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

torsion points on families of squares of elliptic curves in a recent paper we proved that there are at most finitely many complex numbers 0 1 such that the points 2 sqrt 2 2 lambda and 3 sqrt 6 3 lambda are both torsion on the elliptic curve defined by y 2 x x 1 x here we give a generalization to any two points with coordinates algebraic over the field q and even over c this implies a special case of a variant of pink s conjecture for a variety inside a semiabelian scheme namely for any curve inside any scheme isogenous to a fibred product of two isogenous elliptic schemes

big line bundles over arithmetic varieties 5 equidistribution theory 26 5 1 a generic equidistribution theorem 27 5 2 equidistribution at infinite places 30 5 3 equidistribution at finite places 32 5 4 equidistribution of small subvarieties 35 5 5 equidistribution over algebraic dynamical systems 37 5 6 equidistribution over multiplicative groups 39 5 7 equidistribution theory 41

advances on the bessis moussa villani trace conjecture abstract a long standing conjecture asserts that the polynomial p t tr a tb m has nonnegative coefficients whenever m is a positive integer and a and b are any two n n positive semidefinite hermitian matrices the conjecture arises from a question raised by bessis et al d bessis p moussa m villani monotonic converging variational approximations to the functional integrals in quantum statistical mechanics j math phys 16 1975 2318 2325 in connection with a problem in theoretical physics their conjecture as shown recently by lieb and seiringer is equivalent to the trace positivity statement above in this paper we derive a fundamental set of equations satisfied by a and b that minimize or maximize a coefficient of p t applied to the bessis moussa villani bmv conjecture these equations provide several reductions in particular we prove that it is enough to show that 1 it is true for infinitely many m 2 a nonzero matrix coefficient of a tb m always has at least one positive eigenvalue or 3 the result holds for singular positive semidefinite matrices moreover we prove that if the conjecture is false for some m then it is false for all larger m finally we outline a general program to settle the bmv conjecture that has had some recent success

equidistribution quantitative des points de petite hauteur sur la droite projective we introduce a new class of adelic heights on the projective line we estimate their essential minimum and prove a result of equidistribution at every place for points of small height with estimates on the speed of convergence to each rational function r in one variable and defined over a number field k is associated a normalized height on the algebraic closure of k we show that these dynamically defined heights are adelic in our sense and deduce from this equidistribution results for preimages of points under r at every place of k our approach follows that of bilu and relies on potential theory in the complex plane as well as in the berkovich space associated to the projective line over open image in new window for each prime p

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

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

mesures et equidistribution sur les espaces de berkovich the proof by ullmo and zhang of bogomolov s conjecture about points of small height in abelian varieties made a crucial use of an equidistribution property for small points in the associated complex abelian variety we study the analogous equidistribution property at p adic places our results can be conveniently stated within the framework of the analytic spaces defined by berkovich the first one is valid in any dimension but is restricted to algebraic metrics the second one is valid for curves but allows for more general metrics in particular to the normalized heights with respect to dynamical systems

positive line bundles on arithmetic varieties p 5 u integers is defined to count the volume of the lattice i l n of integral sections in the space j7 lon of real sections with supremum norm we want to prove that the leading term of this hilbert function as n f oo is given in terms of the height of x in as 1 this is known as a theorem of gillet and soule gs2 if x has a regular generic fiber beside this known result our proof uses hironaka s theorem on resolutions of singularities and minkowski s theorem on successive minima by hironaka s theorem we may construct

finite index theorems for iterated galois groups of cubic polynomials let k be a number field or a function field let f in k x be a rational function of degree d ge 2 and let beta in mathbb p 1 overline k for all n in mathbb n cup infty the galois groups g n beta mathrm gal k f n beta k beta embed into mathrm aut t n the automorphism group of the d ary rooted tree of level n a major problem in arithmetic dynamics is the arboreal finite index problem determining when mathrm aut t infty g infty beta infty when f is a cubic polynomial and k is a function field of transcendence degree 1 over an algebraic extension of mathbb q we resolve this problem by proving a list of necessary and sufficient conditions for finite index this is the first result that gives necessary and sufficient conditions for finite index and can be seen as a dynamical analog of the serre open image theorem when k is a number field our proof is conditional on both the abc conjecture for k and vojta s conjecture for blowups of mathbb p 1 times mathbb p 1 we also use our approach to solve some natural variants of the finite index problem for modified trees

