three dimensional exact solution for the vibration of functionally graded rectangular plates abstract a three dimensional exact solution is presented for free and forced vibrations of simply supported functionally graded rectangular plates suitable displacement functions that identically satisfy boundary conditions are used to reduce equations governing steady state vibrations of a plate to a set of coupled ordinary differential equations which are then solved by employing the power series method the exact solution is valid for thick and thin plates and for arbitrary variation of material properties in the thickness direction results are presented for two constituent metal ceramic functionally graded rectangular plates that have a power law through the thickness variation of the volume fractions of the constituents the effective material properties at a point are estimated by either the mori tanaka or the self consistent schemes exact natural frequencies displacements and stresses are used to assess the accuracy of the classical plate theory the first order shear deformation theory and a third order shear deformation theory for functionally graded plates parametric studies are performed for varying ceramic volume fractions volume fraction profiles and length to thickness ratios results are also computed for a functionally graded plate that has a varying microstructure in the thickness direction using a combination of the mori tanaka and the self consistent methods forced vibrations of a plate with a sinusoidal spatial variation of the pressure applied on its top surface are scrutinized

fusion of hard and soft information in nonparametric density estimation abstract this paper discusses univariate density estimation in situations when the sample hard information is supplemented by soft information about the random phenomenon these situations arise broadly in operations research and management science where practical and computational reasons severely limit the sample size but problem structure and past experiences could be brought in in particular density estimation is needed for generation of input densities to simulation and stochastic optimization models in analysis of simulation output and when instantiating probability models we adopt a constrained maximum likelihood estimator that incorporates any possibly random soft information through an arbitrary collection of constraints we illustrate the breadth of possibilities by discussing soft information about shape support continuity smoothness slope location of modes symmetry density values neighborhood of known density moments and distribution functions the maximization takes place over spaces of extended real valued semicontinuous functions and therefore allows us to consider essentially any conceivable density as well as convenient exponential transformations the infinite dimensionality of the optimization problem is overcome by approximating splines tailored to these spaces to facilitate the treatment of small samples the construction of these splines is decoupled from the sample we discuss existence and uniqueness of the estimator examine consistency under increasing hard and soft information and give rates of convergence numerical examples illustrate the value of soft information the ability to generate a family of diverse densities and the effect of misspecification of soft information

testing and estimating shape constrained nonparametric density and regression in the presence of measurement error in many applications we can expect that or are interested to know if a density function or a regression curve satisfies some specific shape constraints for example when the explanatory variable x represents the value taken by a treatment or dosage the conditional mean of the response y is often anticipated to be a monotone function of x indeed if this regression mean is not monotone in the appropriate direction then the medical or commercial value of the treatment is likely to be significantly curtailed at least for values of x that lie beyond the point at which monotonicity fails in the case of a density common shape constraints include log concavity and unimodality if we can correctly guess the shape of a curve then nonparametric estimators can be improved by taking this information into account addressing such problems requires a method for testing the hypothesis that the curve of interest satisfies a shape constraint and if the conclusion of the test is positive a technique for e

optimal rates of convergence for deconvolving a density abstract suppose that the sum of two independent random variables x and z is observed where z denotes measurement error and has a known distribution and where the unknown density f of x is to be estimated one application is the estimation of a prior density for a sequence of location parameters a second application arises in the errors in variables problem for nonlinear and generalized linear models when one attempts to model the distribution of the true but unobservable covariates this article shows that if z is normally distributed and f has k bounded derivatives then the fastest attainable convergence rate of any nonparametric estimator of f is only log n k 2 therefore deconvolution with normal errors may not be a practical proposition other error distributions are also treated stefanski carroll 1987a estimators achieve the optimal rates the results given have versions for multiplicative errors where they imply that even optimal rates are exceptionally slow

a connection between schur multiplication and fourier interpolation given m n matrices a ajk and b bjk their schur product is the m n matrix a b ajkbjk for any matrix a define a s max x 1 a x where denotes the usual norm for any y a b c r3 define by f l1 f 1 a f 0 bandf 1 c and set ay abbc our main result is that for any y r3 ay s inff by f 1

