an efficient semiparametric estimator for binary response models this paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of the choice probability function where this function can be characterized by an index the estimator is shown to be consistent asymptotically normally distributed and to achieve the semiparametric efficiency bound monte carlo evidence indicates that there may be only modest efficiency losses relative to maximum likelihood estimation when the distribution of the disturbances is known and that the small sample behavior of the estimator in other cases is good

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

on semilinear elliptic equations involving concave convex nonlinearities and sign changing weight function abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of positive solutions for semilinear elliptic equations with a sign changing weight function with the help of the nehari manifold we prove that there are at least two positive solutions for eq e f in bounded domains

asymptotic efficiency in semi parametric models with censoring abstract we consider a regression model subject to bivariate censoring in which the errors are independent of the explanatory variables our objective is to drop the assumption of bivaraite normality and obtain an information bound on asymptotic efficiency when the error distribution is unrestricted except for smoothness and regularity conditions this bound has simple form if there are no exclusion restrictions on the selection equation then positive information requires a restriction on the regression slope parameters and a continuous distribution for a component of the explanatory variables we also consider a binary choice model under the weak assumption that the error distribution has zero median conditional on the explanatory variables here the semi parametric information bound is zero hence although a consistent estimator exists it is not possible to attain covergence at rate 1 n

application of a nonlinear computational aeroacoustics code to the gust airfoil problem a time domain solution of the gust airfoil problem is obtained using a high accuracy computational aeroacoustics code to solve the nonlinear euler equations for computational efficiency the equations are cast in chain rule curvilinear form and a structured multiblock solver is used on a distributed memory parallel computer cluster to fully investigate the performance of this solver a test matrix of benchmark problems is computed two airfoil geometries and four gust reduced frequencies these results are compared to benchmark solutions both on the airfoil surface and in the flow domain

finite volume treatment of dispersion relation preserving and optimized prefactored compact schemes for wave propagation in developing suitable numerical techniques for computational aero acoustics the dispersion relation preserving drp scheme by tam and co workers and the optimized prefactored compact opc scheme by ashcroft and zhang have shown desirable properties of reducing both dissipative and dispersive errors these schemes originally based on the finite difference attempt to optimize the coefficients for better resolution of short waves with respect to the computational grid while maintaining pre determined formal orders of accuracy in the present study finite volume formulations of both schemes are presented to better handle the nonlinearity and complex geometry encountered in many engineering applications linear and nonlinear wave equations with and without viscous dissipation have been adopted as the test problems highlighting the principal characteristics of the schemes and utilizing linear and nonlinear wave equations with different wavelengths as the test cases the performance of these approaches is documented for the linear wave equation there is no major difference between the drp and opc schemes for the nonlinear wave equations the finite volume version of both drp and opc schemes offers substantially better solutions in regions of high gradient or discontinuity

on theoretical and empirical aspects of marginal distribution choice models in this paper we study the properties of a recently proposed class of semiparametric discrete choice models referred to as the marginal distribution model mdm by optimizing over a family of joint error distributions with prescribed marginal distributions surprisingly the choice probabilities arising from the family of generalized extreme value models of which the multinomial logit model is a special case can be obtained from this approach despite the difference in assumptions on the underlying probability distributions we use this connection to develop flexible and general choice models to incorporate consumer and product level heterogeneity in both partworths and scale parameters in the choice model furthermore the extremal distributions obtained from the mdm can be used to approximate the fisher s information matrix to obtain reliable standard error estimates of the partworth parameters without having to bootstrap the method we use simulated and empirical data sets to test the performance of this approach we evaluate the performance against the classical multinomial logit mixed logit and a machine learning approach that accounts for partworth heterogeneity our numerical results indicate that mdm provides a practical semiparametric alternative to choice modeling this paper was accepted by eric bradlow special issue on business analytics

a smoothed maximum score estimator for the binary response model this paper describes a semiparametric estimator for binary response models in which there may be arbitrary heteroskedasticity of unknown form the estimator is obtained by maximizing a smoothed version of the objective function of c manski s maximum score estimator the smoothing procedure is similar to that used in kernel nonparametric density estimation the resulting estimator s rate of convergence in probability is the fastest possible under the assumptions that are made the centered normalized estimator is asymptotically normally distributed methods are given for consistently estimating the parameters of the limiting distribution and for selecting the bandwidth required by the smoothing procedure copyright 1992 by the econometric society

semiparametric estimation of the random utility model with rank ordered choice data abstract we propose semiparametric methods for estimating random utility models using rank ordered choice data our primary method is the generalized maximum score gms estimator with partially rank ordered data the gms estimator allows for arbitrary forms of interpersonal heteroskedasticity with fully rank ordered data the gms estimator becomes considerably more flexible allowing for random coefficients and alternative specific heteroskedasticity and correlations the gms estimator has a non standard asymptotic distribution and a convergence rate of n 1 3 we proceed to construct its smoothed version which is asymptotically normal with a faster convergence rate of n d 2 d 1 where d 2 increases in the strength of smoothness assumptions

