nonparametric instrumental variables estimation for efficiency frontier the paper investigates endogeneity issues in nonparametric frontier models it considers a nonseparable model for a cost function c y u where c and y are the cost and the output u is uniform in 0 1 and is increasing with respect to u the cost frontier corresponds to u 0 and u can be interpreted as a normalized level of inefficiency the endogeneity issue arises when y is dependent of u for identification and estimation we use a nonparametric instrumental variables estimator of the model for fixed value u and obtain an estimate of the quantile cost frontier y this involves the solution of a non linear integral equation if the true frontier y 0 is wanted it is then estimated by estimating the bias correction y 0 y under additional regularity conditions the procedure is illustrated through a simulated sample and with an empirical application to the efficiency of post offices

space time multiscale model for wave propagation in heterogeneous media abstract a space time multiscale model for wave propagation in heterogeneous media is developed the model builds on the authors previous work on the higher order mathematical homogenization theory with multiple spatial and temporal scales and is aimed at addressing the issues of stability and mathematical consistency starting from the weak forms of homogenized macroscopic equations of motion terms causing the solution secularity are identified and enforced to vanish this condition recovers the missing boundary conditions and gives rise to two secularity constrains imposing the uniform validity of asymptotic expansions finite element semi discretization in space along with an analytical solution in time are employed to incorporate the secularity constrains in the leading order solution and account for the slow time dependence of the leading solution pade approximation is utilized to develop the time stepping schemes on the fast time scale the formulation is verified for wave propagation problems in semi infinite and finite domains

using least squares and tobit in second stage dea efficiency analyses the paper examines second stage dea efficiency analyses within the context of a censoring data generating process dgp and a fractional data dgp when efficiency scores are treated as descriptive measures of the relative performance of units in the sample it is argued that the efficiency scores are not generated by a censoring process but are fractional data tobit estimation in this situation is inappropriate in contrast ordinary least squares is a consistent estimator and if white s white h 1980 a heteroskedastic consistent covariance matrix and a direct test for heteroskedasticity econometrica 48 817 838 heteroskedastic consistent standard errors are calculated large sample tests can be performed which are robust to heteroskedasticity and the distribution of the disturbances for a more refined analysis papke and wooldridge s papke l e wooldridge j m 1996 econometric methods for fractional response variables with an application to 401 k plan participation rates journal of applied econometrics 11 6 619 632 method has some advantages but is more complex and requires special programming

dispersive elastodynamics of 1d banded materials and structures analysis abstract the elastodynamics of 1d periodic materials and finite structures comprising these materials are studied with particular emphasis on correlating their frequency dependent characteristics and on elucidating their pass band and stop band behaviors dispersion relations are derived for periodic materials and are employed in a novel manner for computing both pass band and stop band complex mode shapes through simulations of harmonically induced wave motion within a finite number of unit cells conformity of the frequency band structure between infinite and finite periodic systems is shown in particular only one or two unit cells of a periodic material could be sufficient for frequency bandedness to carry over from the infinite periodic case and only three to four unit cells are necessary for the decay in normalized transmission within a stop band to practically saturate with an increase in the number of cells dominant speeds in the scattered wave field within the same finite set of unit cells are observed to match those of phase and group velocities of the infinite periodic material within the most active pass band dynamic response due to impulse excitation also is shown to capture the infinite periodic material dynamical characteristics finally steady state vibration analyses are conducted on a finite fully periodic structure revealing a conformity in the natural frequency spread to the frequency band layout of the infinite periodic material the steady state forced response is observed to exhibit mode localization patterns that resemble those of the infinite periodic medium and it is shown that the maximum localized response under stop band conditions could be significantly less than in an equivalent homogenous structure and the converse is true for pass band conditions

a gamma moment approach to monotonic boundary estimation the estimation of optimal support boundaries under the monotonicity constraint is relatively unexplored and still in full development this article examines a new extreme value based model which provides a valid alternative for complete envelopment frontier models that often suffer from lack of precision and for purely stochastic ones that are known to be sensitive to model misspecification we provide different motivating applications including the estimation of the minimal cost in production activity and the assessment of the reliability of nuclear reactors