a sharp version of kahan s theorem on clustered eigenvalues let n times n hermitian matrix a have eigenvalues lambda 1 lambda 2 cdots lambda n and let k times k hermitian matrix h have eigenvalues mu 1 le mu 2 le cdots le mu k and let q be an n times k matrix having full column rank so 1 le k le n it is proved that there exist k eigenvalues lambda i 1 le lambda i 2 le cdots le lambda i k of a such that max 1 le j le k mu j lambda i j le frac c sigma min q aq qh 2 always holds with c 1 where sigma min q is the smallest singular value of q and cdot 2 denotes the biggest singular value of a matrix the inequality was proved for c le sqrt 2 in 1967 by kahan who also conjectured that it should be true for c 1

maximum likelihood estimation of a multi dimensional log concave density fn is shown to have smaller mean integrated squared error compared with kernel based methods even when we allow the use of a theoret ical optimal fixed bandwidth for the kernel estimator that would not be available in practice we also present a real data clustering example which shows that our methodology can be used in conjunction with the expectation maximization algorithm to fit finite mixtures of log concave densities

testing a parametric quantile regression model with an endogenous explanatory variable against a nonparametric alternative abstract this paper is concerned with inference about a function g that is identified by a conditional quantile restriction involving instrumental variables the paper presents a test of the hypothesis that g belongs to a finite dimensional parametric family against a nonparametric alternative the test is not subject to the ill posed inverse problem of nonparametric instrumental variable estimation under mild conditions the test is consistent against any alternative model in large samples its power is arbitrarily close to 1 uniformly over a class of alternatives whose distance from the null hypothesis is proportional to n 1 2 where n is the sample size monte carlo simulations illustrate the finite sample performance of the test

an extremal problem in fourier analysis with applications to operator theory a certain minimal extrapolation problem for fourier transforms is known to have consequences for the determination of best possible bounds in some problems in linear operator equations and in perturbation of operators in this paper we estimate the value of the constant in the fourier transform problem by an analytic reformulation

deconvolution of a distribution function abstract we consider the estimation of a distribution function when observations from this distribution are contaminated by measurement error the unknown distribution is modeled as a mixture of a finite number of known distributions model parameters can be estimated and confidence intervals constructed using well known likelihood theory we show that it is also possible to apply this approach to estimation of a unimodal distribution an application is presented using data from a dietary survey simulation results are given to indicate the performance of the estimators and the confidence interval procedures

simultaneous isogeometrical shape and material design of functionally graded structures for optimal eigenfrequencies abstract a new optimization strategy for eigenfrequency optimization of functionally graded fg structures within the framework of isogeometric analysis iga approach is introduced the proposed methodology which utilizes a concurrent procedure by combining the shape and material composition optimization of these structures employs an extended form of the standard iga method by allowing for gradation of material properties through patches the distributions of the graded material properties are considered as imaginary surfaces over the computational domain and captured in a fully isogeometric formulation using the same nurbs based parameterization which is employed for the geometry modeling as well as the solution approximation considering the in plane coordinates of the control points defining the design boundary surfaces as well as the applicates of all the control points describing the variations of material properties as design variables we subsequently adopt a mathematical programming algorithm to simultaneously find the optimum shape and material composition of fg structures a couple of illustrative numerical examples in 2d elasticity with eigenfrequencies as their either constraints or objective functions are presented to demonstrate the high performance of the proposed methodology it will be seen that the obtained results by this concurrent optimization procedure have much better dynamic performance compared to the optimal results of the simple shape or material composition design

closing the gap in a subspace perturbation bound abstract this paper sharpens an operator inequality from perturbation theory suppose x and y are self adjoint operators on a hilbert space kx x and ky y are two closed sets bounded apart by 0 e is the spectral projector for x belonging to kx and f is the spectral projector for y belonging to ky it is known that 2 x y ef for all operators as described and for any unitary invariant norm in this paper we show 2 is best possible in this inequality we then discuss an analogous bound which applies when x and y are normal

