generalised weak disposability and efficiency measurement in environmental technologies abstract weak disposability based models of environmental technologies typically assume equiproportionate trade offs between desired and undesired outputs we postulate a generalised version of weak disposability allowing for different types of trade offs between good and bad outputs and derive a new technology called piecewise cobb douglas environmental technology whose envelopments capture all three types of production structures concavity linearity and convexity to measure environmental performance with reference to this technology we develop radial and non radial directional hyperbolic distance functions we demonstrate that the value of these functions can be simply computed via the directional distance function as linear programs we use data from 112 us power plants to illustrate our approach

amenability properties of the centres of group algebras abstract let g be a locally compact group and zl 1 g be the centre of its group algebra we show that when g is compact zl 1 g is not amenable when g is either non abelian and connected or is a product of infinitely many finite non abelian groups we also study for some non compact groups g some conditions which imply amenability and hyper tauberian property for zl 1 g

a comparison of parametric and non parametric distance functions with application to european railways abstract in this paper we use multi output distance functions to investigate technical inefficiency in european railways the principle aim of the paper is to compare the results obtained from the three alternative methods of estimating multi output distance functions namely the construction of a parametric frontier using linear programming data envelopment analysis dea and corrected ordinary least squares cols input orientated output orientated and constant returns to scale crs distance functions are estimated and compared the results indicate a strong degree of correlation between the input and output orientated results for each of the three methods there are also significant correlations observed between the results obtained using the alternative estimation methods the strongest correlations being between the parametric linear programming and the cols methods finally the paper concludes with the suggestion that a combination of the technical efficiency scores obtained from the three different methods be used as the preferred set of scores this idea is borrowed from the time series forecasting literature

nonparametric least squares estimation of a multivariate convex regression function this paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional we characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs mild sufficient conditions for the consistency of this estimator and its subdifferentials in fixed and stochastic design regression settings are provided we also consider a regression function which is known to be convex and componentwise nonincreasing and discuss the characterization computation and consistency of its least squares estimator

generalized quadratic revenue functions abstract in this paper we focus on the specification of revenue functions in their dual price space we consider two distance functions the shephard output distance function and the directional output distance function and define both in price space the former is multiplicative in nature and satisfies homogeneity whereas the latter is additive and satisfies the translation property functional equation methods yield the translog specification in the case of the shephard distance function and a quadratic specification in the case of the directional distance function monte carlo evidence suggests that the quadratic specification outperforms the translog in large samples and in true models with plenty of curvature

non parametric hypothesis testing procedures and applications to demand analysis abstract this paper proposes a test of the hypothesis that a possibly vector valued regression function g lies in a particular compact family of functions f where f is not necessarily a finite dimensional parametric family under the assumption of a known covariance matrix of the errors the test is shown to be consistent for a broad range of alternatives and an upper bound on the significance level is established it is shown how the test may be used to test the utility maximization hypothesis and homotheticity and the paper indicates how to apply the test to a broad range of other non parametric hypotheses

exponential distance function and duality theory abstract charnes cooper seiford and stutz 1982 1983 and banker and maindiratta 1986 suggested multiplicative radial measures for efficiency gauging more recently peyrache and coelli 2009 presented a multiplicative directional distance function that was elaborated by mehdiloozad sahoo and roshdi 2014 in this paper we extend these studies and propose an exponential approach based upon a new exponential distance function endowed with a multiplicative production structure the main purposes of this paper are twofold one is to provide a general production theoretic basis for the approach and the other is to extend it to a nonparametric framework the first purpose is accomplished as follows 1 the exponential distance function is formally defined and its properties are established 2 it is shown how the exponential distance function is characterized under a napierian technology 3 a duality relationship between napierian profit and the exponential distance functions is established 4 shadow prices of inputs and outputs are derived based on the napierian technology the second purpose is accomplished by providing nonparametric programming extensions which include data envelopment analysis dea models productivity indexes and returns to scale models here the efficacy of our nonparametric theoretical results is demonstrated by applying dea to the data on accommodation establishments in oecd

revealed preference tests for weak separability an integer programming approach we present the revealed preference conditions that characterize the data sets that are consistent with the maximization of a weakly separable utility function we show that verifying these revealed preference conditions is np hard we also present an integer programming approach which is particularly attractive in view of empirical analysis we demonstrate the versatility of this integer programming approach by showing that it allows for testing homothetic separability and weak separability of the indirect utility function we illustrate the practical usefulness of the approach by an empirical application to spanish household consumption data

globally flexible functional forms the neural distance function the output distance function is a key concept in economics however its empirical estimation often violates properties dictated by neoclassical production theory in this paper we introduce the neural distance function ndf which constitutes a global approximation to any arbitrary production technology with multiple outputs given by a neural network nn specification the ndf imposes all theoretical properties such as monotonicity curvature and homogeneity for all economically admissible values of outputs and inputs fitted to a large data set for all us commercial banks 1989 2000 the ndf explains a very high proportion of the variance of output while keeping the number of parameters to a minimum and satisfying the relevant theoretical properties all measures such as total factor productivity tfp and technical efficiency te are computed routinely next the ndf is compared with the translog popular specification and is found to provide very satisfactory results as it possesses the properties thought as desirable in neoclassical production theory in a way not matched by its competing specification

identification and nonparametric estimation of a transformed additively separable model let r x z be a function that along with its derivatives can be consistently estimated nonparametrically this paper discusses the identification and consistent estimation of the unknown functions h m g and f where r x z h m x z m x z g x f z and h is strictly monotonic an estimation algorithm is proposed for each of the model s unknown components when r x z represents a conditional mean function the resulting estimators use marginal integration to separate the components g and f our estimators are shown to have a limiting normal distribution with a faster rate of convergence than unrestricted nonparametric alternatives their small sample performance is studied in a monte carlo experiment we apply our results to estimate generalized homothetic production functions for four industries in the chinese economy

