear absorption term according to the parameter p in p laplacian operator and the growth of the nonlinear absorption term near the origin in order to determine whether the solution to the equations is extinctive or positive in addition we also give upper bounds for extinction times of solutions

sources of nonmonotonic power when testing for a shift in mean of a dynamic time series sources of nonmonotonic power are uncovered for a wide variety of tests for a shift in the mean of a dynamic time series two main sources of nonmonotonic power are found the first source is the behavior of the estimate of error variance under the alternative hypothesis of a shift in mean in particular if the error variance is estimated under the null hypothesis nonmonotonic power can result the second source is the presence of a lagged dependent variable in the estimated regression

behaviour of solutions of a singular diffusion equation near the extinction time abstract we prove that if 2 and 0 u0 l1 r2 lp r2 for some constant p 1 is a radially symmetric function u0 0 and u is the unique solution of the equation u t log u u 0 in r 2 0 t u x 0 u 0 x in r2 which satisfies r 2 u x t d x r 2 u 0 d x 2 t 0 and rur x t u x t uniformly on a b as r x for any 0 t r 2 u 0 d x 2 then there exist unique constants 0 1 2 2 1 such that the rescaled function v y s u y t t t t t with s log t t will converge uniformly on every compact subset of r2 to the solution y of the ode r r r 0 in 0 with r 0 0 0 1 for some constant 0 as s

testing for parameter constancy in linear regressions an empirical distribution function approach this paper proposes some tests for parameter constancy in linear regressions the tests use weighted empirical distribution functions of estimated residuals and are asymptotically distribution free the local power analysis reveals that the proposed tests have nontrivial local power against a wide range of alternatives in particular the tests are capable of detecting error heterogeneity that is not necessarily manifested in the form of changing variances the model allows for both dynamic and trending regressors the residuals may be obtained based on any root n consistent estimator under the null of regression parameters as an intermediate result some weak convergence for stochastically weighted sequential empirical processes is established

multiscale change point inference summary we introduce a new estimator the simultaneous multiscale change point estimator smuce for the change point problem in exponential family regression an unknown step function is estimated by minimizing the number of change points over the acceptance region of a multiscale test at a level the probability of overestimating the true number of change points k is controlled by the asymptotic null distribution of the multiscale test statistic further we derive exponential bounds for the probability of underestimating k by balancing these quantities will be chosen such that the probability of correctly estimating k is maximized all results are even non asymptotic for the normal case on the basis of these bounds we construct asymptotically honest confidence sets for the unknown step function and its change points at the same time we obtain exponential bounds for estimating the change point locations which for example yield the minimax rate up to a log term finally the simultaneous multiscale change point estimator achieves the optimal detection rate of vanishing signals as n even for an unbounded number of change points we illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions the performance of the multiscale approach proposed is illustrated by simulations and in two cutting edge applications from genetic engineering and photoemission spectroscopy

application of generalized differential quadrature method to structural problems summary this paper presents the first endeavour to exploit a generalized differential quadrature method as an accurate efficient and simple numerical technique for structural analysis firstly drawbacks existing in the method of differential quadrature dq are evaluated and discussed then an improved and simpler generalized differential quadrature method gdq is introduced to overcome the existing drawback and to simplify the procedure for determining the weighting coefficients subsequently the generalized differential quadrature is systematically employed to solve problems in structural analysis numerical examples have shown the superb accuracy efficiency convenience and the great potential of this method numerical approximation methods for solving partial differential equations have been widely used in various engineering fields classical techniques such as finite element and finite difference methods are well developed and well known these methods can provide very accurate results by using a large number of grid points however in a large number of cases reasonably approximate solutions are desired at only a few specific points in the physical domain in order to get results even at or around a point of interest with acceptable accuracy conventional finite element and finite difference methods still require the use of a large number of grid points consequently the requirement for computer capacity is often unnecessarily large in such cases in seeking an alternate numerical method using fewer grid points to find results with acceptable accuracy the method of differential quadrature dq was introduced by bellman et a the method of dq is a global approximate method this method is based on the ideas that the derivative of a function with respect to a co ordinate direction can be expressed as a weighted linear sum of all the function values at all mesh points along that direction and that a continuous function can be approximated by a higher order polynomial in the overall domain the dq method differs from the finite element method fem in two aspects firstly the fem uses lower order polynomials to approximate a function on a local element level while the dq method approximates a function on the global area using higher order polynomials secondly the dq method directly approximates the derivatives of a function at a point while the fem approximates a function over a local element and the derivatives can then be derived from the approximate function in this aspect the dq method is more similar to the finite difference method fdm however the fdm is also a local approximation method based on lower order polynomial approximation in fact it can be shown that the fdm is just a special case of the dq method where it is applied locally on the range xi xi l owing to the higher order

testing for change points in time series models and limiting theorems for ned sequences this paper first establishes a strong law of large numbers and a strong invariance principle for forward and backward sums of near epoch dependent sequences using these limiting theorems we develop a general asymptotic theory on the wald test for change points in a general class of time series models under the no change point hypothesis as an application we verify our assumptions for the long memory fractional arima model