high order low dispersive and low dissipative explicit schemes for multiple scale and boundary problems explicit high order numerical schemes are proposed for the accurate computation of multiple scale problems and for the implementation of boundary conditions specific high order node centered finite differences and selective filters removing grid to grid oscillations are first designed for the discretization of the buffer region between a x grid domain and 2 x grid domain the coefficients of these matching schemes are chosen so that the maximum order of accuracy is reached non centered finite differences and selective filters are then developed with the aim of accurately computing boundary conditions they are constructed by minimizing the dispersion and the dissipation errors in the wave number space for waves down to four points per wavelength the dispersion and dissipation properties of the matching and the boundary schemes are described in detail and their accuracy limits are determined to show that these schemes calculate accurately waves with at least five points per wavelength test problems including linear convection wall reflection and acoustic scattering around a cylinder are finally solved to illustrate the accuracy of the schemes

applications of high order optimized upwind schemes for computational aeroacoustics high order optimized upwind dispersion relation preserving finite difference schemes are used for solving multidimensional acoustic wave propagation problems the accuracy and the robustness of the schemes are tested for acoustic problems with various geometry and boundary conditions excellent agreements between the numerical and the analytical solutions indicate that the high order optimized upwind schemes minimize not only the dispersion error but also the dissipation error while retaining the numerical stability the simulation results have also demonstrated that the optimized upwind schemes damp out the spurious short waves automatically without the need of filter or explicit dissipation terms the overall effectiveness of the high order optimized upwind schemes is verified the good numerical result of the problem of acoustic scattering by a sphere suggests that the optimized upwind schemes may be used to solve acoustic problems involving a relatively complex geometry

information and asymptotic efficiency in parametric nonparametric models asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems for regular estimates and asymptotic minimax bounds the methods used involve i the notion of a hellinger differentiable root density where part of the differentiation is with respect to the nonparametric part of the model to obtain appropriate scores and ii calculation of the effective score for the real or vector finite dimensional parameter of interest as that component of the score function orthogonal to all nuisance parameter scores perhaps infinite dimensional the resulting asymptotic information for estimation of the parametric component of the model is just 4 times the squared l 2 norm of the effective score a corollary of these results is a simple necessary condition for adaptive estimation adaptation is possible only if the scores for the parameter of interest are orthogonal to the scores for the nuisance function or nonparametric part of the model examples considered include the one sample location model with and without symmetry mixture models the two sample shift model and cox s proportional hazards model

nonparametric and distribution free estimation of the binary threshold crossing and the binary choice models in this paper it is shown that it is possible to identify binary threshold crossing models and binary choice models without imposing any parametric structure either on the systematic function of observable exogenous variables or on the distribution of the random term this identification result is employed to develop a fully nonparametric maximum likelihood estimator for both the function of observable exogenous variables and the distribution of the random term the estimator is shown to be strongly consistent and a two step procedure for its calculation is developed the paper also includes examples of economic models that satisfy the conditions that are necessary to apply the results

a nonparametric multiple choice method within the random utility framework abstract many researchers use categorical data analysis to recover individual consumption preferences but the standard discrete choice models require restrictive assumptions to improve the flexibility of discrete choice data analysis we propose a nonparametric multiple choice model that applies the penalized likelihood method within the random utility framework we show that the deterministic component of the random utility function in the model is a cubic smoothing spline function the method subsumes the conventional conditional logit model mcfadden 1973 in zarembka p ed frontiers in econometrics as a special case in this paper we present the model describe the estimator provide the computational algorithm of the model and demonstrate the model by applying it to nonmarket valuation of recreation sites

a semilinear elliptic system involving nonlinear boundary condition and sign changing weight function abstract in this paper we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system e involving nonlinear boundary condition and sign changing weight function with the help of the nehari manifold we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters belongs to a certain subset of r 2

distribution free maximum likelihood estimator of the binary choice model1 is a given function of the exogenous variables z and unknown parameters 9 representing the systematic component of the utility difference and f is the distribution function of the random component of the utility difference this paper describes a method of estimating the parameters 9 without assuming any functional form for the distribution function f and proves that this estimator is consistent f is also consistently estimated the method uses maximum likelihood estimation in which the likelihood is maximized not only over the parameter 9 but also over a space which contains all distribution functions

space time mapping analysis of airfoil nonlinear interaction with unsteady inviscid flow a new computational method of space time mapping analysis is applied to nonlinear inviscid computation of unsteady airfoil response to an upstream flow with a finite amplitude of a time harmonic vortical perturbation the unique feature of the method is that it solves the unsteady problem as a steady state one by treating the time coordinate identically to space directions the periodic nature of the flow is used to design the mesh covering one period of the vortical gust in the time direction with a periodic boundary condition applied at the time inflow and time outflow boundaries the computed solution is thus driven directly to the final long time periodic solution using a pseudotime marching with a high order discretization scheme computed unsteady aerodynamic and aeroacoustic airfoil responses are compared against available numerical solutions results obtained for a high amplitude impinging gust identify zones in the computational domain where nonlinear response effects appear most significant