on some perturbation inequalities for operators abstract an estimate for the norm of the solution to the equation ax xb s obtained by r bhatia c davis and a mcintosh for normal operators a and b is shown to be valid for a larger class some other inequalities in the same spirit are obtained including a sin theorem for singular vectors some inequalities concerning the continuity of the map a ita obtained recently by kittaneh and kosaki are extended using these ideas

a survey of chandler davis chandler davis is a very unusual interesting and complex person this short sketch however is restricted to his contributions to linear algebra and to operator theory although we begin with a brief biography

analyzing specific cases of an operator inequality abstract let h and k be hilbert spaces and suppose a e b h and b e b k are self adjoint operators with dist a b 0 in 1983 bhatia davis and mcintosh showed that for any q e b k h we must have 2 aq qb q in this paper we specialize their inequality to the case where a q and b are 2 2 or 3 3 matrices and give sharp estimates doing so we illustrate one way that bounds on the norm of the schur product of two matrices have applications to perturbation theory by specializing the fourier transform used in the proof of the theorem above we also obtain sharp estimates in two fourier interpolation problems

maximal spectral distance abstract the exact upper bound for the norm distance between two normal matrices is given as a function of their eigenvalues among the applications we obtain an inequality related to the cartesian decomposition of a matrix and the evaluation of the hadamard multiplier norms for matrices in a certain broad class

weakly coupled bound state of 2 d schrodinger operator with potential measure abstract we consider a self adjoint two dimensional schrodinger operator h which corresponds to the formal differential expression where is a finite compactly supported positive radon measure on r 2 from the generalized kato class and 0 is the coupling constant it was proven earlier that ess h 0 we show that for sufficiently small the condition d h 1 holds and that the corresponding unique eigenvalue has the asymptotic expansion c o 1 exp 4 r 2 0 with a certain constant c 0 we also obtain a formula for the computation of c the asymptotic expansion of the corresponding eigenfunction is provided the statements of this paper extend the results of simon 41 to the case of potentials measures also for regular potentials our results are partially new

residual bounds for unitarily invariant norms on clustered eigenvalues abstract let n n hermitian matrix a have eigenvalues 1 2 n let k k hermitian matrix h have eigenvalues 1 2 k and let q be an n k matrix having full column rank so 1 k n it is proved that there exist k eigenvalues i1 i2 ik of a such that diag i 1 2 i 2 k i k c min q aq qh always holds with c 2 where min q is the smallest singular value of q and denotes any unitarily invariant norm the assumptions q q i and h q aq in stewart and sun s book are deleted we improve it applicable to practical computation

nonparametric kernel regression subject to monotonicity constraints we suggest a method for monotonizing general kernel type estimators for example local linear estimators and nadaraya watson estimators attributes of our approach include the fact that it produces smooth estimates indeed with the same smoothness as the unconstrained estimate the method is applicable to a particularly wide range of estimator types it can be trivially modified to render an estimator strictly monotone and it can be employed after the smoothing step has been implemented therefore an experimenter may use his or her favorite kernel estimator and their favorite bandwidth selector to construct the basic nonparametric smoother and then use our technique to render it monotone in a smooth way implementation involves only an off the shelf programming routine the method is based on maximizing fidelity to the conventional empirical approach subject to monotonicity we adjust the unconstrained estimator by tilting the empirical distribution so as to make the least possible change in the sense of a distance measure subject to imposing the constraint of monotonicity