a consistent test of functional form via nonparametric estimation techniques abstract this paper presents a consistent test of functional form of nonlinear regression models the test combines the methodology of the conditional moment test and nonparametric estimation techniques using degenerate and nondegenerate u statistic theories the test statistic is shown to be asymptotically distributed standard normal under the null hypothesis that the parametric model is correct while diverging to infinity at a rate arbitrarily close to n the sample size if the parametric model is misspecified therefore the test is consistent against all deviations from the parametric model the test is robust to heteroskedasticity a version of the test can be constructed which will have asymptotic power equal to 1 against any local alternatives approaching the null at rates slower than the parametric rate 1 n a simulation study reveals that the test has good finite sample properties

estimation of large dimensional factor models with an unknown number of breaks abstract in this paper we study the estimation of a large dimensional factor model when the factor loadings exhibit an unknown number of changes over time we propose a novel three step procedure to detect the breaks if any and then identify their locations in the first step we divide the whole time span into subintervals and fit a conventional factor model on each interval in the second step we apply the adaptive fused group lasso to identify intervals containing a break in the third step we devise a grid search method to estimate the location of the break on each identified interval we show that with probability approaching one our method can identify the correct number of changes and estimate the break locations simulation studies indicate superb finite sample performance of our method we apply our method to investigate stock and watson s 2009 u s monthly macroeconomic dataset and identify five breaks in the factor loadings spanning 1959 2006

causality tests and conditional heteroskedasticity monte carlo evidence abstract this paper investigates the reliability of causality tests based on least squares when conditional heteroskedasticity exists monte carlo evidence documents considerable size distortion if the conditional variances are correlated inference based on a heteroskedasticity and autocorrelation consistent covariance matrix offers little improvement this size distortion traces to an inability to discriminate between causality in mean and causality in variance as a result this paper endorses conducting causality tests based on an empirical specification that explicitly models the conditional means and conditional variances the relationship between money and prices serves as an illustrative example

application of differential quadrature to static analysis of structural components the numerical technique of differential quadrature for the solution of linear and non linear partial differential equations first introduced by bellman and his associates is applied to the equations governing the deflection and buckling behaviour of one and two dimensional structural components separate transformations are used for higher order derivatives as suggested by mingle thus extending the method to treat fourth order equations and to include multiple boundary conditions in the respective co ordinate directions results are obtained for various boundary and loading conditions and are compared with existing exact and numerical solutions by other methods the application of differential quadrature to this class of problems is seen to lead to accurate results with relatively small computational effort

τ estimators of regression models with structural change of unknown location abstract this paper concerns with robust estimation of linear regression models with structural change of unknown location under possibly contaminated distributions both for the regressors and for the perturbance term existing estimators will be inefficient in this context furthermore they may protect against outlying yt but cannot cope with leverage points namely outliers in the factor space which could have large influence on the fit as a result these estimators could not discriminate between outlier observations and structural break points misplacing the shift location this fact can be of special importance in practice therefore it may be advisable to consider robust estimators under possible leverage points in a structural change context thus we propose the estimator introduced by yohai and zamar j am stat assoc 83 1988 406 in the standard context of no change this type of estimator is qualitatively robust with the best possible breakdown point and highly efficient under normal errors the asymptotic distribution of the break location estimator is obtained both for fixed magnitude of shift and for shift with magnitude converging to zero as the sample size increases the analysis is carried out in the framework of general ned dependence conditions for the data monte carlo experiments illustrates the performance of our estimators in finite samples

interactions among multi nonlinearities in a nonlinear diffusion system with absorptions and nonlinear boundary flux abstract this paper deals with a nonlinear diffusion system with inner absorptions and coupled nonlinear boundary conditions two parameters which solve an introduced matrix equation covering all the eight nonlinear exponents of the system are used to get a simple description for the interactions among the multi nonlinearities in the system blow up or not of the solutions is determined by the signs of the two parameters in order to obtain the critical properties of the solutions for the critical sign of the parameters some further analysis on the absorption coefficients and the geometry of is given in addition to the discussion for the eight nonlinear exponents in the system

finite extinction time for nonlinear parabolic equations with nonlinear mixed boundary data the last theorem in the article i e theorem 4 2 and the subsequent example on pp 10 11 have to be deleted there is an error in the construction of the upper solution u w t h x in the proof of theorem 4 2 since w s 1 m p w w s p w p w m 2 2 condition i in the statement of the theorem implies that w s 0 consequently u is not an upper solution as claimed since this is the very last theorem of the paper the rest of the article from p 1 to the end of theorem 4 1 on p 10 all remain valid without any change

bandwidth selection in nonparametric kernel testing we propose a sound approach to bandwidth selection in nonparametric kernel testing the main idea is to find an edgeworth expansion of the asymptotic distribution of the test concerned due to the involvement of a kernel bandwidth in the leading term of the edgeworth expansion we are able to establish closed form expressions to explicitly represent the leading terms of both the size and power functions and then determine how the bandwidth should be chosen according to certain requirements for both the size and power functions for example when a significance level is given we can choose the bandwidth such that the power function is maximized while the size function is controlled by the significance level both asymptotic theory and methodology are established in addition we develop an easy implementation procedure for the practical realization of the established methodology and illustrate this on two simulated examples and a real data example