generalized additive and index models with shape constraints summary we study generalized additive models with shape restrictions e g monotonicity convexity and concavity imposed on each component of the additive prediction function we show that this framework facilitates a non parametric estimator of each additive component obtained by maximizing the likelihood the procedure is free of tuning parameters and under mild conditions is proved to be uniformly consistent on compact intervals more generally our methodology can be applied to generalized additive index models here again the procedure can be justified on theoretical grounds and like the original algorithm has highly competitive finite sample performance practical utility is illustrated through the use of these methods in the analysis of two real data sets our algorithms are publicly available in the r package scar short for shape constrained additive regression

lp fourier and fourier stieltjes algebras for locally compact groups abstract let g be a locally compact group and 1 p a continuous unitary representation g b h of g is an l p representation if the matrix coefficient functions s s x x lie in l p g for sufficiently many x h the l p fourier algebra a l p g is defined to be the set of matrix coefficient functions of l p representations similarly the l p fourier stieltjes algebra b l p g is defined to be the weak closure of a l p g in the fourier stieltjes algebra b g these are always ideals in the fourier stieltjes algebra containing the fourier algebra a g in this paper we investigate how these spaces reflect properties of the underlying group and study the structural properties of these algebras as an application of this theory we characterize the fourier stieltjes ideals of sl 2 r

a superlative indicator for the luenberger hicks moorsteen productivity indicator theory and application abstract consisting of the difference between an output indicator and an input indicator the luenberger hicks moorsteen lhm productivity indicator allows straightforward interpretation however its computation requires estimating distance functions that are inherently unknown this paper shows that a computationally simple bennet indicator is a superlative indicator for the lhm indicator when one can assume profit maximizing behavior and the input and output directional distance functions can be represented up to the second order by a quadratic functional form we also show that the luenberger and lhm approximating bennet indicators coincide for an appropriate choice of directional vectors focusing on a large sample of italian food and beverages companies for the years 1995 2007 we empirically investigate the extent to which this theoretical equivalence translates into similar estimates we find that the bennet indicator is a close empirical alternative to the lhm indicator for the sample

hyper tauberian algebras and weak amenability of figa talamanca herz algebras abstract we study certain commutative regular semisimple banach algebras which we call hyper tauberian algebras we first show that they form a subclass of weakly amenable tauberian algebras then we investigate the basic and hereditary properties of them moreover we show that if a is a hyper tauberian algebra then the linear space of bounded derivations from a into any banach a bimodule is reflexive we apply these results to the figa talamanca herz algebra a p g of a locally compact group g for p 1 we show that a p g is hyper tauberian if the principal component of g is abelian finally by considering the quantization of these results we show that for any locally compact group g a p g equipped with an appropriate operator space structure is a quantized hyper tauberian algebra this in particular implies that a p g is operator weakly amenable

orthogonally additive polynomials on banach function algebras abstract for a banach function algebra a we consider the problem of representing a continuous d homogeneous polynomial p a x where x is an arbitrary banach space that satisfies the property p f g p f p g whenever f g a are such that supp f supp g we show that such a polynomial can be represented as p f t f d f a for some continuous linear map t a x for a variety of banach function algebras such as the algebra of continuous functions c 0 for any locally compact hausdorff space the algebra of lipschitz functions lip k for any compact metric space k and 0 1 the figa talamanca herz algebra a p g for some locally compact groups g and p 1 the algebras a c a b and b v c a b of absolutely continuous functions and of continuous functions of bounded variation on the interval a b in the case where a c n a b p can be represented as p f t n 1 n d f n 1 f n d where the sum is taken over n 1 n d z d with 0 n 1 n d n for appropriate continuous linear maps t n 1 n d c n n d a b x

weak amenability of fourier algebras and local synthesis of the anti diagonal abstract we show that for a connected lie group g its fourier algebra a g is weakly amenable only if g is abelian our main new idea is to show that weak amenability of a g implies that the anti diagonal g g g 1 g g is a set of local synthesis for a g g we then show that this cannot happen if g is non abelian we conclude for a locally compact group g that a g can be weakly amenable only if it contains no closed connected non abelian lie subgroups in particular for a lie group g a g is weakly amenable if and only if its connected component of the identity g e is abelian

the influence curve approach in data envelopment analysis the behavior of efficiency in the stochastic dea model is examined here in terms of the influence curve approach which quantifies the influence of observed data on the empirical fit of the production frontier data influence is analyzed here through robustness two types of robustness and sensitivity issues are analyzed here in terms of a a new class of minimax measures and b a set nonlinear efficiency measures and it is shown through empirical applications that in suitable cases these measures outperform the conventional ones

technical efficiency estimation with multiple inputs and multiple outputs using regression analysis regression and linear programming provide the basis for popular techniques for estimating technical efficiency regression based approaches are typically parametric and can be both deterministic or stochastic where the later allows for measurement error in contrast linear programming models are nonparametric and allow multiple inputs and outputs the purported disadvantage of the regression based models is the inability to allow multiple outputs without additional data on input prices in this paper deterministic cross sectional and stochastic panel data regression models that allow multiple inputs and outputs are developed notably technical efficiency can be estimated using regression models characterized by multiple input multiple output environments without input price data we provide multiple examples including a monte carlo analysis