nonparametric efficiency analysis a multivariate conditional quantile approach this paper focuses on nonparametric efficiency analysis based on robust estimation of partial frontiers in a complete multivariate setup multiple inputs and multiple outputs it introduces quantile efficiency scores a nonparametric estimator is proposed achieving strong consistency and asymptotic normality then if increases to one as a function of the sample size we recover the properties of the fdh estimator but our estimator is more robust to the perturbations in data since it attains a finite gross error sensitivity environmental variables can be introduced to evaluate efficiencies and a consistent estimator is proposed numerical examples illustrate the usefulness of the approach

non parametric unconditional quantile estimation for efficiency analysis with an application to federal reserve check processing operations abstract this paper examines the technical efficiency of us federal reserve check processing offices over 1980 2003 we extend results from park et al park b simar l weiner c 2000 fdh efficiency scores from a stochastic point of view econometric theory 16 855 877 and daouia and simar daouia a simar l 2007 nonparametric efficiency analysis a multivariate conditional quantile approach journal of econometrics 140 375 400 to develop an unconditional hyperbolic quantile estimator of efficiency our new estimator is fully non parametric and robust with respect to outliers when used to estimate distance to quantiles lying close to the full frontier it is strongly consistent and converges at rate root n thus avoiding the curse of dimensionality that plagues data envelopment analysis dea estimators our methods could be used by policymakers to compare inefficiency levels across offices or by managers of individual offices to identify peer offices

an asymptotic theory for a weakly nonlinear beam equation with a quadratic perturbation in this paper an initial boundary value problem for a weakly nonlinear beam equation with a quadratic nonlinearity will be studied the initial boundary value problem can be regarded as a simple model describing free oscillations of flexible structures like suspension bridges using a two timescales perturbation method an approximation for the solution of this initial boundary problem will be constructed for a class of initial boundary value problems the existence and uniqueness of solutions and the asymptotic validity of approximations on a large timescale are shown it will be shown that for specific values of the beam parameters complicated internal resonances occur

nonparametric stochastic frontiers a local maximum likelihood approach this paper proposes a new approach to handle nonparametric stochastic frontier sf models it is based on local maximum likelihood techniques the model is presented as encompassing some anchorage parametric model in a nonparametric way first we derive asymptotic properties of the estimator for the general case local linear approximations then the results are tailored to a sf model where the convoluted error term efficiency plus noise is the sum of a half normal and a normal random variable the parametric anchorage model is a linear production function with a homoscedastic error term the local approximation is linear for both the production function and the parameters of the error terms the performance of our estimator is then established in finite samples using simulated data sets as well as with a cross sectional data on us commercial banks the methods appear to be robust numerically stable and particularly useful for investigating a production process and the derived efficiency scores

influence of geometric and physical nonlinearities on the internal resonances of a finite continuous rod with a microstructure abstract in this work nonlinear longitudinal vibrations of a finite composite rod are studied including geometric and physical nonlinearities an original boundary value problem for a heterogeneous rod yielded by the macroscopic approximation obtained earlier by the higher order asymptotic homogenization method is used the effects of internal resonances and modes coupling are predicted validated and analyzed the defined novel continuous problem governed by pdes is solved using space discretization and the method of multiple time scales we are aimed at understanding and analyzing how the presence of the microstructure influences the processes of mode interaction it is shown that depending on a scaling relation between the amplitude of the vibrations and the size of the unit cell different scenarios of the modes coupling can be realized additionally to the asymptotic solution numerical simulation of the modes coupling is performed by means of the runge kutta fourth order method the obtained numerical and analytical results demonstrate good qualitative agreement

