stochastic data envelopment analysis in measuring the efficiency of taiwan commercial banks conventional data envelopment analysis dea for measuring the efficiency of a set of decision making units dmus requires the input output data to be constant in reality however many observations are stochastic in nature consequently the resulting efficiencies are stochastic as well this paper discusses how to obtain the efficiency distribution of each dmu via a simulation technique the case of taiwan commercial banks shows that firstly the number of replications in simulation analysis has little effect on the estimation of efficiency means yet 1000 replications are recommended to produce reliable efficiency means and 2000 replications for a good estimation of the efficiency distributions secondly the conventional way of using average data to represent stochastic variables results in efficiency scores which are different from the mean efficiencies of the presumably true efficiency distributions estimated from simulation thirdly the interval data approach produces true efficiency intervals yet the intervals are too wide to provide valuable information in conclusion when multiple observations are available for each dmu the stochastic data approach produces more reliable and informative results than the average data and interval data approaches do

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

bootstrapping regression models the regression and correlation models are considered it is shown that the bootstrap approximation to the distribution of the least squares estimates is valid and some error bounds are given

non parametric tests of returns to scale this paper discusses various statistics for testing hypotheses regarding returns to scale in the context of non parametric models of technical efficiency in addition the paper presents bootstrap estimation procedures which yield appropriate critical values for the test statistics evidence on the true sizes and power of the various proposed tests is obtained from monte carlo experiments this paper is an extension of earlier work in manage sci 44 1998 49 j appl statist 27 2000b 779 c 2002 elsevier science b v all rights reserved

on estimation of monotone and concave frontier functions abstract when analyzing the productivity of firms one may want to compare how the firms transform a set of inputs x typically labor energy or capital into an output y typically a quantity of goods produced the economic efficiency of a firm is then defined in terms of its ability to operate close to or on the production frontier the boundary of the production set the frontier function gives the maximal level of output attainable by a firm for a given combination of its inputs the efficiency of a firm may then be estimated via the distance between the attained production level and the optimal level given by the frontier function from a statistical viewpoint the frontier function may be viewed as the upper boundary of the support of the population of firms density in the input and output space it is often reasonable to assume that the production frontier is a concave monotone function then a famous estimator in the univariate input and output case is the data envelopment analysis dea estimato

stochastic efficiency measures for production units with correlated data abstract while the real world is stochastic in nature in many cases deterministic data envelopment analysis dea models are used to measure the relative efficiency of a set of production units for simplicity however deterministic dea models are not able to differentiate efficient units more seriously the decision maker will be over confident with the presumably uncertain and probably misleading results by applying a standard normal transformation this paper develops a stochastic dea model which is able to take the correlation between the input output factors of each production unit to be evaluated into account to obtain the distribution of the stochastic efficiency the efficiency distribution is more discriminative and informative than the single valued efficiency in that the probability that the stochastic efficiency of a unit is greater than that of another unit can be calculated the case of twenty five taiwanese commercial banks discussed in a previous study that assumed the input output factors to be independent is used to illustrate the characteristics of different models the data is shown to be correlated and the results confirm that ignoring the correlations between the input output factors in measuring efficiency obtains misleading rankings

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

interior regularity estimates in high conductivity homogenization and application in this paper uniform pointwise regularity estimates for the solutions of conductivity equations are obtained in a unit conductivity medium reinforced by an e periodic lattice of highly conducting thin rods the estimates are derived only at a distance e1 for some 0 away from the fibres this distance constraint is rather sharp since the gradients of the solutions are shown to be unbounded locally in lp as soon as p 2 one key ingredient is the derivation in dimension two of regularity estimates to the solutions of the equations deduced from a fourier series expansion with respect to the fibres direction and weighted by the high contrast conductivity the dependence on powers of e of these two dimensional estimates is shown to be sharp the initial motivation for this work comes from imaging and enhanced resolution phenomena observed experimentally in the presence of micro structures lerosey et al science 315 1120 1124 2007 we use these regularity estimates to characterize the signature of low volume fraction heterogeneities in the fibred reinforced medium assuming that the heterogeneities stay at a distance e1 away from the fibres

estimating and bootstrapping malmquist indices this paper develops a consistent bootstrap estimation procedure for obtaining confidence intervals for malmquist indices of productivity and their decompositions although the exposition is in terms of input oriented indices the techniques can be trivially extended to the output orientation the bootstrap methodology is an extension of earlier work described in simar and wilson simar l wilson p w 1998 management science some empirical examples are also given using data on swedish pharmacies c 1999 published by elsevier science b v all rights reserved