sensitivity analysis of efficiency scores how to bootstrap in nonparametric frontier models efficiency scores of production units are generally measured relative to an estimated pro duction frontier nonparametric estimators dea fdh are based on a finite sample of observed production units the bootstrap is one easy way to analyze the sensitivity of efficiency scores relative to the sampling variations of the estimated frontier the main point in order to validate the bootstrap is to define a reasonable data generating process in this complex framework and to propose a reasonable estimator of it this paper provides a general methodology of bootstrapping in nonparametric frontier models some adapted methods are illustrated in analyzing the bootstrap sampling variations of input efficiency measures of electricity plants

a canonical process for estimation of convex functions the invelope of integrated brownian motion t4 a process associated with integrated brownian motion is introduced that characterizes the limit behavior of nonparametric least squares and maximum likelihood estimators of convex functions and convex densities respectively we call this process the invelope and show that it is an almost surely uniquely defined function of integrated brownian motion its role is comparable to the role of the greatest convex minorant of brownian motion plus a parabolic drift in the problem of estimating monotone functions an iterative cubic spline algorithm is introduced that solves the constrained least squares problem in the limit situation and some results obtained by applying this algorithm are shown to illustrate the theory

multivariate convex regression with adaptive partitioning we propose a new nonparametric method for multivariate regression subject to convexity or concavity constraints on the response function convexity constraints are common in economics statistics operations research financial engineering and optimization but there is currently no multivariate method that is stable and computationally feasible for more than a few thousand observations we introduce convex adaptive partitioning cap which creates a globally convex regression model from locally linear estimates fit on adaptively selected covariate partitions cap is a computationally efficient consistent method for convex regression we demonstrate empirical performance by comparing the performance of cap to other shape constrained and unconstrained regression methods for predicting weekly wages and value function approximation for pricing american basket options

operator space structure and amenability for figa talamanca herz algebras column and row operator spaces which we denote by col and row respectively over arbitrary banach spaces were introduced by the first named author for hilbert spaces these definitions coincide with the usual ones given a locally compact group g and p p 1 with 1p 1p 1 we use the operator space structure on cb col lp g to equip the figa talamanca herz algebra ap g with an operator space structure turning it into a quantized banach algebra moreover we show that for p q 2 or 2 q p and amenable g the canonical inclusion aq g ap g is completely bounded with cb norm at most kg2 where kg is grothendieck s constant as an application we show that g is amenable if and only if ap g is operator amenable for all and equivalently for one p 1 this extends a theorem by ruan

one stage and two stage dea estimation of the effects of contextual variables abstract two stage data envelopment analysis 2 dea is commonly used in productive efficiency analysis to estimate the effects of operational conditions and practices on performance in this method the dea efficiency estimates are regressed on contextual variables representing the operational conditions we re examine the statistical properties of the 2 dea estimator and find that it is statistically consistent under more general conditions than earlier studies assume we further show that the finite sample bias of dea in the first stage carries over to the second stage regression causing bias in the estimated coefficients of the contextual variables this bias is particularly severe when the contextual variables are correlated with inputs to address this shortcoming we apply the result that dea can be formulated as a constrained special case of the convex nonparametric least squares cnls regression applying the cnls formulation we develop a new semi nonparametric one stage estimator for the coefficients of the contextual variables that directly incorporates contextual variables to the standard dea problem the proposed method is hence referred to as one stage dea 1 dea evidence from monte carlo simulations suggests that the new 1 dea estimator performs systematically better than the conventional 2 dea estimator both in deterministic and noisy scenarios

an improved afriat diewert parkan nonparametric production function estimator abstract recent developments in the production frontier literature include nonparametric estimators with shape constraints a few of these estimators rely on the afriat inequalities to provide piecewise linear approximations to the production function frontier we show in this paper that these afriat diewert parkan adp estimators have deficiencies in the presence of moderate statistical noise including overfitting and a relatively high estimator variance we propose new estimators with lower variance and a relatively low bias we consider such alternative estimators based on weighted averages of random hinge functions with parameter restrictions small sample properties of the estimators are presented that show our new estimators outperform the existing adp estimators when moderate to large amounts of noise are present

bayesian measurement of productivity and efficiency in the presence of undesirable outputs crediting electric utilities for reducing air pollution abstract many studies have measured productivity change and efficiency when an undesirable output is a by product we flexibly treat the bad as a technology shifter of an input distance function and model a system of nonlinear equations subject to endogeneity theory dictates that we impose monotonicity on all inputs outputs and the bad since a bayesian full information likelihood approach can easily be misspecified we utilize the kim j econometrics 107 2002 175 limited information likelihood lil derived by minimizing the entropy distance subject to the moment conditions from the generalized method of moments gmm estimator this represents an extension of the bayesian method of moments approach of zellner and chen macroeconom dyn 5 2001 673 zellner and tobias int econom rev 42 2001 121 and zellner in bayesian analysis in econometrics and statistics the zellner view and papers edward elgar cheltenham 1997 j econometrics 83 1998 185 which uses entropy maximization but does not incorporate a specific likelihood using bayes theorem we combine traditional priors with the lil which has a mode at the standard multiple equation gmm estimator yielding a limited information posterior distribution we generalize the approach of kim j econometrics 107 2002 175 by incorporating an unknown covariance matrix in a gibbs sampling framework and applying the methodology to nonlinear equations this allows us to estimate shadow prices technical efficiency and productivity change for a panel of electric utilities yielding results that differ substantially from those obtained using standard gmm

notes on technical efficiency estimation with multiple inputs and outputs collier johnson and ruggiero 2011 deal with the problem of estimating technical efficiency using regression analysis that allows multiple inputs and outputs this revives an old problem in the analysis of production in this note we provide an alternative maximum likelihood estimator that addresses the concerns a monte carlo experiment shows that the technique works well in practice a test for homotheticity a critical assumption in collier johnson and ruggiero 2011 is constructed and its behavior is examined using monte carlo simulation and an empirical application to european banking