unobserved heterogeneity and endogeneity in nonparametric frontier estimation in production theory and eciency analysis rm eciencies are measured by their distances to a production frontier which is the geometrical locus of optimal combinations of inputs and outputs it is today recognized that in the presence of heterogenous conditions like environmental factors that influence the shape and the position of the frontier traditional measures of efficiency obtained in the space of inputs outputs have no sensible economic meaning this is because the benchmark frontier may not be attainable for a firm facing different heterogenous conditions using a nonparametric approach this can be corrected by using conditional frontiers and conditional efficiency scores developed in the literature in this paper we extend these concepts in the case where the heterogeneity is not observed we propose and analyze a model where the heterogeneity variable is linked to a particular input or output it is defined as the part of the input or the output independent from some instrumental variable through a nonseparable nonparametric model we discuss endogeneity issues involved in this model under certain regularity assumptions we show that the model is identified we propose nonparametric estimators of the conditional frontier and the conditional efficiency score and analyze their asymptotic properties when using fdh estimators we prove the asymptotic convergence to a weibull distribution whereas when using the robust order m estimators we obtain the asymptotic normality of the estimators the method is illustrated with some simulated and real data examples a monte carlo experiment shows how the procedure works for finite samples

sigma mu efficiency analysis a methodology for evaluating units through composite indicators abstract we propose a methodology to employ composite indicators for performance analysis of units of interest using and extending the family of stochastic multiattribute acceptability analysis we start evaluating each unit by means of weighted sums of their elementary indicators in the whole set of admissible weights for each unit we compute the mean and the standard deviation of its evaluations clearly the former has to be maximized while the latter has to be minimized as it denotes instability in the evaluations with respect to the variability of weights we consider a unit to be pareto koopmans efficient with respect to and if there is no convex combination of and of the rest of the units with a value of that is not smaller and a value of that is not greater with at least one strict inequality the set of all pareto koopmans efficient units constitutes the first pareto koopmans frontier in the spirit of context dependent data envelopment analysis we assign each unit to one of the sequence of pareto koopmans frontiers we measure the local efficiency of each unit with respect to each frontier but also its global efficiency taking into account all frontiers in the plane thus enhancing the explicative power of the proposed approach to illustrate its potential we present a case study of world happiness based on the data of the homonymous report that is annually produced by the united nations sustainable development solutions network

parametric approximations of nonparametric frontiers the maximal achievable level of output for a given level of inputs defines the production frontier that can serve as benchmark to evaluate individual firm efficiencies nonparametric envelopment estimators free disposal hull data envelopment analysis have been mostly used because they rely on very few assumptions whereas parametric forms for the frontier allow for richer economic interpretation most of the parametric approaches rely on standard regression fitting the shape of the center of the cloud of points in this paper we investigated a new approach which captures the shape of the cloud points near its boundary it offers parametric approximations of nonparametric frontiers we provide the statistical theory asymptotic some simulated examples show the advantages of our method compared with the usual regression type estimators c 2004 elsevier b v all rights reserved

a symbolic approach to qualitative kinematics abstract an important problem for mechanism design and analysis is reasoning about the relationship between object shapes and their kinematic function such reasoning is difficult because of the unstructured influence of the shapes metric dimensions in this paper we show how a qualitative kinematic analysis can be based solely on symbolic reasoning and evaluation of predicates on metric dimensions this allows symbolic reasoning about kinematics without explicit numerical representations of object dimensions and automatic generation of operators relating kinematic goals to shape modifications which may achieve them

regularization of nonparametric frontier estimators in production theory and efficiency analysis we estimate the production frontier the locus of the maximal attainable level of an output the production given a set of inputs the production factors in other setups we estimate rather an input or cost frontier the minimal level of the input cost attainable for a given set of outputs goods or services produced in both cases the problem can be viewed as estimating a surface under shape constraints monotonicity in this paper we derive the theory of an estimator of the frontier having an asymptotic normal distribution it is based on the order mpartial frontier where we let the ordermto converge to infinity when n but at a slow rate the final estimator is then corrected for its inherent bias we thus can view our estimator as a regularized frontier in addition the estimator is more robust to extreme values and outliers than the usual nonparametric frontier estimators like fdh and than the unregularized order mn estimator of cazals et al 2002 converging to the frontier with a weibull distribution if m n fast enough when n the performances of our estimators are evaluated in finite samples and compared to other estimators through some monte carlo experiments showing a better behavior in terms of robustness bias mse and achieved coverage of the resulting confidence intervals the practical implementation and the robustness properties are illustrated through simulated data sets but also with a real data set