stochastic multicriteria acceptability analysis using the data envelopment model abstract data envelopment analysis dea and stochastic multicriteria acceptability analysis smaa 2 are methods for evaluating alternatives based on multiple criteria while dea is mainly an ex post tool used for classifying alternatives into efficient and inefficient ones smaa 2 is an ex ante tool for supporting multiple criteria decision making both methods use a kind of value function where the importance of criteria is modeled using weights unlike many other methods neither dea nor smaa 2 requires decision makers weights as input instead these so called non parametric methods explore the weight space in order to identify weights favorable for each alternative this paper introduces the smaa d method which is a combination of dea and smaa 2 smaa d can be characterized as an extension of dea to handle uncertain or imprecise data to provide stochastic efficiency measures alternatively the combined method can be seen as a variant of smaa 2 with a dea type value function

preperiodic points and unlikely intersections in this article we combine complex analytic and arithmetic tools to study the preperiodic points of one dimensional complex dynamical systems we show that for any fixed a b c and any integer d 2 the set of c c for which both a and b are preperiodic for z c is infinite if and only if a b this provides an affirmative answer to a question of zannier which itself arose from questions of masser concerning simultaneous torsion sections on families of elliptic curves using similar techniques we prove that if rational functions c z have infinitely many preperiodic points in common then all of their preperiodic points coincide and in particular the maps must have the same julia set this generalizes a theorem of mimar who established the same result assuming that and are defined over q the main arithmetic ingredient in the proofs is an adelic equidistribution theorem for preperiodic points over number fields and function fields with non archimedean berkovich spaces playing an essential role

estimating output targets to evaluate output specific efficiencies a statistical framework this paper presents a statistical framework for estimating output specific efficiencies for the 2 output case based upon a dea frontier estimate the key to this approach are estimated output targets which are used to identify proper reference points for efficiency comparisons being usually unobserved output targets of firms are modelled as missing data and estimated jointly with output specific efficiencies the involved likelihood function is analytically intractable so a data augmented bayesian approach is proposed for estimation and adapted to the present purpose some implementation issues are discussed leading to an empirical bayes setup with data informed priors a prove of scale invariance is provided

estimation of returns to scale using data envelopment analysis abstract generalization of the measure of returns to scale from a single number to an interval permits extension of the concept to dea data domains with multiple inputs and multiple outputs the key new approach is a partition of the optimal frontier into three parts corresponding respectively to increasing constant and decreasing returns to scale these parts are characterized in terms of optimal primal solutions and optimal dual solutions for both the original charnes cooper rhodes model 1978 and the later banker charnes cooper model 1984 and relying on concepts developed by r d banker 1984 and r m thrall 1988

a simulation study of dea and parametric frontier models in the presence of heteroscedasticity abstract this paper studies the effects of heteroscedasticity on the following five types of estimators 1 data envelopment analysis dea per se as well as dea joined to regression forms 2 corrected ordinary least squares based on maximum residual cols r 3 corrected ordinary least squares based on moments of residuals cols m 4 maximum likelihood estimation mle and 5 goal programming with one sided deviations as in aigner and chu a c this is accomplished with simulated data in an experiment designed around a single output single input production function which is piecewise cobb douglas robustness of results is confirmed with another experiment employing a shifted smooth cobb douglas production function the model has a composed error term consisting of two components one for measurement error and the other for inefficiency the simulation results indicate that heteroscedasticity does not have an adverse impact on dea based estimators and that dea based estimators are the best estimators of efficient output even under heteroscedasticity

distribution of rational maps with a preperiodic critical point let f lambda be a family of rational maps of a fixed degree with a marked critical point c lambda under a natural assumption we first prove that the hypersurfaces of parameters for which c lambda is periodic converge as a sequence of positive closed 1 1 currents to the bifurcation current attached to c and defined by demarco we then turn our attention to the parameter space of polynomials of a fixed degree d by intersecting the d 1 currents attached to each critical point of a polynomial bassaneli and berteloot obtained a positive measure mu rm bif of finite mass which is supported on the connectedness locus they showed that its support is included in the closure of the set of parameters admitting d 1 neutral cycles we show that the support of this measure is precisely the closure of the set of strictly critically finite polynomials i e of misiurewicz points

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

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

torsion anomalous points and families of elliptic curves we prove that there are at most finitely many complex lambda neq 0 1 such that two points on the legendre elliptic curve y 2 x x 1 x lambda with coordinates x 2 3 both have finite order this is a very special case of some conjectures on unlikely intersections in semiabelian schemes

methods of critical value reduction for type 2 fuzzy variables and their applications a type 2 fuzzy variable is a map from a fuzzy possibility space to the real number space it is an appropriate tool for describing type 2 fuzziness this paper first presents three kinds of critical values cvs for a regular fuzzy variable rfv and proposes three novel methods of reduction for a type 2 fuzzy variable secondly this paper applies the reduction methods to data envelopment analysis dea models with type 2 fuzzy inputs and outputs and develops a new class of generalized credibility dea models according to the properties of generalized credibility when the inputs and outputs are mutually independent type 2 triangular fuzzy variables we can turn the proposed fuzzy dea model into its equivalent parametric programming problem in which the parameters can be used to characterize the degree of uncertainty about type 2 fuzziness for any given parameters the parametric programming model becomes a linear programming one that can be solved using standard optimization solvers finally one numerical example is provided to illustrate the modeling idea and the efficiency of the proposed dea model