a computational framework for multivariate convex regression and its variants we study the nonparametric least squares estimator lse of a multivariate convex regression function the lse given as the solution to a quadratic program with o n2 linear constraints n being t

directional distance functions and slacks based measures of efficiency abstract in this paper we introduce a sbm slacks based measure of efficiency based on directional distance functions this measure is contrasted with the sbm due to professor tone tone k 2001 a slacks based measure of efficiency in data envelopment analysis european journal of operational research 130 498 509

global approximation to arbitrary cost functions a bayesian approach with application to us banking this paper proposes and estimates a globally flexible functional form for the cost function which we call neural cost function ncf the proposed specification imposes a priori and satisfies globally all the properties that economic theory dictates the functional form can be estimated easily using markov chain monte carlo mcmc techniques or standard iterative sure we use a large panel of u s banks to illustrate our approach the results are consistent with previous knowledge about the sector and in accordance with mathematical production theory

a reliable data based bandwidth selection method for kernel density estimation we present a new method for data based selection of the bandwidth in kernel density estimation which has excellent properties it improves on a recent procedure of park and marron which itself is a good method in various ways first the new method has superior theoretical performance second it also has a computational advantage third the new method has reliably good performance for smooth densities in simulations performance that is second to none in the existing literature these methods are based on choosing the bandwidth to approximately minimize good quality estimates of the mean integrated squared error the key to the success of the current procedure is the reintroduction of a non stochastic term which was previously omitted together with use of the bandwidth to reduce bias in estimation without inflating variance

statistical inference for dea estimators of directional distances in productivity and efficiency analysis the technical efficiency of a production unit is measured through its distance to the efficient frontier of the production set the most familiar non parametric methods use farrell debreu shephard or hyperbolic radial measures these approaches require that inputs and outputs be non negative which can be problematic when using financial data recently chambers et al 1998 have introduced directional distance functions which can be viewed as additive rather than multiplicative measures efficiency directional distance functions are not restricted to non negative input and output quantities in addition the traditional input and output oriented measures are nested as special cases of directional distance functions consequently directional distances provide greater flexibility however until now only free disposal hull fdh estimators of directional distances and their conditional and robust extensions have known statistical properties simar and vanhems 2012 this paper develops the statistical properties of directional d estimators which are especially useful when the production set is assumed convex we first establish that the directional data envelopment analysis dea estimators share the known properties of the traditional radial dea estimators we then use these properties to develop consistent bootstrap procedures for statistical inference about directional distance estimation of confidence intervals and bias correction the methods are illustrated in some empirical examples

how to generate regularly behaved production data a monte carlo experimentation on dea scale efficiency measurement abstract monte carlo experimentation is a well known approach used to test the performance of alternative methodologies under different hypotheses in the frontier analysis framework whatever the parametric or non parametric methods tested experiments to date have been developed assuming single output multi input production functions the data generated have mostly assumed a cobb douglas technology among other drawbacks this simple framework does not allow the evaluation of dea performance on scale efficiency measurement the aim of this paper is twofold on the one hand we show how reliable two output two input production data can be generated using a parametric output distance function approach a variable returns to scale translog technology satisfying regularity conditions is used for this purpose on the other hand we evaluate the accuracy of dea technical and scale efficiency measurement when sample size and output ratios vary our monte carlo experiment shows that the correlation between true and estimated scale efficiency is dramatically low when dea analysis is performed with small samples and wide output ratio variations

quantile stochastic frontiers abstract in this paper based on jradi and ruggiero 2019 stochastic data envelopment analysis a quantile regression approach to estimate the production frontier european journal of operational research 278 2 385 393 we propose a novel quantile stochastic frontier model sfm and develop markov chain monte carlo techniques for numerical bayesian inference in an empirical application to us large banks we document important differences between the quantile and the traditional sfm in terms of several aspects of the data we also document considerable heterogeneity among different quantiles in terms of returns to scale technical change efficiency change technical efficiency as well as productivity growth

using information about technologies markets and firm behaviour to decompose a proper productivity index this paper uses distance functions to define new output and input quantity indexes that satisfy important axioms from index number theory e g identity transitivity proportionality and time space reversal dividing the output index by the input index yields a new productivity index that can be decomposed into a measure of technical change a measure of environmental change and several measures of efficiency change a problem with this new index is that it cannot be computed without estimating the production frontier the paper shows how assumptions concerning technologies markets and firm behaviour can be used to inform the estimation process the focus is on the asymptotic properties of least squares estimators when the explanatory variables in the production frontier model are endogenous in this case the ordinary least squares estimator is usually inconsistent however there is one situation where it is super consistent a fully modified ordinary least squares estimator is also available in this case to illustrate the main ideas the paper uses us state level farm data to estimate a stochastic production frontier the parameter estimates are then used to obtain estimates of the economically relevant components of productivity change

estimating nonparametric convex functions using gradient data abstract the estimation and use of nonparametric convex functions has been discussed in the recent literature where it is assumed that the data used in the estimation consists of a sample of observations of the convex function however an important additional or alternative source of data consists of observations on the sub gradient of the function in the present paper we discuss how to use such sub gradient data to estimate nonparametric functions this a allows us to estimate nonparametric convex functions when other point observation data is unavailable or unobservable or unreliable or costly to obtain b allows us an alternative even when other point observation data is available and c allows us to improve our estimates by using both types of data together the resultant function estimators may not be unique hence we compute bounds on the convex set of estimators we also consider introducing other data in addition to the gradient data the discussion is illustrated by reference to estimating production functions benefit functions and demand functions