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

perturbation of spectra and spectral subspaces we consider the problem of variation of spectral subspaces for linear self adjoint operators with emphasis on the case of off diagonal perturbations we prove a number of new optimal results on the shift of the spectrum and obtain sharp estimates on the norm of the difference of two spectral projections associated with isolated parts of the spectrum of the perturbed and unperturbed operators respectively

convergence of the block lanczos method for eigenvalue clusters the lanczos method is often used to solve a large scale symmetric matrix eigenvalue problem it is well known that the single vector lanczos method can only find one copy of any multiple eigenvalue unless certain deflating strategy is incorporated and encounters slow convergence towards clustered eigenvalues on the other hand the block lanczos method can compute all or some of the copies of a multiple eigenvalue and with a suitable block size also compute clustered eigenvalues much faster the existing convergence theory due to saad for the block lanczos method however does not fully reflect this phenomenon since the theory was established to bound approximation errors in each individual approximate eigenpairs here it is argued that in the presence of an eigenvalue cluster the entire approximate eigenspace associated with the cluster should be considered as a whole instead of each individual approximate eigenvectors and likewise for approximating clusters of eigenvalues in this paper we obtain error bounds on approximating eigenspaces and eigenvalue clusters our bounds are much sharper than the existing ones and expose true rates of convergence of the block lanczos method towards eigenvalue clusters furthermore their sharpness is independent of the closeness of eigenvalues within a cluster numerical examples are presented to support our claims

on deconvolution with repeated measurements in a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known although in many applications it is unrealistic to make this assumption the problem is often insoluble without it however if additional data are available then it is possible to estimate consistently the unknown error density data are seldom available directly on the transformation but repeated or replicated measurements increasingly are becoming available such data consist of intrinsic values that are measured several times with errors that are generally independent working in this setting we treat the nonparametric deconvolution problems of density estimation with observation errors and regression with errors in variables we show that even if the number of repeated measurements is quite small it is possible for modified kernel estimators to achieve the same level of performance they would if the error distribution were known indeed density and regression estimators can be constructed from replicated data so that they have the same first order properties as conventional estimators in the known error case without any replication but with sample size equal to the sum of the numbers of replicates practical methods for constructing estimators with these properties are suggested involving empirical rules for smoothing parameter choice

higher order piezoelectric plate theory derived from a three dimensional variational principle a three dimensional mixed variational principle is used toderive a kth order two dimensional lineartheory for an anisotropichomogeneouspiezoelectric pzt plate themechanicaldisplacements theelectricpotential theinplane components of the stress tensor and the in plane components of the electric displacement are expressed as a e niteseries of orderk inthethickness coordinate bytakinglegendrepolynomialsas thebasisfunctions however the transverse shear stress the transverse normal stress and the transverse electric displacement are expressed as a e nite series of order k 2 in the thickness coordinate the formulation accounts for the double forces without moments that may change the thickness of the plate results obtained by using the plate theory are given for the bending of a cantilever thick plate loaded on the top and the bottom surfaces by uniformly distributed 1 normal tractions and 2 tangential tractions results are also computed for the bending of a cantilever thick pzt beam loaded by 1 a uniformly distributed charge density on the top and the bottom surfaces and 2 equal and opposite normal tractions distributed uniformly only on a part of the beam the seventh order plate theory captures well the boundary layer effects near the clamped and the free edges and adjacent to the top and the bottom surfaces of a thick orthotropic cantilever beam with the span to the thickness ratio of two also through the thickness variation of the transverse shear and the transverse normal stresses agree well with those computed from the analytical solution of the three dimensional elasticity equations the governing partial differential equations are second order so that lagrange basis functions can be used to solve the problem by the e nite element method

monotone smoothing with application to dose response curves and the assessment of synergism a spline based procedure for monotone curve smoothing is proposed and is illustrated by application to dose response curves it is then shown how such smoothing can be applied to assess possible synergism or antagonism of two drugs

using simex for smoothing parameter choice in errors in variables problems simex methods are attractive for solving curve estimation problems in errors in variables regression using parametric or semiparametric techniques however nonparametric approaches are generally of quite a different type being based on for example kernels local linear modeling ridging orthogonal series or splines all of these techniques involve the challenging and not well studied issue of empirical smoothing parameter choice we show that simex can be used effectively for selecting smoothing parameters when applying nonparametric methods to errors in variable regression in particular we suggest an approach based on multiple error inflated or remeasured data sets and extrapolation