spurious waves in discrete computation of wave phenomena and flow problems in the present work we focus on spurious propagating disturbances q waves to establish the existence of q waves in computations we compare properties of different numerical methods drawn from finite difference finite volume and finite element methods existence and properties of q waves are demonstrated with propagation of wave packets following one dimensional 1d convection equation skewed wave propagation and by solution of linearized rotating shallow water wave equation lrswe specific numerical experiments are performed with parameters that convert a wave packet into a q wave we also show the case where q waves are created additionally to physical disturbances those propagate downstream formation of q waves are shown in the case of a discrete shielded vortex in the uniform flow and incompressible transitional flow past an aerofoil by solving the navier stokes equation in performing this exercise we establish critical wavenumber range beyond which q waves are created relevance of this information for dns and les is discussed we have further discussed the case of spurious caustics in discrete computing

the analysis of transformed data abstract recently it was suggested bickel and doksum 1981 that when data are used to select a transformation the post transformation analysis of those data may need to be modified considerably from standard form so as to allow for the selection we argue that common sense and the work of box and cox 1964 point to a contrary conclusion our argument is based on considerations of parameter interpretation and subsequent bayesian analysis within the context of fitting normal error linear models numerical examples are used to illustrate the main points

on prediction and the power transformation family summary the power transformation family is often used for transforming to a normal linear model the variance of the regression parameter estimators can be much larger when the transformation parameter is unknown and must be estimated compared to when the transformation parameter is known we consider prediction of future untransformed observations when the data can be transformed to a linear model when the transformation must be estimated the prediction error is not much larger than when the parameter is known

semiparametric estimation of a proportional hazard model with unobserved heterogeneity the proportional hazard model with unobserved heterogeneity gives the hazard function of a random variable conditional on covariates and a second random variable representing unobserved heterogeneity this paper shows how to estimate the baseline hazard function and the distribution of the unobserved heterogeneity nonparametrically the baseline hazard function and heterogeneity distribution are assumed to satisfy smoothness conditions but are not assumed to belong to known finite dimensional parametric families existing estimators assume that the baseline hazard function or heterogeneity distribution belongs to a known parametric family thus the estimators presented here are more general than existing ones

the limiting distribution of the maximum rank correlation estimator han s maximum rank correlation mrc estimator is shown to be 4 consistent and asymptotically normal the proof rests on a general method for determining the asymptotic distribution of a maximization estimator a simple u statistic decomposition and a uniform bound for degenerate u processes a consistent estimator of the asymptotic covariance matrix is provided along with a result giving the explicit form of this matrix for any model within the scope of the mrc estimator the latter result is applied to the binary choice model and it is found that the mrc estimator does not achieve the semiparametric efficiency bound

misspecified nonconvex statistical optimization for sparse phase retrieval existing nonconvex statistical optimization theory and methods crucially rely on the correct specification of the underlying true statistical models to address this issue we take a first step towards taming model misspecification by studying the high dimensional sparse phase retrieval problem with misspecified link functions in particular we propose a simple variant of the thresholded wirtinger flow algorithm that given a proper initialization linearly converges to an estimator with optimal statistical accuracy for a broad family of unknown link functions we further provide extensive numerical experiments to support our theoretical findings

efficiency bounds for distribution free estimators of the binary choice and the censored regression models we derive lower bounds on the asymptotic variances for regular distribution free estimators of the parameters of the binary choice model and the censored regression tobit model a distribution free or semiparametric estimator is one that does not require any assumption about the distribution of the stochastic error term in the model apart from regularity conditions for the binary choice model we obtain an explicit lower bound for the asymptotic variance for the slope parameters or more generally the parameters of a nonlinear regression function in the underlying latent variable model but we find that there is no regular semiparametric estimator of the constant term identified by requiring the error distribution to have zero median lower bounds are also obtained under the further assumption that the error distribution is symmetric and in this case there is a finite lower bound for the constant term too comparison of the bounds with those for the classical parametric problem shows the loss of information due to lack of a priori knowledge of the functional form of the error distribution we give the conditions for equality of the parametric and semiparametric lower bounds in which case adaptive estimation may be possible both with and without the assumption of a symmetric error distribution in general adaptive estimation is not possible but one special case where these conditions hold is when the regression function is linear and the explanatory variables have a multivariate normal distribution the tobit model considered here is the censored nonlinear regression model with a fixed censoring point we again give an explicit lower bound for the asymptotic variance for the regression parameters this time including a constant term if the error term has zero median comparison with the corresponding lower bound for the parametric case shows that adaptive estimation is in general not possible for this model

non parametric analysis of a generalized regression model the maximum rank correlation estimator the paper considers estimation of a model yi d f x i 0 ui where the composite transformation d f is only specified that d r r is non degenerate monotonic and f r2 r is strictly monotonic in each of its variables the paper thus generalizes standard data analysis which assumes that the functional form of d f is known and additive the estimator which it proposes is the maximum rank correlation estimator which is non parametric in the functional form of d f and non parametric in the distribution of the error terms ui the estimator is shown to be strongly consistent for the parameters 0 up to a scale coefficient