nonlinear curvature based model and resonant finite amplitude vibrations of symmetric cross ply laminates abstract moving from a general plate theory a modified general classical laminated plate theory mgclpt exhibiting nonlinear curvatures but still allowing for some worth features of linear curvature models von karman is formulated starting from mgclpt partial differential equations a minimal discretized model suitable for the analysis of resonant finite amplitude vibrations of symmetric cross ply laminates with immovable or movable supports is obtained via the galerkin procedure periodic responses of a single mode model and of a 3 1 internally resonant two mode model excited at primary resonance are obtained via the multiple time scale method the influence of various system parameters thickness ratio plate aspect number of laminae kind of material mode number is addressed and the comparison of nonlinear vibration results as obtained with the mgclpt and the von karman models for different boundary conditions shows some interesting differences

nonparametric frontier estimation a robust approach most nonparametric methods for estimating production frontiers data envelopment analysis and free disposal hall fdh are based on envelopment techniques statistical inference based on these estimators is available but by construction they are very sensitive to extreme values or outliers we propose a nonparametric estimator which is more robust to these extreme values it is based on a concept of expected minimum input function or expected maximal output function we show how this function is related to the efficient frontier itself the resulting estimator is related to the fdh estimator but it will not envelop all the data the asymptotic theory is provided our approach includes the multiple input and multiple output cases c 2002 elsevier science s a all rights reserved

comparing efficiency across markets an extension and critique of the zhang and bartels 1998 methodology abstract the use of non parametric frontier methods for the evaluation of product market efficiency in heterogeneous markets seems to have gained some popularity recently however the statistical properties of these frontier estimators have been largely ignored the main point is that non parametric frontier estimators are biased and that the degree of bias depends on specific sample properties most importantly sample size and number of dimensions of the model to investigate the effect of this bias on comparing market efficiency this contribution estimates the efficiency for several datasets for two main product categories following zhang y bartels r 1998 the effect of sample size on the mean efficiency in dea with an application to electricity distribution in australia sweden and new zealand journal of productivity analysis 9 3 187 204 these results comprise re estimates for the larger samples limiting their size to that of the smaller samples when the model dimensions for different samples are identical furthermore sample sizes are adjusted to mitigate the eventual differences in dimensions in specification this allows comparing market efficiency for different markets on a more equal footing since it reduces the bias effect to a minimum making the comparison of market efficiency possible however the article also points out the critical limitations of this zhang y bartels r 1998 the effect of sample size on the mean efficiency in dea with an application to electricity distribution in australia sweden and new zealand journal of productivity analysis 9 3 187 204 approach in certain respects apart from reporting these negative results we also offer some suggestions for future work

a smooth nonparametric conditional quantile frontier estimator abstract traditional estimators for nonparametric frontier models dea fdh are very sensitive to extreme values outliers recently aragon et al 2005 nonparametric frontier estimation a conditional quantile based approach econometric theory 21 358 389 proposed a nonparametric frontier model and estimator based on a suitably defined conditional quantile which is more robust to extreme values outliers their estimator is based on a nonsmooth empirical conditional distribution in this paper we propose a new smooth nonparametric conditional quantile estimator for the frontier model our estimator is a kernel based conditional quantile estimator that builds on early work of azzalini 1981 a note on the estimation of a distribution function and quantiles by a kernel method biometrika 68 326 328 it is computationally simple resistant to outliers and extreme values and smooth in addition the estimator is shown to be consistent and n asymptotically normal under mild regularity conditions we also show that our estimator s variance is smaller than that of the estimator proposed by aragon et al a simulation study confirms the asymptotic theory predictions and contrasts our estimator with that of aragon et al