dynamics of rational maps lyapunov exponents bifurcations and capacity let l f log df d f denote the lyapunov exponent of a rational map f p 1 p 1 in this paper we show that for any holomorphic family of rational maps f x of degree d 1 t f dd c l f defines a natural positive 1 1 current on x supported exactly on the bifurcation locus of the family the proof is based on the following potential theoretic formula for the lyapunov exponent here f c 2 c 2 is a homogeneous polynomial lift of f g f is the escape rate function of f and capk f is the homogeneous capacity of the filled julia set of f we show in particular that the capacity of k f is given explicitly by the formula where res f is the resultant of the polynomial coordinate functions of f we introduce the homogeneous capacity of compact circled and pseudoconvex sets k c 2 and show that the levi measure determined by the geometry of k is the unique equilibrium measure such k c 2 correspond to metrics of non negative curvature on p 1 and we obtain a variational characterization of curvature

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 and the discriminant analysis of ratios for ranking units the purpose of this study is to develop a new method which provides for given inputs and outputs the best common weights for all the units that discriminate optimally between the efficient and inefficient units as pregiven by the data envelopment analysis dea in order to rank all the units on the same scale this new method discriminant data envelopment analysis of ratios dr dea presents a further post optimality analysis of dea for organizational units when their multiple inputs and outputs are given we construct the ratio between the composite output and the composite input where their common weights are computed by a new non linear optimization of goodness of separation between the two pregiven groups a practical use of dr dea is that the common weights may be utilized for ranking the units on a unified scale dr dea is a new use of a two group discriminant criterion that has been presented here for ratios rather than the traditional discriminant analysis which applies to a linear function moreover non parametric statistical tests are employed to verify the consistency between the classification from dea efficient and inefficient units and the post classification as generated by dr dea

two stage estimation of the impact of contextual variables in stochastic frontier production function models using data envelopment analysis second stage ols versus bootstrap approaches abstract banker and natarajan 2008 identified sufficient conditions in a stochastic framework to justify the popular two stage approach of data envelopment analysis followed by ordinary least squares dea ols to estimate the impact of contextual variables on productivity simar and wilson 2007 suggested an alternative approach involving a second stage truncated regression model and bootstrap method to estimate confidence intervals we show that the effectiveness of the simar wilson approach critically depends on the assumption that the actual data generating process dgp exactly matches their assumed dgp and their approach does not yield correct inferences in environments characterized by stochastic noise extensive simulations from a stochastic frontier data generating process document that the simple two stage dea ols model significantly outperforms the more complex simar wilson model with lower mean absolute deviation mad lower median absolute deviation mead as well as higher coverage rates when the contextual variables significantly impact productivity subject classifications data envelopment analysis productivity two stage contextual variables performance nonparametric simulation area of review optimization

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

scaling units via the canonical correlation analysis in the dea context abstract this paper deals with the evaluation of decision making units which have multiple inputs and outputs a new method cca dea is developed where the canonical correlation analysis cca is utilized to provide a full rank scaling for all the units rather than a categorical classification for efficient and inefficient units as done by the data envelopment analysis dea the cca dea approach is an attempt to bridge the gap between the frontier approach of dea and the average tendencies of statistics econometrics nonparametric statistical tests are employed to validate the consistency between the classification from the dea and the postclassification that was generated by the cca dea

a monte carlo comparison of two production frontier estimation methods corrected ordinary least squares and data envelopment analysis abstract this paper reports the results of an experiment with simulated data that compares the estimation accuracy of two simple and very different production frontier methods corrected ordinary least squares and data envelopment analysis the experimental design extends a previously published paper by introducing measurement errors a factor we show to be critical for comparative analysis of the frontier methods both low and high measurement error distributions are used resulting in 95 error intervals of roughly 10 and 40 respectively of outputs other variations include four inefficiency distributions covering a wide range of behavior four sample sizes from 25 to 200 and two piecewise cobb douglas technologies with two inputs and one output each results include 1 selection of the proper estimation method for a case can result in substantial gains in estimation accuracy for technical efficiencies from 15 to 40 in mean absolute deviations 2 cols performs better for the classical distribution case with sample sizes of 50 or over 3 dea performs better for all nonclassical inefficiency distributions even with relatively high measurement errors 4 dea provides surprisingly accurate estimates for the small sample size of 25 for all cases in the experiment 5 cols fails to decompose deviations into efficiency and measurement error components it assumes that deviations from the frontier are either totally due to measurement errors or technical inefficiencies and 6 neither method performs satisfactorally for high measurement errors