some remarks on a three critical points theorem abstract some remarks on a strict minimax inequality which plays a fundamental role in ricceri s three critical points theorem are presented as a consequence some recent applications of ricceri s theorem to nonlinear boundary value problems are revisited by obtaining more precise conclusions

estimation of the binary response model using a mixture of distributions estimator mod abstract in this paper we develop a semiparametric sieve estimator which is termed a mixture of distributions estimator mod to estimate a binary response model when the distribution of the errors is unknown the estimator of the distribution function is composed of a mixture of smooth distributions where the number of mixtures increases with the sample size the model is semiparametric because it is assumed that a parametric index type restriction holds optimal rates of convergence are established for the distribution function under the l 2 norm and conditions are derived under which estimates of the parametric component are asymptotically normal an appealing feature about mod is that it is possible to restrict the estimator of the distribution function a priori to be smooth nonnegative nondecreasing and to integrate to one this has important practical and theoretical implications

an extension of the proportional hazards model for grouped data summary a family of transformations for probabilities is considered for the analysis of grouped survival data additive and multiplicative models for the hazard function are compared a method is suggested for estimating the scale on which an additive representation of the hazard in terms of explanatory variables is appropriate computations are performed using glim a test for departures from the grouped proportional hazards model is introduced an example is analyzed by the methods put forward in the analysis of survival data the effects of explanatory variables on failure time t are of great interest these effects are perhaps most conveniently investigated by establishing simple models for the hazard function in terms of explanatory variables we focus attention on additive and multiplicative models for the hazard the approach taken is to analyze sequences of contingency tables constructed from the data this follows mantel 1966 though the way in which we determine the sequences parallels work by holford 1976 certain similarities to problems involving binary data are exploited in particular a family of transformations for probabilities is defined which includes both additive and multiplicative models as special cases generalized linear models nelder and wedderburn 1972 associated with the transformations may be tried on the data and their fits compared in 3 a test for departures from the grouped multiplicative model in the direction of the grouped additive model is proposed and the forms of two simple estimates of the survivor function are given the methods are applied to an example in 4

radiated noise from airfoils in realistic mean flows the long term objective of the research described is to use computational aeroacoustics methodology and parallel computers to increase the understanding of broadband blade noise in a systematic progression toward simulations of completely realistic configurations and conditions some simplified problems that address the important features of the flow are investigated a two dimensional navier stokes code implemented using the message passing library and fortran 90 on the ibm sp2 is used to perform the calculations results are presented for the interaction of a vortical gust and naca airfoils including nonlinear effects the influence of gust frequency and airfoil thickness is described a multigrid method is used to obtain converged steady state solutions before the gust is introduced in a source region inside the domain

the nehari manifold and the existence of multiple solutions for a singular quasilinear elliptic equation abstract in this paper we are concerned with the existence of multiple positive solutions for the singular quasilinear elliptic problem div x a p u p 2 u h x u m 2 u h x u n 2 u x u x 0 x where r n n 3 is a bounded domain with smooth boundary 0 1 p n 0 a n p p 1 m p n p n n 1 a p 0 h x h x are lebesgue measurable functions which may change sign on we prove that there exist at least two positive solutions by using the nehari manifold and the fibrering maps associated with the energy functional for this problem

estimation of marginal effects in semiparametric selection models with binary outcomes this paper addresses the estimation of a semiparametric sample selection index model where both the selection rule and the outcome variable are binary since the marginal effects are often of primary interest and are difficult to recover in a semiparametric setting we focus on developing an estimator for the marginal effects this marginal effect estimator uses only observations where the selection probability is above a certain threshold a key innovation is that this high probability set is adaptive to the data we establish the large sample properties of the marginal effect estimator as well as those for an index estimator upon which it depends monte carlo studies show that these estimators perform well in finite samples

semiparametric estimation of monotone and concace utility functions for polychotomous choice models this paper introduces a semiparametric estimation method for polychotomous choice models the method does not require a parametric structure for the systematic subutility of observable exogenous variables the distribution of the random terms is assumed to be known up to a finite dimensional parameter vector in contrast previous semiparametric methods of estimating discrete choice models have concentrated on relaxing parametric subutility parametrically specified the systematic subutility is assumed to possess properties such as monotonicity and concavity that are typically assumed in microeconomic theory the estimator for the systematic subutility and the parameter vector of the distribution is shown to be strongly consistent a computational technique to calculate the estimators is developed copyright 1991 by the econometric society

subcritical perturbations of a singular quasilinear elliptic equation involving the critical hardy sobolev exponent abstract in this work we improve some known results for a singular operator and also for a wide class of lower order terms by proving a multiplicity result the proof is made by applying the generalized mountain pass theorem due to ambrosetti and rabinowitz to do this we show that the minimax levels are in a convenient range by combining a special class of approximating functions due to gazzola and ruf with the concentrating functions of the best sobolev constant