theory and statistical properties of quantile data envelopment analysis abstract this research proposes quantile data envelopment analysis qdea as a procedure that accounts for the sensitivity of data envelopment analysis dea to data or firm outliers when using dea to estimate comparative efficiency or benchmarking performance metrics the qdea methodology endogenously identifies the distance to a qdea hyperplane while allowing up to proportion q 1 of the data observations to lie external to the qdea hyperplane the ability of qdea to provide more conventional quantile based benchmarking information is discussed the statistical properties of the qdea estimator are examined utilizing ncm subsampling and monte carlo procedures monte carlo simulations indicate that qdea distance estimates share the desirable root n convergence and large sample normality properties of the robust free disposal hull fdh based order m and order estimators

nonparametric frontier estimation via local linear regression abstract in this paper we propose a nonparametric regression frontier model that assumes no specific parametric family of densities for the unobserved stochastic component that represents efficiency in the model nonparametric estimation of the regression frontier is obtained using a local linear estimator that is shown to be consistent and nh n asymptotically normal under standard assumptions the estimator we propose envelops the data but is not inherently biased as free disposal hull fdh or data envelopment analysis dea estimators it is also more robust to extreme values than the aforementioned estimators a monte carlo study is performed to provide preliminary evidence on the estimator s finite sample properties and to compare its performance to a bias corrected fdh estimator

environmental factors in frontier estimation a monte carlo analysis we compare three recently developed frontier estimators namely the conditional dea daraio and simar 2005 2007b the latent class sfa greene 2005 orea and kumbhakar 2004 and the stonezd approach johnson and kuosmanen 2011 by means of monte carlo simulation we focus on their ability to identify production frontiers and efficiency rankings in the presence of environmental factors our simulations match features of real life datasets and cover a wide range of scenarios with variations in sample size distribution of noise and inefficiency as well as in distributions intensity and number of environmental variables our results provide insight in the finite sample properties of the estimators while also identifying estimator specific characteristics overall the latent class approach is found to perform best although in many cases stonezd shows a similar performance performance of cdea is most often inferior

geometric mean quantity index numbers with benefit of the doubt weights abstract geometric mean index numbers are a multiplicative aggregation of price or quantity ratios with their importance exponents weights derived from one or more observed budget shares in the specific context of composite indicator construction we propose to use the budget shares as naturally generated by the linear benefit of the doubt model this approach is directly inspired by the literature on index number theory our basic model is easily extended to provide transitive composite indicator orderings in a multilateral setting also a multi factor decomposition is proposed to explain the intertemporal evolution of a single entity we illustrate our results with social inclusion data for the eu countries

non linear vibration of beams with internal resonance by the hierarchical finite element method the hierarchical nite element hfem and the harmonic balance methods hbm are used to investigate the geometrically non linear free and steady state forced vibrations of uniform slender beams the beam analogue of von kah rmah n s non linear strain displacement relationships are employed and the middle plane in plane displacements are included in the model the equations of motion are developed by applying the principle of virtual work and are solved by a continuation method 1 3 and 1 5 internal resonances are discovered and their consequences are discussed the convergence properties of the hfem are analyzed and it is demonstrated that the hfem model requires far fewer degrees of freedom than the h version of the fem models presented in the literature 1999 academic press

non parametric tests of productive efficiency with errors in variables we develop a non parametric test of productive efficiency that accounts for errors in variables following the approach of varian 1985 nonparametric analysis of optimizing behavior with measurement error journal of econometrics 30 1 2 445 458 the test is based on the general pareto koopmans notion of efficiency and does not require price data statistical inference is based on the sampling distribution of the l norm of errors the test statistic can be computed using a simple enumeration algorithm the finite sample properties of the test are analyzed by means of a monte carlo simulation using real world data of large eu commercial banks