testing procedures for detection of linear dependencies in efficiency models the validity of many efficiency measurement methods rely upon the assumption that variables such as input quantities and output mixes are independent of or uncorrelated with technical efficiency however few studies have attempted to test these assumptions in a recent paper wilson 2003 investigates a number of independence tests and finds that they have poor size properties and low power in moderate sample sizes in this study we discuss the implications of these assumptions in three situations i bootstrapping non parametric efficiency models ii estimating stochastic frontier models and iii obtaining aggregate measures of industry efficiency we propose a semi parametric hausmann type asymptotic test for linear independence uncorrelation and use a monte carlo experiment to show that it has good size and power properties in finite samples we also describe how the test can be generalized in order to detect higher order dependencies such as heteroscedasticity so that the test can be used to test for full independence when the efficiency distribution has a finite number of moments finally an empirical illustration is provided using data on us electric power generation

estimation and inference in two stage semi parametric models of production processes many papers have regressed non parametric estimates of productive efficiency on environmental variables in two stage procedures to account for exogenous factors that might affect firms performance none of these have described a coherent data generating process dgp moreover conventional approaches to inference employed in these papers are invalid due to complicated unknown serial correlation among the estimated efficiencies we first describe a sensible dgp for such models we propose single and double bootstrap procedures both permit valid inference and the double bootstrap procedure improves statistical efficiency in the second stage regression we examine the statistical performance of our estimators using monte carlo experiments

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

local likelihood tracking of fault lines and boundaries summary we suggest locally parametric methods for estimating curves such as boundaries of density supports or fault lines in response surfaces in a variety of spatial problems the methods are based on spatial approximations to the local likelihood that the curve passes through a given point in the plane as a function of that point the local likelihood might be a regular likelihood computed locally with kernel weights e g in the case of support boundary estimation or a local version of a likelihood ratio statistic e g in fault line estimation in either case the local likelihood surface represents a function which is relatively large near the target curve and relatively small elsewhere therefore the curve may be estimated as a ridge line of the surface we require only a numerical algorithm for tracking the projection of a ridge into the plane this approach offers several potential advantages over alternative methods first the local log likelihood surface can be graphed and the degree of ridginess assessed visually to determine how the level of local smoothing should be varied in different spatial locations in order to emphasize the ridge and hence the curve adequately secondly the local likelihood surface does not need to be computed in anything like its entirety once we have a reasonable approximation to a point on the curve we may track it by numerically walking along the ridge line thirdly the method is appropriate without change for many different types of spatial explanatory vanables gridded stochastic or otherwise three examples are explored in detail fault lines in response surfaces and in intensity or density surfaces and boundaries of supports of probability densities

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

a statistical test for detecting influential observations in dea this paper deals with the problem of detecting influential observations in deterministic nonparametric dea models the technique we present is intended to classify for a further analysis those sample observations considerably affecting the measured efficiency for the remaining units then the analyst will have to check whether these observations are contaminated by data errors or not this approach also allows to determine when efficiency changes due to the presence of a given unit in the sample are statistically significant thus ours is a statistical alternative to approach the problem of detecting influential observations in deterministic nonparametric dea models

transconcave data envelopment analysis transconcave data envelopment analysis tdea extends standard data envelopment analysis dea in order to account for non convex production technologies such as those involving increasing returns to scale or diseconomies of scope tdea introduces non convexities by transforming the range and the domain of the production frontier thus replacing the standard assumption that the production frontier is concave with the more general assumption that the frontier is concave transformable tdea gives statistically consistent estimates for all monotonically increasing and concave transformable frontiers in addition monte carlo simulations suggest that tdea can substantially improve inefficiency estimation in small samples compared to the standard banker charnes and cooper model and the full disposable hull model fdh

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

efficient estimation of monotone boundaries let g 0 1 0 1 be a monotone nondecreasing function and let g be the closure of the set x y is an element of 0 1 x 0 1 0 less than or equal to y less than or equal to g x we consider the problem of estimating the set g from a sample of i i d observations uniformly distributed in g the estimation error is measured in the hausdorff metric we propose the estimator which is asymptotically efficient in the minimax sense

a statistical test for nested radial dea models some problems in economics operations research and engineering may be approached by means of a pair of radial dea models that are nested i e that the set of constraints of one of them is included in that of the other in this paper we have focused on analyzing the marginal role of a given variable called candidate with respect to the efficiency measured by means of a dea model first we have defined a new efficiency contribution measure ecm which finally compares the efficiency scores of the two radial dea models differing in the candidate this can be either one input or one output then based on ecm we have also approached the problem from a statistical point of view to be precise we have developed a statistical test that allows us to evaluate the significance of the observed efficiency contribution of the candidate eventually solving this test may provide some useful insights in order to decide the incorporation or the deletion of a variable into from a given dea model on the basis of the information supplied by the data two procedures for progressive selection of variables were designed by sequentially applying the test a forward selection and a backward elimination these can be very helpful in the initial selection of variables when building a radial dea model