analysis of spectral variation and some inequalities a geometric method based on a decomposition of the space of complex matrices is employed to study the variation of the spectrum of a matrix when adapted to special cases this leads to some classical inequalities as well as some new ones as an example of the latter we show that if u v are unitary matrices and k is a skew hermitian matrix such that uv exp k then for every unitary invariant norm the distance between the eigenvalues of v and those of vis bounded by k this generalises two earlier results which used particular unitary invariant norms

spectral variation of normal matrices abstract it has been a durable conjecture that the distance appropriately defined between the spectra of two normal matrices is bounded by the operator norm of their difference we report on some numerical studies that show that this conjecture is in general false in fact even in the 3 x 3 case the spectral distance may exceed the norm distance by between 1 and 2 percent we also describe the background of the conjecture and offer an analysis of extremal counterexamples

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

intentionally biased bootstrap methods summary a class of weighted bootstrap techniques called biased bootstrap or b bootstrap methods is introduced it is motivated by the need to adjust empirical methods such as the uniform bootstrap in a surgical way to alter some of their features while leaving others unchanged depending on the nature of the adjustment the b bootstrap can be used to reduce bias or to reduce variance or to render some characteristic equal to a predetermined quantity examples of the last application include a b bootstrap approach to hypothesis testing in nonparametric contexts where the b bootstrap enables simulation under the null hypothesis even when the hypothesis is false and a b bootstrap competitor to tibshirani s variance stabilization method an example of the bias reduction application is adjustment of nadaraya watson kernel estimators to make them competitive with local linear smoothing other applications include density estimation under constraints outlier trimming sensitivity analysis skewness or kurtosis reduction and shrinkage

making a non parametric density estimator more attractive and more accurate by data perturbation summary motivated by both the shortcomings of high order density estimators and the increasingly large data sets in many areas of modern science we introduce new high order non parametric density estimators that are guaranteed to be positive and do not have highly oscillatory tails our approach is based on data perturbation e g by tilting or data sharpening it leads to new estimators that are more accurate than conventional kernel techniques that use positive kernels but which nevertheless enjoy the positivity property and are far less wiggly than high order kernel estimators we investigate performance by theoretical analysis and in a numerical study

natural frequencies of a functionally graded anisotropic rectangular plate we use the first order shear deformation theory fsdt coupled with the finite element method fem to study free vibrations of a functionally graded fg anisotropic rectangular plate with the objective of maximizing one of its first five natural frequencies the following edge conditions are considered i all edges clamped ii all edges simply supported iii two opposite edges clamped and the other two free and iv two opposite edges simply supported and the other two free an advantage of a functionally graded plate over a laminated plate is that material properties vary continuously through the plate thickness thus no sudden discontinuities in stresses occur across an interface between any two adjoining laminae thereby eliminating the delamination mode of failure whereas there have been numerous works on studying the response of fg plates made of isotropic elastic constituents with the homogenized material also modeled as isotropic elastic e g see refs 1 2 and references cited therein the only other study on fg anisotropic plate 3 has assumed that all elastic constants vary exponentially through the plate thickness at the same rate it is highly unlikely that elastic moduli of a fg anisotropic plate will exhibit this property here we consider a fg anisotropic plate in which the fiber orientation varies smoothly through the plate thickness

natural frequencies of thick plates made of orthotropic monoclinic and hexagonal materials by a meshless method abstract we use the first order shear deformation theory and a meshless method based on radial basis functions in a pseudospectral framework for predicting the free vibration behavior of thick orthotropic monoclinic and hexagonal plates the shape parameter is obtained by an optimization procedure the three translational and two rotational degrees of freedom of a point of the laminate are independently approximated through numerical experiments the capability and efficiency of the radial basis functions pseudospectral method for eigenvalue problems are demonstrated and the numerical accuracy and convergence are examined