semiparametric estimation of binary response models with endogenous regressors abstract in this paper we propose a two step semiparametric maximum likelihood sml estimator for the coefficients of a single index binary choice model with endogenous regressors when identification is achieved via a control function approach the first step consists of estimating a reduced form equation for the endogenous regressors and extracting the corresponding residuals in the second step the latter are added as control variates to the outcome equation which is in turn estimated by sml we establish the estimator s n consistency and asymptotic normality in a simulation study we compare the properties of our estimator with those of existing alternatives highlighting the advantages of our approach

compact implicit maccormack type schemes with high accuracy in this work the maccormack methodology is extended to implicit compact differencing schemes a prefactorization method is developed which splits the implicit matrix into two independent upper and lower matrices which are easier to invert using this method a new class of high order accurate compact maccormack type schemes is derived two fourth order schemes are described and results are shown for three linear and nonlinear caa benchmark problems

rates of convergence for estimating regression coefficients in heteroskedastic discrete response models abstract in this paper we consider estimation of discrete response models exhibiting conditional heteroskedasticity of a multiplicative form where the latent error term is assumed to be the product of an unknown scale function and a homoskedastic error term it is first shown that for estimation of the slope coefficients in a binary choice model under this type of restriction the semiparametric information bound is zero even when the homoskedastic error term is parametrically specified hence it is impossible to attain the parametric convergence rate for the parameters of interest however for ordered response models where the response variable can take at least three different values the parameters of interest can be estimated at the parametric rate under the multiplicative heteroskedasticity assumption two estimation procedures are proposed the first estimator based on a parametric restriction on the homoskedastic component of the error term is a two step maximum likelihood estimators where the unknown scale function is estimated nonparametrically in the first stage the second procedure which does not require the parametric restriction estimates the parameters by a kernel weighted least squares procedure under regularity conditions which are standard in the literature both estimators are shown to be n consistent and asymptotically normal

the effects of discontinuous boundary conditions on the directivity of sound from a piston abstract the radiation patterns of sound from a baffled oscillating piston are studied via a numerical method to investigate the effects of discontinuous boundary condition on the sound radiation from a piston we introduce three piston models that have respectively definite characteristics at their own edges linearized euler s equations in cartesian co ordinates are solved by the dispersion relation preserving finite difference scheme the numerical results are compared with the analytic results derived from the kirchhoff helmholtz integral theorem through the comparison of numerical results of each boundary condition we find that discontinuity at the edge of the piston as well as the helmholtz number of the vibrating piston is an important factor in determining the sound radiation pattern of the piston the validity of numerical simulation for discontinuity effects is confirmed by comparison of the numerical and analytic results

operational characteristics of maximum score estimation abstract this paper reports on the operational characteristics of maximum score estimation of a linear model from binary response data a series of previous articles have shown that in theory the maximum score method makes possible binary response analysis under very weak distributional assumptions here we present evidence on the properties of maximum score estimation in practice after reviewing the known asymptotic theory of maximum score estimation the paper describes an algorithm for maximum score estimation and characterizes its performance then findings from a monte carlo study comparing maximum score and logit maximum likelihood estimation are reported finally the accuracy of bootstrap estimation of maximum score root mean square errors is evaluated

nehari manifold and existence of positive solutions to a class of quasilinear problems abstract in this paper existence and multiplicity results to the following nonlinear elliptic equation p u u q 2 u u p 2 u u 0 in r n together with mixed dirichlet neumann or neumann boundary conditions are established here p u denotes the p laplacian operator 1 q p n p np n p and is a positive real parameter the study is based on the extraction of palais smale sequences in the nehari manifold

fast calculations of dyadic green s functions for electromagnetic scattering in a multilayered medium abstract in this paper we introduce a novel acceleration method for the calculation of dyadic green s functions for the mixed potential integral equation formulation of electromagnetic scattering of scatterers embedded in a multilayered medium numerical results are provided to demonstrate the efficiency and accuracy of the proposed method

existence and multiplicity of weak solutions for a singular quasilinear elliptic equation abstract in this paper we consider the singular quasilinear elliptic equation 0 1 div x a p d u p 2 d u v x u p 2 u h x u q 2 u h x u r 2 u x r n 0 where 0 a n p p 1 p n 1 q r p n p n p the function v x is continuous and nonnegative the functions h x h x l b r 1 b with 0 r 0 r using variational methods we obtain a number of results on existence and multiplicity of solutions by considering all possible orderings of exponents p q r

semiparametric analysis of discrete response asymptotic properties of the maximum score estimator abstract this paper is concerned with the estimation of the model med y x x from a random sample of observations on sgn y x manski 1975 introduced the maximum score estimator of the normalized parameter vector in the present paper strong consistency is proved it is also proved that the maximum score estimate lies outside any fixed neighborhood of with probability that goes to zero at exponential rate