optimal bandwidth selection for conditional efficiency measures a data driven approach in productivity analysis an important issue is to detect how external environmental factors exogenous to the production process and not under the control of the producer might in uence the production process and the resulting efficiency of the rms most of the traditional approaches proposed in the literature have serious drawbacks an alternative approach is to describe the production process as being conditioned by a given value of the environmental variables cazals florens and simar 2002 daraio and simar 2005 this de nes conditional efficiency measures where the production set in the input output space may depend on the value of the external variables the statistical properties of nonparametric estimators of these conditional measures are now established jeong park and simar 2008 these involve the estimation of a nonstandard conditional distribution function which requires the speci cation of a smoothing parameter a bandwidth so far only the asymptotic optimal order of this bandwidth has been established this is of little interest for the practitioner in this paper we ll this gap and we propose a data driven technique for selecting this parameter in practice the approach based on a least squares cross validation procedure lscv provides an optimal bandwidth that minimizes an appropriate weighted integrated squared error ise the method is carefully described and exempli ed with some simulated data with univariate and multivariate environmental factors an application on real data performances of mutual funds illustrates how this new optimal method of bandwidth selection works in practice

probabilistic characterization of directional distances and their robust versions in productivity analysis the performance of production units is measured through the distance of the individual decision making units dmu to the technology which is defined as the frontier of the production set most of the existing methods farrell debreu and shephard radial measures input or output oriented and hyperbolic distance functions rely on multiplicative measures of the distance and so require to deal with strictly positive inputs and outputs this can be critical when the data contain zero or negative values as in financial data bases for the measure of funds performances directional distance function is an alternative that can be viewed as an additive measure of e ciency we show in this paper that using a probabilistic formulation of the production process the directional distance can be expressed as simple radial or hyperbolic distance up to a simple transformation of the inputs outputs space this allows to propose simple methods of estimation but also to transfer easily most of the known properties of the estimators shared by the radial and hyperbolic distances in addition the formulation allows to define robust directional distances in the lines of quantileor order m partial frontiers finally we can also define conditional directional distance functions conditional to environmental factors to illustrate the methodology we show how it can be implemented using a mutual funds database

robustness and inference in nonparametric partial frontier modeling abstract a major aim in recent nonparametric frontier modeling is to estimate a partial frontier well inside the sample of production units but near the optimal boundary two concepts of partial boundaries of the production set have been proposed an expected maximum output frontier of order m 1 2 and a conditional quantile type frontier of order 0 1 in this paper we answer the important question of how the two families are linked for each m we specify the order for which both partial production frontiers can be compared we show that even one perturbation in data is sufficient for breakdown of the nonparametric order m frontiers whereas the global robustness of the order frontiers attains a higher breakdown value nevertheless once the frontiers break down they become less resistant to outliers than the order m frontiers moreover the m frontiers have the advantage to be statistically more efficient based on these findings we suggest a methodology for identifying outlying data points we establish some asymptotic results contributing to important gaps in the literature the theoretical findings are illustrated via simulations and real data

stochastic non convex envelopment of data applying isotonic regression to frontier estimation abstract isotonic nonparametric least squares inls is a regression method for estimating a monotonic function by fitting a step function to data in the literature of frontier estimation the free disposal hull fdh method is similarly based on the minimal assumption of monotonicity in this paper we link these two separately developed nonparametric methods by showing that fdh is a sign constrained variant of inls we also discuss the connections to related methods such as data envelopment analysis dea and convex nonparametric least squares cnls further we examine alternative ways of applying isotonic regression to frontier estimation analogous to corrected and modified ordinary least squares cols mols methods known in the parametric stream of frontier literature we find that inls is a useful extension to the toolbox of frontier estimation both in the deterministic and stochastic settings in the absence of noise the corrected inls cinls has a higher discriminating power than fdh in the case of noisy data we propose to apply the method of non convex stochastic envelopment of data non convex stoned which disentangles inefficiency from noise based on the skewness of the inls residuals the proposed methods are illustrated by means of simulated examples