vibration of an incompressible isotropic linear elastic rectangular plate with a higher order shear and normal deformable theory abstract we use a mixed higher order shear and normal deformable plate theory hosndpt of batra and vidoli with poisson s ratio equal to 0 49 and the finite element method to analyze vibrations of a homogeneous isotropic rectangular plate made of an incompressible linear elastic material through the thickness integrals are evaluated exactly and those over an element in the midplane of the plate are evaluated by using the 2 2 gauss quadrature rule the plate theory equations are used to ascertain frequencies of a clamped clamped and a clamped free square rectangular plate of different aspect ratios through the thickness modes of vibration valid for compressible and incompressible materials and missed by previous investigators are also identified computed frequencies are found to match well with those deduced from the analytical solution

perturbation of spectral subspaces and solution of linear operator equations abstract let a and b be normal operators on a hilbert space let k a and k b be subsets of the complex plane at distance at least from each other let e be the spectral projector for a belonging to k a and let f be the spectral projector for b belonging to k b our main results are estimates of the form ef c e a b f in some special situations the constant c is as low as 1 as an application we prove for an absolute constant d that if the space is finite dimensional and if a and b are normal with a b d then the spectrum of b can be obtained from that of a multiplicities counted by moving each eigenvalue by at most our main results have equivalent formulations as statements about the operator equation aq qb s let a and b be normal operators on perhaps different hilbert spaces assume a k a and b k b where k a k b and are as before then we give estimates of the forms q c aq qb

a note on the lyapunov equation some results on the sensitivity of the solution of the stable lyapunov equation are shown to follow easily from well known theorems of functional analysis

parametrically assisted nonparametric estimation of a density in the deconvolution problem nonparametric estimation of a density from contaminated data is a difficult problem for which convergence rates are notoriously slow we introduce parametrically assisted nonparametric estimators which can dramatically improve on the performance of standard nonparametric estimators when the assumed model is close to the true density without degrading much the quality of purely nonparametric estimators in other cases we establish optimal convergence rates for our problem and discuss estimators that attain these rates the very good numerical properties of the methods are illustrated via a simulation study supplementary materials for this article are available online

a design adaptive local polynomial estimator for the errors in variables problem local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature their simplest version the local constant estimator can be easily extended to the errors in variables context by exploiting its similarity with the deconvolution kernel density estimator the generalization of the higher order versions of the estimator however is not straightforward and has remained an open problem for the last 15 years we propose an innovative local polynomial estimator of any order in the errors in variables context derive its design adaptive asymptotic properties and study its finite sample performance on simulated examples we provide not only a solution to a long standing open problem but also provide methodological contributions to error in variable regression including local polynomial estimation of derivative functions

treatment of material discontinuity in two meshless local petrov galerkin mlpg formulations of axisymmetric transient heat conduction summary we use two meshless local petrov galerkin mlpg formulations to analyse heat conduction in a bimetallic circular disk the continuity of the normal component of the heat flux at the interface between two materials is satisfied either by the method of lagrange multipliers or by using a jump function the convergence of the h 0 and h 1 error norms for the four numerical solutions with an increase in the number of equally spaced nodes and in the number of quadrature points is scrutinized with an increase in the number of uniformly spaced nodes the two error norms decrease monotonically for the mlpg5 formulation but are essentially unchanged for the mlpg1 formulation to our knowledge this is the first study comparing the performance of the two methods of modelling a discontinuity in the gradient of a field variable at the interface between two different materials copyright 2004 john wiley sons ltd

on perturbations of matrix pencils with real spectra perturbation bounds for the generalized eigenvalue problem of a diagonalizable matrix pencil a ab with real spectrum are developed it is shown how the chordal distances between the generalized eigenvalues and the angular distances between the generalized eigenspaces can be bounded in terms of the angular distances between the matrices the applications of these bounds to the spectral variations of definite pencils are conducted in such a way that extra attention is paid to their peculiarities so as to derive more sophisticated perturbation bounds our results for generalized eigenvalues are counterparts of some celebrated theorems for the spectral variations of hermitian matrices such as the weyl lidskii theorem and the hoffman wielandt theorem and those for generalized eigenspaces are counterparts of the celebrated davis kahan sin 0 sin 20 theorems for the eigenspace variations of hermitian matrices the paper consists of two parts part i is for generalized eigenvalue perturbations while part ii deals with generalized eigenspace perturbations