time domain numerical computation of noise reduction by diffraction and finite impedance of barriers a new time domain numerical method is presented for the estimation of noise reduction by the diffraction and finite impedance of barriers high order finite difference schemes conventionally used for computational aeroacoustics and time domain impedance boundary conditions are utilized for the development of the time domain method compared with other methods this method can be applied more easily to the problems related to nonlinear noise propagation such as impulsive noise and broadband noise linearized euler equations in cartesian co ordinates are considered and solved numerically straight and t shaped barriers with and without surface admittance are calculated in order to assess the accuracy of this time domain method comparison with the results of sysnoise software ver 5 3 are made there are very good agreements between the results of the present time domain numerical method and the boundary element method of the sysnoise software

wavenumber extended high order upwind biased finite difference schemes for convective scalar transport this paper proposes some new wavenumber extended high order upwind biased schemes the dispersion and dissipation errors of upwind biased finite difference schemes are assessed and compared by means of a fourier analysis of the difference schemes up to 11th order upwind biased schemes are analyzed it is shown that both the upwind biased scheme of order 2n 1 and the corresponding centered differencing scheme of order 2nhave the same dispersion characteristics thus the former can be considered to be the latter plus a correction that reduces the numerical dissipation the new second order wavenumber extended scheme is tested and compared with some well known schemes the range of wavenumbers that are accurately treated by the upwind biased schemes is improved by using additional constraints from the fourier analysis to construct the new schemes the anisotropic behavior of the dispersion and dissipation errors is also analyzed for both the conventional and the new wavenumber extended upwind biased finite difference schemes

two stage least absolute deviations estimators1 in this paper the method of least absolute deviations is applied to the estimation of the parameters of a structural equation in the simultaneous equations model a class of estimators called two stage least absolute deviations estimators is defined their asymptotic properties are derived and the problem of finding the optimal member of the class is considered in this paper we apply the method of least absolute deviations to the estimation of the parameters of a structural equation in the simultaneous equations model we define a class of estimators called two stage least absolute deviations estimators 2slad and derive their asymptotic properties they are so named as their relationship to the two stage least squares estimator 2sls is analogous to the relationship of the least absolute deviations estimator lad to the least squares estimator ls in the standard regression model the lad estimation has been extensively studied in the context of the standard regression model and its usefulness is universally recognized in this paper we show that the advantage of 2slad over 2sls in the simultaneous equations model can be as great as that of lad over ls in the standard regression model if 2slad is properly defined this last clause is very important since the results of this paper indicate that the lad analogue of 2sls that has been considered before in the literature is not an appropriate method

time domain inflow boundary condition for turbulence airfoil interaction noise prediction using synthetic turbulence modeling abstract the present paper deals with development of the synthetic turbulence inflow boundary condition stibc to predict inflow broadband noise generated by interaction between turbulence and an airfoil a cascade of airfoils in the time domain the stibc is derived by combining inflow boundary conditions that have been successfully applied in external and internal computational aeroacoustics caa simulations with a synthetic turbulence model the random particle mesh rpm method based on a digital filter is used as the synthetic turbulence model gaussian and liepmann spectra are used to define the filters for turbulence energy spectra the linearized euler equations are used as governing equations to evaluate the suitability of the stibc in time domain caa simulations first the velocity correlations and energy spectra of the synthesized turbulent velocities are compared with analytic ones the comparison results reveal that the stibc can reproduce a turbulent velocity field satisfying the required statistical characteristics of turbulence particularly the liepmann filter representing a non gaussian filter is shown to be effectively described by superposing the gaussian filters each gaussian filter has a different turbulent kinetic energy and integral length scale second two inflow noise problems are numerically solved using the stibc the turbulence airfoil interaction and the turbulence a cascade of airfoils interaction problems the power spectrum of noise due to an isolated flat plate airfoil interacting with incident turbulence is predicted and its result is successfully validated against amiet s analytic model amiet 1975 4 the prediction results of the upstream and downstream acoustic power spectra from a cascade of flat plates are then compared with cheong s analytic model cheong et al 2006 30 these comparisons are also in excellent agreement on the basis of these illustrative computation results the stibc is expected to be applied to investigate more complicated inflow noise problems including the effects of non uniform mean flow nonlinear interaction and real airfoil shapes

on efficient estimation of the ordered response model in this paper we derive efficiency bounds for the ordered response model when the distribution of the errors is unknown furthermore we develop an estimator that is efficient under suitable conditions interestingly neither the bounds nor the estimator are trivial extensions of what has been proposed in the literature for the binary response model the estimator is composed of quadratic b splines and estimation is performed by the method of sieves in addition the estimator of the distribution function is restricted to be a proper distribution function an empirical example on the effect of fees on attendance rates at universities and community colleges is also included we get substantively different results by relaxing the assumption that the distribution of the errors is normal