nonparametric option pricing under shape restrictions frequently economic theory places shape restrictions on functional relationships between economic variables this paper develops a method to constrain the values of the first and second derivatives of nonparametric locally polynomial estimators we apply this technique to estimate the state price density spd or risk neutral density implicit in the market prices of options the option pricing function must be monotonic and convex simulations demonstrate that nonparametric estimates can be quite feasible in the small samples relevant for day to day option pricing once appropriate theory motivated shape restrictions are imposed using s p 500 option prices we show that unconstrained nonparametric estimators violate the constraints during more than half the trading days in 1999 unlike the constrained estimator we propose

nonparametric tests of regularity farrell efficiency and goodness of fit abstract the goal of this paper is to reveal the links among several seemingly unrelated literatures 1 1 the nonparametric regularity test literature see afriat 1972 diewert and parkan 1983 hanoch and rothschild 1972 varian 1984 2 2 the efficiency measurement literature farrell 1957 is the classic reference but also included is what has been dubbed data envelopment analysis and 3 3 the goodness of fit approach associated with varian 1990 the unifying threads are the shephard type distance function and the mahler inequality mahler 1939 our synthesis yields regularity tests of cost minimization and technical change which are nonparametric yet provide information as to goodness of fit based on farrell type efficiency measures

linear production functions and the data envelopment analysis abstract this paper shows that the data envelopment analysis or farrell method is not nonparametric in the sense that the method implicitly employs linear production functions frontiers to measure efficiency deriving positive multiplier linear production frontiers and grouping the dmus by their corresponding frontiers can simplify the estimation procedures when there are new dmus included and can easily determine how many inputs should be reduced or and how many outputs should be increased to make an inefficient dmu efficiently this procedure can also circumvent the problems of the non archimedean infinitesmal in the ccr literature it is also shown that because of the linear production functions both banker s and the banker charnes cooper methods fail in testing for returns to scale

measurement of technical inefficiency and total factor productivity growth a semiparametric stochastic input distance frontier approach and the case of lithuanian dairy farms abstract this paper presents a four component stochastic frontier model in which the frontier function is represented by an unknown smooth input distance function and inefficiency is decomposed into persistent and transient inefficiencies furthermore the pre truncation mean and variance of the transient inefficiency are functions of the environmental variables by differentiating the four component input distance frontier with respect to the time trend total factor productivity tfp growth is estimated under the semiparametric smooth coefficient framework and is decomposed into six components i e technical change scale component allocative component external component efficiency change and residual component the empirical example focuses on the lithuanian dairy sector with multiple outputs our results show that there are some persistent and transient inefficiencies in lithuanian dairy farms however these farms maintained tfp growth of 2 per annum on average during 2004 2016 and much of it is attributed to the technical change and scale components

a homothetic reference technology in data envelopment analysis abstract the assumption of a homothetic production function is often maintained in production economics in this paper we explore the possibility of maintaining homotheticity within a nonparametric dea framework the main contribution of this paper is to use the approach suggested by hanoch and rothschild 1972 to define a homothetic reference technology we focus on the largest subset of data points that is consistent with such a homothetic production function we use the hr approach to define a piecewise linear homothetic convex reference technology we propose this reference technology with the purpose of adding structure to the flexible non parametric bcc dea estimator motivation for why such additional structure sometimes is warranted is provided an estimation procedure derived from the bcc model and from a maintained assumption of homotheticity is proposed the performance of the estimator is analyzed using simulation

maximum likelihood consistency and data envelopment analysis a statistical foundation this paper provides a formal statistical basis for the efficiency evaluation techniques of data envelopment analysis dea dea estimators of the best practice monotone increasing and concave production function are shown to be also maximum likelihood estimators if the deviation of actual output from the efficient output is regarded as a stochastic variable with a monotone decreasing probability density function while the best practice frontier estimator is biased below the theoretical frontier for a finite sample size the bias approaches zero for large samples the dea estimators exhibit the desirable asymptotic property of consistency and the asymptotic distribution of the dea estimators of inefficiency deviations is identical to the true distribution of these deviations this result is then employed to suggest possible statistical tests of hypotheses based on asymptotic distributions

local derivations and local automorphisms in this paper we show that if l is a completely distributive commutative subspace lattice or a j subspace lattice then the space of all bounded derivations of algl is reflexive we also study when local automorphisms on some algebras are automorphisms

dea with efficiency classification preserving conditional convexity abstract we propose to relax the standard convexity property used in data envelopment analysis dea by imposing additional qualifications for feasibility of convex combinations we specifically focus on a condition that preserves the koopmans efficiency classification this yields an efficiency classification preserving conditional convexity property which is implied by both monotonicity and convexity but not conversely substituting convexity by conditional convexity we construct various empirical dea approximations as the minimal sets that contain all dmus and are consistent with the imposed production assumptions imposing an additional disjunctive constraint to standard convex dea formulations can enforce conditional convexity computation of efficiency measures relative to conditionally convex production set can be performed through disjunctive programming dp

consistency of multidimensional convex regression convex regression is concerned with computing the best fit of a convex function to a data set of n observations in which the independent variable is possibly multidimensional such regression problems arise in operations research economics and other disciplines in which imposing a convexity constraint on the regression function is natural this paper studies a least squares estimator that is computable as the solution of a quadratic program and establishes that it converges almost surely to the true function as n under modest technical assumptions in addition to this multidimensional consistency result we identify the behavior of the estimator when the model is misspecified so that the true function is nonconvex and we extend the consistency result to settings in which the function must be both convex and nondecreasing as is needed for consumer preference utility functions