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

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

on the number of bootstrap simulations required to construct a confidence interval abstract the purpose of this document is to make two points about the effect of the number of bootstrap simulations b on percentile t bootstrap confidence intervals the first point concerns coverage probability the second distance of the simulated critical point form the true critical point derived with b infinity in both cases the author has in mind applications to smooth statistics such as the studentized mean of a sample drawn from a continuous distribution he indicates the change that have to be made if the distribution of the statistic is not smooth additional keywords exponentive functions

jackknife bootstrap and other resampling methods in regression analysis motivated by a representation for the least squares estimator we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time they are unbiased for homoscedastic errors and a special case the delete one jackknife is almost unbiased for heteroscedastic errors the method is extended to cover nonlinear parameters regression m estimators nonlinear regression and generalized linear models interval estimators can be constructed from the jackknife histogram three bootstrap methods are considered two are shown to give biased variance estimators and one does not have the bias robustness property enjoyed by the weighted delete one jackknife a general method for resampling residuals is proposed it gives variance estimators that are bias robust several bias reducing estimators are proposed some simulation results are reported

sensitivity analysis of network dea nsbm versus nram abstract users of data envelopment analysis dea often presume efficiency estimates to be robust while traditional dea has been exposed to various sensitivity studies network dea has so far escaped similar scrutiny thus there is a need to investigate the sensitivity of efficiency estimates further compounded by the recent attention network dea has been receiving in literature we compare network slacks based measure nsbm with network range adjusted measure nram where the latter is developed for the first time following various data perturbations overall findings indicate positive and significant rank correlations when new results are compared against baseline results suggesting resilience key findings show that a as in traditional dea greater sample size brings greater discrimination b removing a relevant input improves discrimination c introducing an extraneous input leads to a moderate loss of discrimination d simultaneously adjusting data in opposite directions for inefficient versus efficient branches shows a mostly stable estimates e swapping divisional weights produces a substantial drop in discrimination f stacking perturbations has the greatest impact on efficiency estimates with substantial loss of discrimination and g layering suggests that the core inefficient cohort is resilient against omission of benchmark branches further insight gained by comparing nsbm with nram includes h identical benchmark groups across both formulations i a narrower range of efficiency estimates and a more stable mean across different sample sizes under nram j distribution of nram efficiency estimates is negatively skewed whereas nsbm estimates are mostly positively skewed and k there is no evidence of inefficient unit size bias among nram estimates whereas larger inefficient units appear more inefficient under nsbm

comparative analysis of affine scaling algorithms based on simplifying assumptions we analyze several affine potential reduction algorithms for linear programming based on simplifying assumptions we show that under a strong probabilistic assumption regarding the distribution of the data in an iteration the decrease in the primal potential function will be omega rho sqrt log n with high probability compared to the guaranteed 1 2n is a parameter in the potential function andn is the number of variables under the same assumption we further show that the objective reduction rate of dikin s affine scaling algorithm is 1 1 sqrt log n with high probability compared to no guaranteed convergence rate

bootstrapped efficiency estimates for a model for groups and hierarchies in dea abstract we apply some recently introduced bootstrap techniques to derive bias corrected efficiency scores for a model for groups and hierarchies in dea the use of the bootstrap makes it possible to overcome some deficiencies of the original formulation of this model which rests on rescaling individual efficiency scores using average efficiencies calculated from different subsets of the data these average or structural efficiencies are differently biased and bias varies with sample size when standard dea techniques are used bias correction makes it possible to identify the true differences in efficiency and thus to compare dmus belonging to different groups via their rescaled individual efficiency scores on one common basis moreover this type of bias problem is present in other dea applications therefore the method proposed to deal with it has many potential applications beyond the groups and hierarchies model

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

the bootstrap to smooth or not to smooth summary the bootstrap and smoothed bootstrap are considered as alternative methods of estimating properties of unknown distributions such as the sampling error of parameter estimates criteria are developed for determining whether it is advantageous to use the smoothed bootstrap rather than the standard bootstrap key steps in the argument leading to these criteria include the study of the estimation of linear functionals of distributions and the approximation of general functionals by linear functionals consideration of an example the estimation of the standard error in the variance stabilized sample correlation coefficient elucidates previously published simulation results and also illustrates the use of computer algebraic manipulation as a useful technique in asymptotic statistics finally the various approximations used are vindicated by a simulation study