time and frequency domain computations of broadband noise due to interaction between incident turbulence and rectilinear cascade of flat plates abstract time domain computational aeroacoustic caa techniques are developed to investigate the broadband noise resulting from the interaction of a rectilinear cascade of flat plates with incident homogeneous isotropic turbulence the investigation is carried out by comparing the prediction results obtained by employing the time domain caa method with those using existing frequency domain methods a semi analytic model wei cheong 2010 and a full three dimensional rectilinear cascade model lloyd peake 2008 lloyd 2009 are adopted for the frequency domain computations by comparing these computation results the three dimensional characteristics of inflow turbulence noise are investigated in particular the effects of the wavenumber components of ingested turbulence in the spanwise direction are taken into consideration in the investigation first caa results are compared with those from the semi analytic model the results for the acoustic modes of relatively low spanwise wavenumbers obtained using both methods show good agreement but as the spanwise wavenumber increases the results obtained by the two methods become increasingly different to investigate in detail the reason for these differences mode decomposition analysis is performed by adopting a hybrid method as well as by employing the caa and the semi analytic method the hybrid method involves the following two sequential computations i the upwash velocities on the flat plate airfoils of the rectilinear cascade are first predicted using the frequency domain method and ii the acoustic wave propagation is subsequently analyzed using time domain caa techniques with these upwash velocities applied as the boundary conditions on the flat plate it is seen that the results of the time domain caa technique and the hybrid method show good agreement irrespective of the wavenumber and frequency however comparisons of the acoustic solutions from three computations reveal that the prediction results of the semi analytic model deviate more from the other two predictions as the spanwise wavenumber of the acoustic wave increases and the frequency decreases on a basis of this observation a formulation is derived for the error in the pressure jump across the flat plate predicted by using the semi analytic method this formulation shows that the error is approximately inversely proportional to the sound speed in the spanwise direction of the concerned acoustic modes this result quantitatively clarifies the limitations of applying the frequency domain method of wei cheong 2010 to the three dimensional turbulence cascade interaction problems secondly the prediction results using the time domain caa method are compared with those from the full three dimensional rectilinear model that is believed to be exact model for the cascade geometry considered in this paper this comparison shows the good agreements between two predictions which support the above arguments for the error and the successful application of the time domain caa methods it is expected that these methods can be extended to the broadband noise problem in an annular cascade including the nonlinear interaction of the real airfoil cascade with the incident nonhomogeneous gust

optimized prefactored compact schemes the numerical simulation of aeroacoustic phenomena requires high order accurate numerical schemes with low dispersion and dissipation errors in this paper we describe a strategy for developing high order accurate prefactored compact schemes requiring very small stencil support these schemes require fewer boundary stencils and offer simpler boundary condition implementation than existing compact schemes the prefactorization strategy splits the central implicit schemes into forward and backward biased operators using fourier analysis we show it is possible to select the coefficients of the biased operators such that their dispersion characteristics match those of the original central compact scheme and their numerical wavenumbers have equal and opposite imaginary components this ensures that when the forward and backward stencils are added the original central compact scheme is recovered to extend the resolution characteristic of the schemes an optimization strategy is employed in which formal order of accuracy is sacrificed in preference to enhanced resolution characteristics across the range of wavenumbers realizable on a given mesh the resulting optimized schemes yield improved dispersion characteristics compared to the standard sixth and eighth order compact schemes making them more suitable for high resolution numerical simulations in gas dynamics and computational aeroacoustics the efficiency accuracy and convergence characteristics of the new optimized prefactored compact schemes are demonstrated by their application to several test problems

semiparametric maximum likelihood estimation of polychotomous and sequential choice models abstract this article considers semiparametric estimation of discrete choice models the estimation method is a semiparametric maximum likelihood method which generalizes klein and spady 1993 to the estimation of polychotomous choice and sequential choice models special emphasis is on the estimation of models with indices of which the density function is not bounded away from zero issues on trimming indices the correction of asymptotic bias and issues of negative kernel density estimation a semiparametric efficiency bound is derived for the polychotomous choice model with index restrictions our estimator is shown to be n consistent asymptotically normal and almost asymptotically efficient monte carlo experiments are provided to evaluate the finite sample performance of the estimator

a consistent bootstrap procedure for the maximum score estimator abstract in this paper we propose a new model based smoothed bootstrap procedure for making inference on the maximum score estimator of manski 1975 1985 and prove its consistency we provide a set of sufficient conditions for the consistency of any bootstrap procedure in this problem we compare the finite sample performance of different bootstrap procedures through simulation studies the results indicate that our proposed smoothed bootstrap outperforms other bootstrap schemes including the m out of n bootstrap additionally we prove a convergence theorem for triangular arrays of random variables arising from binary choice models which may be of independent interest

some efficiency bounds for semiparametric discrete choice models abstract this paper presents lower bounds on the asymptotic variance of estimators for various semiparametric models of discrete choice no greatest lower bound exists for some partial observability models where the dependent variable consists of a single binary indicator no regular estimators exist for these models even though the models are identified for other partial observability models the greatest lower bound is finite and coincides with the asymptotic efficiency of certain index estimators however some examples show that index estimators do not achieve the efficiency bound in general when choices are fully observed

multiple solutions for a degenerate elliptic equation involving sublinear terms at infinity some multiplicity results are presented for the eigenvalue problem div x 2a u x 2b f u x 2c g u in u 0o n