the weighted additive distance function abstract distance functions in production theory are mathematical structures that characterize the belonging to the reference technology through a numerical value behave as technical efficiency measures when the focus is analyzing an observed input output vector within its production possibility set and present a dual relationship with some support function profit revenue cost function in this paper we endow the well known weighted additive models in data envelopment analysis with a distance function structure introducing the weighted additive distance function and showing its main properties

directional distance functions optimal endogenous directions a substantial literature has dealt with the problem of estimating multiple input and multiple output production functions where inputs and outputs can be good and bad numerous studies can be found in the areas of productivity analysis industrial organization labor economics and health economics while many papers have estimated the more restrictive output and input oriented distance functions here we estimate a more general directional distance function a seminal paper on directional distance functions by chambers 1998 as well as papers by fare et al 1997 chambers et al 1998 fare and grosskopf 2000 grosskopf 2003 fare et al 2005 and hudgins and primont 2007 do not address the issue of how to choose an optimal direction set typically the direction is arbitrarily selected to be 1 for good outputs and 1 for inputs and bad outputs by estimating the directional distance function together with the first order conditions for cost minimization and profit maximization using bayesian methods we are able to estimate optimal firm specific directions for each input and output which are consistent with allocative and technical efficiency we apply these methods to an electric utility panel data set which contains firm specific prices and quantities of good inputs and outputs as well as the quantities of bad inputs and outputs estimated firm specific directions for each input and output are quite different from those normally assumed in the literature the computed firm specific technical efficiency technical change and productivity change based on estimated optimal directions are substantially higher than those calculated using fixed directions

semiparametric stochastic frontier models a generalized additive model approach abstract the choice of the functional form of the frontier into a stochastic frontier model is typically neglected in applications and canonical functions are usually considered this paper introduces a semiparametric approach for stochastic frontier estimation that extends previous works based on pseudo likelihood estimators allowing flexibility in model selection and capability of imposing monotonicity and concavity constraints for these purposes the present work introduces a generalized additive framework that moreover permits to model the influence of contextual environmental factors to the hypothesized production process by the relative extension given by generalized additive models for location scale and shape through some monte carlo simulations and an application to european agricultural data the flexibility of the proposed framework in analyzing efficiency is illustrated

inhomogeneous markov approach to percolation theory based propagation in random media in recent years it has been shown that ray propagation in two dimensional 2d uniform random percolation lattices is well approximated by stochastic processes two of the probabilistic interpretations can be solved exactly but impose some additional restrictions on the ray dynamics the 1999 model by g franceschetti demands that ray reflections inside the lattice are independent and identically distributed iid and the 2006 model by a martini assumes that for the analysis of vertical ray penetration reflections on vertical lattice cell faces can be neglected in this paper we present a 2d generalization of the 1999 model that does not rely on the iid assumption it is based on a set of coupled iteration formulas for right stochastic matrices that describe a time inhomogeneous markov process upon expanding the space of transition states the iterative process can be recast in the projection of a time homogeneous markov chain thus the perron frobenius theorem can be applied to analyze the stationary states of the process which leads to a simple analytical expression for the probability of a ray ensemble reaching a specified lattice level after infinitely many reflections we discuss different boundary conditions at the absorbing barriers of the ray propagation process and show that 1 by imposing the iid assumption the 1999 model by g francescetti can be recovered and 2 a one dimensional reduction of the approach exactly leads to the 2006 model by a martini the presented stochastic approach provides a framework in which basic assumptions of probabilistic interpretations of percolation theory based ray propagation can be studied in some detail it also allows for the consistent derivation of the stationary probability states which are needed to apply the approach to a wider range of phenomena such as internal source ray propagation in both uniform and nonuniform random media

estimation and confidence regions for parameter sets in econometric models this paper develops a framework for performing estimation and inference in econometric models with partial identification focusing particularly on models characterized by moment inequalities and equalities applications of this framework include the analysis of game theoretic models revealed preference restrictions regressions with missing and corrupted data auction models structural quantile regressions and asset pricing models specifically we provide estimators and confidence regions for the set of minimizers i of an econometric criterion function q in applications the criterion function embodies testable restrictions on economic models a parameter value that describes an economic model satisfies these restrictions if q attains its minimum at this value interest therefore focuses on the set of minimizers called the identified set we use the inversion of the sample analog q n of the population criterion q to construct estimators and confidence regions for the identified set and develop consistency rates of convergence and inference results for these estimators and regions to derive these results we develop methods for analyzing the asymptotic properties of sample criterion functions under set identification

data envelopment analysis as nonparametric least squares regression data envelopment analysis dea is known as a nonparametric mathematical programming approach to productive efficiency analysis in this paper we show that dea can be alternatively interpreted as nonparametric least squares regression subject to shape constraints on the frontier and sign constraints on residuals this reinterpretation reveals the classic parametric programming model by aigner and chu aigner d s chu 1968 on estimating the industry production function amer econom rev 58 826 839 as a constrained special case of dea applying these insights we develop a nonparametric variant of the corrected ordinary least squares cols method we show that this new method referred to as corrected concave nonparametric least squares c2nls is consistent and asymptotically unbiased the linkages established in this paper contribute to further integration of the econometric and axiomatic approaches to efficiency analysis