majorizations and inequalities in matrix theory abstract in matrix theory majorization plays a significant role for instance majorization relations among eigenvalues and singular values of matrices produce a lot of norm inequalities and even matrix inequalities this survey article is intended as a review of recent results in matrix theory related to majorization

monotone nonparametric regression in monotone regression procedures one utilizes only the monotonicity of the regression function in nonparametric regression one utilizes only the assumed smoothness the analytic and asymptotic properties of the estimator are superior in the latter case however monotonicity is not guaranteed we study a hybrid procedure that produces monotone estimators with properties similar to those of nonparametric regression estimators

some inequalities for norm ideals several inequalities for norms of operators are extended to more operators and or to more norms these include results of halmos and bouldin on approximating a normal operator by another with restricted spectrum the powers stormer and the van hemmen ando inequalities for the distance between the square roots of two positive operators and also some recent generalisations of these latter results by kittaneh

estimation of a convex function characterizations and asymptotic theory we study nonparametric estimation of convexregression and density functions by methods of least squares in the regression and density cases and maximum likelihood in the density estimation case we provide characterizations of these estimators prove that they are consistent and establish their asymptotic distributions at a fixed point of positive curvature of the functions estimated the asymptotic distribution theory relies on the existence of an invelope function for integrated two sided brownian motion t 4 which is established in a companion paper by groeneboom jongbloed and wellner

bootstrap simultaneous error bars for nonparametric regression simultaneous error bars are constructed for nonparametric kernel estimates of regression functions the method is based on the bootstrap where resampling is done from a suitably estimated residual distribution the error bars are seen to give asymptotically correct coverage probabilities uniformly over any number of gridpoints applications to an economic problem are given and comparison to both pointwise and bonferroni type bars is presented through a simulation study

estimation of integrated squared density derivatives from a contaminated sample we propose a kernel estimator of integrated squared density derivatives from a sample that has been contaminated by random noise we derive asymptotic expressions for the bias and the variance of the estimator and show that the squared bias term dominates the variance term this coincides with results that are available for non contaminated observations we then discuss the selection of the bandwidth parameter when estimating integrated squared density derivatives based on contaminated data we propose a data driven bandwidth selection procedure of the plug in type and investigate its finite sample performance via a simulation study

nonparametric regression with errors in variables the effect of errors in variables in nonparametric regression estimation is examined to account for errors in covariates deconvolution is involved in the construction of a new class of kernel estimators it is shown that optimal local and global rates of convergence of these kernel estimators can be characterized by the tail behavior of the characteristic function of the error distribution in fact there are two types of rates of convergence according to whether the error is ordinary smooth or super smooth it is also shown that these results hold uniformly over a class of joint distributions of the response and the covariate which is rich enough for many practical applications furthermore to achieve optimality we show that the convergence rates of all possible estimators have a lower bound possessed by the kernel estimators

specification testing in nonparametric instrumental variable estimation abstract in nonparametric instrumental variable estimation the function being estimated is the solution to an integral equation a solution may not exist if for example the instrument is not valid this paper discusses the problem of testing the null hypothesis that a solution exists against the alternative that there is no solution we give necessary and sufficient conditions for existence of a solution and show that uniformly consistent testing of an unrestricted null hypothesis is not possible uniformly consistent testing is possible however if the null hypothesis is restricted by assuming that any solution to the integral equation is smooth many functions of interest in applied econometrics including demand functions and engel curves are expected to be smooth the paper presents a statistic for testing the null hypothesis that a smooth solution exists the test is consistent uniformly over a large class of probability distributions of the observable random variables for which the integral equation has no smooth solution the finite sample performance of the test is illustrated through monte carlo experiments