derivation of high order compact finite difference schemes for non uniform grid using polynomial interpolation in this paper simple polynomial interpolation is used to derive arbitrarily high order compact schemes for the first derivative and tridiagonal compact schemes for the second derivative consisting of three second derivative nodes in the interior and two on the boundary on non uniform grids boundary and near boundary schemes of the same order as the interior are also developed using polynomial interpolation and for a general compact scheme on a non uniform grid it is shown that polynomial interpolation is more efficient than the conventional method of undetermined coefficients for finding coefficients of the scheme the high order non uniform schemes along with boundary closure of up to 14th order thus obtained are shown to be stable on a non uniform grid with appropriate stretching so that more grid points are clustered near the boundary the stability and resolution properties of the high order non uniform grid schemes are studied and the results of three numerical tests on stability and accuracy properties are also presented

prediction and power transformations when the choice of power is restricted to a finite set abstract we study the family of power transformations proposed by box and cox 1964 when the choice of the power parameter is restricted to a finite set r the behavior of the box cox procedure is as anticipated in two extreme cases when the true parameter is an element of r and when is far from r we study the case in which 0 is close to r finding that the resulting methods can be very different from unrestricted maximum likelihood and that inferences may depend on the design the values of the regression parameters and the distance of to r

grid optimized dispersion relation preserving schemes on general geometries for computational aeroacoustics abstract in this paper we investigate the dispersion relation preserving property of a finite difference scheme on general geometries for computational aeroacoustics where nondispersive and nondissipative properties are of critical importance the analysis pertains to the application of the optimization algorithm of the dispersion relation preserving drp scheme in wave number space to the general geometries nonuniform cartesian and curvilinear grids in many computational aeroacoustics applications the drp schemes have often been favored for their accuracy and efficiency drp schemes however are implemented only on uniform cartesian grids practical problems in aeroacoustics however are seldom confined to uniform cartesian grids with the associated computing grids often being nonuniform cartesian or curvilinear grid optimized dispersion relation preserving godrp finite difference schemes are proposed based on optimization that gives finite difference equations locally the same dispersion relation as the original partial differential equations on the grid points in the nonuniform cartesian or curvilinear mesh this local dispersion relation preserving property guarantees global accuracy of numerical schemes in the wave number space over the full domain the basic idea behind mathematical formulations of godrp schemes is that the optimization in the wave number space is carried out not on the computational domain but on the physical domain because the properties of cartesian and curvilinear grids differ whether the coupling of the coordinate variables between the physical and computational domains exists or not different mathematical formulations are developed for each grid type to investigate the effectiveness of godrp schemes a sequence of benchmark problems is executed through many numerical test problems it is shown that the use of godrp schemes can broaden the application area of conventional drp schemes to aeroacoustic phenomena enhancing both the speed and accuracy of the computation using nonuniform cartesian or curvilinear grids

a novel strategy for deriving high order stable boundary closures based on global conservation i basic formulas abstract it is well known that for initial boundary value problems one may need to decrease the order of boundary closures to ensure strict stability also called time stability of finite difference schemes for high order schemes this often reduces the global convergence rate significantly to cure this issue we derive high order accurate boundary closures that satisfy a global conservation property we show that the boundary closures cannot be both high order accurate and conservative in the l 2 inner product if the grid is equidistant therefore we derive particular sets of nonuniform solution points and quadrature weights near the domain boundaries the new schemes are high order accurate on the modified grids and conservative in the derived quadrature rules although we have no theoretical stability proof numerical eigenvalue analysis suggests that the new schemes are strictly stable up to eleventh order global accuracy for scalar linear advection equations numerical experiments with one and two dimensional linear equations corroborate the design orders of the schemes

on the use of a uniformly valid analytical cascade response function for fan broadband noise predictions the present paper extends an existing analytical model of the aeroacoustic response of a rectilinear cascade of flat plate blades to three dimensional incident vortical gusts to the prediction of the noise generated by a three dimensional annular blade row the extended formulation is meant to be implemented in a fan broadband noise prediction tool the intended applications include the modern turbofan engines for which analytical modelling is believed to be a good alternative to more expensive numerical techniques the prediction noise model resorts to a strip theory approach based on a three dimensional rectilinear cascade model the latter is based on the wiener hopf technique and yields the pressure field in the blade passage and the unsteady blade loading the analytical pressure solution is derived by making an extensive use of the residue theorem the obtained unsteady blade loading distribution over the blades is then used as a dipole source distribution in an acoustic analogy applied in the annular rigid duct with uniform mean flow the new achievements are then tested on threedimensional annular benchmark configurations and compared with three dimensional lifting surface models and three dimensional euler linearized codes available in the literature the accuracy of the model is shown for high hub to tip ratio cases when used as such in a true rectilinear cascade configuration it also reproduces the exact radiated field that can be derived directly for low hub to tip ratio configurations the model departs from three dimensional computations both regarding the blade loading and the acoustic radiation a correction is proposed to account for the actual annular dispersion relation in the rectilinear cascade response function the results suggest that the proposed correction is necessary to get closer to the underlying physics of the annular space wave equation but that it is yet not sufficient to fully reproduce three dimensional results