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

on endogenizing direction vectors in parametric directional distance function based models abstract empirical studies of production technologies using directional distance functions have traditionally resorted to ad hoc ways of choosing direction vectors for these functions yet it is well known that the assumptions placed on the direction vector can have a non negligible impact on the estimation results several recent studies have attempted to address this issue using econometric estimation and data envelopment analysis we demonstrate the use of parametric nonlinear programming to select the direction vector optimally data on the us electric power plants from early 2000s are used to show the difference between results obtained with endogenously determined direction vectors and ad hoc vectors

riemann manifold langevin and hamiltonian monte carlo methods the paper proposes metropolis adjusted langevin and hamiltonian monte carlo sampling methods defined on the riemann manifold to resolve the shortcomings of existing monte carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations the methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for metropolis hastings or indeed hamiltonian monte carlo and metropolis adjusted langevin algorithms this allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the markov chain the methodology proposed exploits the riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold providing highly efficient convergence and exploration of the target density the performance of these riemann manifold monte carlo methods is rigorously assessed by performing inference on logistic regression models log gaussian cox point processes stochastic volatility models and bayesian estimation of dynamic systems described by non linear differential equations substantial improvements in the time normalized effective sample size are reported when compared with alternative sampling approaches matlab code that is available from http www ucl ac uk statistics research rmhmc allows replication of all the results reported

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

estimating the hyperbolic distance function a directional distance function approach abstract fare grosskopf and lovell 1985 merged farrell s input and output oriented technical efficiency measures into a new graph type approach known as hyperbolic distance function hdf in spite of its appealing special structure in allowing for the simultaneous and equiproportionate reduction in inputs and increase in outputs hdf is a non linear optimization and it is hard to solve particularly when dealing with technologies operating under variable returns to scale by connecting hdf to the directional distance function we propose a linear programming based procedure for estimating the exact value of hdf within the non parametric framework of data envelopment analysis we illustrate the computational effectiveness of the algorithm on several real world and simulated data sets generating the optimal value of hdf through generally solving at most two linear programs moreover our approach has several desirable properties such as 1 introducing a computational dual formulation for the hdf and providing an economic interpretation in terms of shadow prices 2 being readily adaptable to measure hyperbolic oriented super efficiency and 3 being flexible to deal with hdf based efficiency measures on environmental technologies

stochastic estimation of firm technology inefficiency and productivity growth using shadow cost and distance functions it is well known that a firm s technology allocative efficiency technical efficiency and productivity growth can be estimated using a shadow cost system comprised of a shadow cost function and its share equations whose arguments are outputs and shadow input prices prices internal to the firm we provide a dual characterization to estimate these measures using a shadow distance system this system is comprised of a shadow distance function expressed in terms of shadow input quantities and output quantities plus the first order conditions from the cost minimization problem an advantage of the distance system over the cost system is that we obtain direct estimates of input inefficiency with the former but indirect estimates with the latter we also show how to express cost function derivatives in terms of distance function derivatives which allows calculation of returns to scale and price elasticities of demand from the estimated distance system using panel data on us electric utilities we estimate both systems and find a strong similarity between their associated measures

markov approach to percolation theory based propagation in random media for line of sight links in random media or urban areas propagation may be approximated through sequential reflections of an optical ray in a two dimensional medium of disordered lossless scatterers franceschetti approximated such percolation based optical ray propagation by a markov process with two absorbing barriers provided numerical solutions for the probability of a ray passing through the percolation lattice and solved both approximately and exactly a corresponding problem based on the theory of martingales in this paper we solve exactly the markov theoretical formulation of the problem and prove that both the markov and martingale approaches are equivalent our proof is an application of the perron frobenius theory which provides an elegant framework for the study of the asymptotic behavior of stochastic processes we demonstrate that for a wide range of vacancies and incident angles the exact solution of the markov theoretical formulation performs significantly better than the commonly used wald approximation in the martingale approach this has a number of implications on the accuracy of the model especially for low density propagation media

a bayesian approach to imposing curvature on distance functions the estimated parameters of output distance functions frequently violate the monotonicity quasi convexity and convexity constraints implied by economic theory leading to estimated elasticities and shadow prices that are incorrectly signed and ultimately to perverse conclusions concerning the effects of input and output changes on productivity growth and relative efficiency levels we show how a bayesian approach can be used to impose these constraints on the parameters of a translog output distance function implementing the approach involves the use of a gibbs sampler with data augmentation a metropolis hastings algorithm is also used within the gibbs to simulate observations from truncated pdfs our methods are developed for the case where panel data is available and technical inefficiency effects are assumed to be time invariant two models a fixed effects model and a random effects model are developed and applied to panel data on 17 european railways we observe significant changes in estimated elasticities and shadow price ratios when regularity restrictions are imposed c 2004 elsevier b v all rights reserved

direction selection in stochastic directional distance functions abstract researchers rely on the distance function to model multiple product production using multiple inputs a stochastic directional distance function sddf allows for noise in potentially all input and output variables yet when estimated the direction selected will affect the functional estimates because deviations from the estimated function are minimized in the specified direction specifically the parameters of the parametric sddf are point identified when the direction is specified we show that the parameters of the parametric sddf are set identified when multiple directions are considered further the set of identified parameters can be narrowed via data driven approaches to restrict the directions considered we demonstrate a similar narrowing of the identified parameter set for a shape constrained nonparametric method where the shape constraints impose standard features of a cost function such as monotonicity and convexity our monte carlo simulation studies reveal significant improvements as measured by out of sample radial mean squared error in functional estimates when we use a directional distance function with an appropriately selected direction and the errors are uncorrelated across variables we show that these benefits increase as the correlation in error terms across variables increase this correlation is a type of endogeneity that is common in production settings from our monte carlo simulations we conclude that selecting a direction that is approximately orthogonal to the estimated function in the central region of the data gives significantly better estimates relative to the directions commonly used in the literature for practitioners our results imply that selecting a direction vector that has non zero components for all variables that may have measurement error provides a significant improvement in the estimator s performance we illustrate these results using cost and production data from samples of approximately 500 us hospitals per year operating in 2007 2008 and 2009 respectively and find that the shape constrained nonparametric methods provide a significant increase in flexibility over second order local approximation parametric methods