plane wave solutions and modal analysis in higher order shear and normal deformable plate theories abstract we use the three dimensional hellinger reissner mixed variational principle to derive a k th order k 0 1 2 shear and normal deformable plate theory the balance laws the constitutive relations and the boundary conditions for the plate theory are deduced the constitutive relations incorporate the shear and the normal tractions applied on the top and the bottom surfaces of the plate for a k th order plate theory with displacements expressed as a power series in the thickness co ordinate z with terms up to z k the transverse shear and the transverse normal stresses involve terms upto z k 2 while in plane stress components have terms up to z k the equations for the plate theory are expressed in a compact form by taking legendre polynomials as the basis functions the plate theory is used to study plane travelling waves and in particular the lengths of decay of the displacement components this allows for a rigorous ordering of the importance of the displacement descriptors in terms of decaying properties finally we study the free vibrations of a simply supported rectangular orthotropic thick plate results from the present theory are compared with an exact three dimensional solution and with other plate theories to this end a k th order compatible plate theory is also deduced the term compatible alludes to the fact that the reduction map for the stress fields is induced by the kinematical reduction map whilst in the mixed models it is postulated independently it is found that the frequencies up to the fifth mode of vibration computed with the fifth order theory and without introducing any shear correction factors match very well with the corresponding analytical solution also through the thickness distribution of all of the stress components is found to agree well with the three dimensional elasticitysolution while the stress distribution obtained from the compatible plate theories deviatesconsiderably especially for the higher modes

the monotone smoothing of scatterplots we consider the problem of summarizing a scatterplot with a smooth monotone curve a solution that combines local averaging and isotonic regression is proposed and we demonstrate its use with two examples in the second example the procedure is applied in a regression setting to some data from box and cox 1964 and it is shown how this new procedure generalizes box and cox s well known family of transformations in the same example the bootstrap is applied to obtain a measure of the variability of the procedure

on perturbations of matrix pencils with real spectra ii a well known result on spectral variation of a hermitian matrix due to mirsky is the following let a and a be two n x n hermitian matrices and let 1 n and 1 n be their eigenvalues arranged in ascending order then diag 1 1 n n a a for any unitarily invariant norm in this paper we generalize this to the perturbation theory for diagonalizable matrix pencils with real spectra the much studied case of definite pencils is included in this

exact solution for thermoelastic deformations of functionally graded thick rectangular plates an exact solution is obtained for three dimensional deformations of a simply supported functionally graded rectangular plate subjected to mechanical and thermal loads on its top and or bottom surfaces suitable temperature and displacement functions that identically satisfy boundary conditions at the edges are used to reduce the partial differential equations governing the thermomechanical deformations to a set of coupled ordinary differential equations in the thickness coordinate which are then solved by employing the power series method the exact solution is applicable to both thick and thin plates results are presented for two constituent metal ceramic functionally graded rectangular plates that have a power law through the thickness variation of the volume fractions of the constituents the effective material properties at a point are estimated by either the mori tanaka or the self consistentschemes exact displacementsand stressesatseveral locations for mechanical and thermal loads are used toassess theaccuracyof the classical plate theory thee rst ordershear deformation theory and athird order shear deformation theory for functionally graded plates results are alsocomputed for a functionally graded plate with material properties derived by the mori tanaka method the self consistent scheme and a combination of these two methods

nonparametric errors in variables models with measurement errors on both sides of the equation abstract measurement errors are often correlated as in surveys where respondent s biases or tendencies to err affect multiple reported variables we extend schennach 2007 to identify moments of the conditional distribution of a true y given a true x when both are measured with error the measurement errors in y and x are correlated and the true unknown model of y given x has nonseparable model errors after showing nonparametric identification we provide a sieve generalized method of moments based estimator of the model and apply it to nonparametric engel curve estimation in our application measurement errors on the expenditures of a good y are by construction correlated with measurement errors in total expenditures x this problem which is present in many consumption data sets has been ignored in most demand applications we find that accounting for this problem casts doubt on hildenbrand s 1994 increasing dispersion assumption

spectral variations and hadamard products some problems abstract many perturbation problems in matrix theory are related to three matrix minimization problems involving hadamard products possible solutions to the problems are conjectured the problems if solved may imply significant advances in eigenvalue generalized eigenvalue variations and perhaps in other aspects in matrix theory too