propagation without wave equation toward an urban area model propagation in random media is a topic of great interest whose application fields include among others the so called last mile problem as well as the modeling of dense urban area radio communication channels a simple scenario for this issue is considered with an optical ray propagation across a medium of disordered lossless scatterers the propagation medium behaves like a percolating lattice and the goal is to characterize statistically the propagation depth in the medium as a function of the density g of scatterers and of spl theta the ray incidence angle to the best of our knowledge this approach is totally new the problem is mathematically formulated as a random walk and the solutions are based on the theory of the martingale random processes the obtained approximate analytical formulas have been validated by means of numerical simulations demonstrating the applicability of the proposed model for a wide range of the global parameters q and spl theta we believe that our results may constitute a promising first step toward the solution of more complicated propagation models and a wide class of communication problems

a penalized method for multivariate concave least squares with application to productivity analysis abstract we propose a penalized method for the least squares estimator of a multivariate concave regression function this estimator is formulated as a quadratic programing qp problem with o n2 constraints where n is the number of observations computing such an estimator is a very time consuming task and the computational burden rises dramatically as the number of observations increases by introducing a quadratic penalty function we reformulate the concave least squares estimator as a qp with only non negativity constraints this reformulation can be adapted for estimating variants of shape restricted least squares i e the monotonic concave convex least squares the experimental results and an empirical study show that the reformulated problem and its dual are solved significantly faster than the original problem the matlab and r codes for implementing the penalized problems are provided in the paper

a generalized multiplicative directional distance function for efficiency measurement in dea abstract for measuring technical efficiency relative to a log linear technology a generalized multiplicative directional distance function gmddf is developed using the framework of multiplicative directional distance function mddf furthermore a computational procedure is suggested for its estimation the gmddf serves as a comprehensive measure of efficiency in revealing pareto efficient targets as it accounts for all possible input and output slacks this measure satisfies several desirable properties of an ideal efficiency measure such as strong monotonicity unit invariance translation invariance and positive affine transformation invariance this measure can be easily implemented in any standard dea software and provides the decision makers with the option of specifying preferable direction vectors for incorporating their decision making preferences finally to demonstrate the ready applicability of our proposed measure an illustrative empirical analysis is conducted based on real life data set of 20 hardware computer companies in india

amenability and the structure of the algebras _ a number of characterizations are given of the class of amenable locally compact groups in terms of the ideal structure of the algebras ap g an almost connected group is amenable if and only if for some 1 p oo and some closed ideal i of ap g i has a bounded approximate identity furthermore g is amenable if and only if every derivation of ap g into a banach ap g bimodule is continuous

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

reflexivity algebraic reflexivity and linear interpolation introduction this paper was motivated by a discovery that most finite dimensional subalgebras of b h for h an infinite dimensional hilbert space are reflexive with the only obstructions to reflexivity being finite rank considerations proofs section 2 do not depend on multiplicative structure nor on topology so extend to linear subspaces of transformations in an abstract setting abstract reflexivity has been studied in 3 4 7 primarily for singly generated algebras reflexivity properties can be interpreted as linear interpolation properties and we shall adopt this point of view the results of section 2 extend in section 3 to algebraic reflexivity counterparts for countably generated algebraically linear subspaces of bounded linear transformations acting on a banach space as consequences in section 4 we obtain generalizations of two single operator results one is a multivariate version of the result due to kaplansky 10 theorem 15 that a bounded locally algebraic operator acting on a banach space is algebraic the other is a multivariate version of the result due to douglas and foias 5 for hilbert space and to hadwin 7 for a general banach space extending work of fillmore 6 that a bounded non algebraic operator acting on a banach space is topologically algebraically reflexive in section 5 we give an application kindly suggested by d hadwin concerning joint strong similarity orbits of n tupules of operators we wish to thank e azoff k davidson j erdos d hadwin j kraus c lance and a sourour for conversations and some correspon

characteristics of a polluting technology theory and practice abstract we use a quadratic directional output distance function to measure the technical efficiency of 209 electric utilities that produce electricity and a polluting byproduct so 2 before 1993 and after 1997 implementation of phase i regulations of the acid rain program we also estimate the shadow price of so 2 and the output elasticity of substitution between electricity and so 2 and find that electric utilities can reduce emissions by 4000 6000 tons by reducing inefficiency the shadow price of so 2 increases from 1993 to 1997 and that the elasticity of substitution indicates that the ability to trade reductions in electricity production for reductions in so 2 emissions became more difficult between 1993 and 1997

amenability and weak amenability of the fourier algebra let g be a locally compact group we show that its fourier algebra a g is amenable if and only if g has an abelian subgroup of finite index and that its fourier stieltjes algebra b g is amenable if and only if g has a compact abelian subgroup of finite index we then show that a g is weakly amenable if the component of the identity of g is abelian and we prove some partial results towards the converse

flexible functional forms and global curvature conditions empirically estimated flexible functional forms frequently fail to satisfy the appropriate theoretical curvature conditions lau and gallant and golub have worked out methods for imposing the appropriate curvature conditions locally but those local techniques frequently fail to yield satisfactory results we develop two methods for imposing curvature conditions globally in the context of cost function estimation the first method adopts lau s technique to a generalization of a functional form first proposed by mcfadden using this generalized mcfadden functional form it turns out that imposing the appropriate curvature conditions at one data point imposes the conditions globally the second method adopts a technique used by mcfadden and barnett which is based on the fact that a non negative sum of concave functions will be concave our various suggested techniques are illustrated using the u s manufacturing data utilized by berndt and khaled