asymptotics for euclidean minimal spanning trees on random points asymptotic results for the euclidean minimal spanning tree onn random vertices inrd can be obtained from consideration of a limiting infinite forest whose vertices form a poisson process in allrd in particular we prove a conjecture of robert bland the sum of thed th powers of the edge lengths of the minimal spanning tree of a random sample ofn points from the uniform distribution in the unit cube ofrd tends to a constant asn

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

on the negative squares of indefinite sturm liouville operators abstract the number of negative squares of all self adjoint extensions of a simple symmetric operator of defect one with finitely many negative squares in a krein space is characterized in terms of the behaviour of an abstract titchmarsh weyl function near 0 and these results are applied to a large class of symmetric and self adjoint indefinite sturm liouville operators with indefinite weight functions

consistency of spectral clustering consistency is a key property of all statistical procedures analyzing randomly sampled data surprisingly despite decades of work little is known about consistency of most clustering algorithms in this paper we investigate consistency of the popular family of spectral clustering algorithms which clusters the data with the help of eigenvectors of graph laplacian matrices we develop new methods to establish that for increasing sample size those eigenvectors converge to the eigenvectors of certain limit operators as a result we can prove that one of the two major classes of spectral clustering normalized clustering converges under very general conditions while the other unnormalized clustering is only consistent under strong additional assumptions which are not always satisfied in real data we conclude that our analysis provides strong evidence for the superiority of normalized spectral clustering

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

eigencurves for two parameter sturm liouville equations this paper concerns two parameter sturm liouville problems of the form p x y q x y lambda r x mu y quad a leqslant x leqslant b with self adjoint boundary conditions at a and b the set of lambda mu in bf r 2 for which there exists a nontrivial y satisfying the differential equation and the boundary conditions turns out to be a countable union of graphs of analytic functions our focus is on these graphs which are termed eigencurves in the literature although eigencurves have been used in a variety of ways for about a century they seem comparatively underdeveloped in their own right our plan is to give motivation for the topic elementary properties of eigencurves illustrations on a simple example first studied by richardson in 1918 and since then by several authors and some natural questions which may whet the reader s appetite some of these questions lead to new types of inverse sturm liouville problems

nested support vector machines one class and cost sensitive support vector machines svms are state of the art machine learning methods for estimating density level sets and solving weighted classification problems respectively however the solutions of these svms do not necessarily produce set estimates that are nested as the parameters controlling the density level or cost asymmetry are continuously varied such nesting not only reflects the true sets being estimated but is also desirable for applications requiring the simultaneous estimation of multiple sets including clustering anomaly detection and ranking we propose new quadratic programs whose solutions give rise to nested versions of one class and cost sensitive svms furthermore like conventional svms the solution paths in our construction are piecewise linear in the control parameters although here the number of breakpoints is directly controlled by the user we also describe decomposition algorithms to solve the quadratic programs these methods are compared to conventional non nested svms on synthetic and benchmark data sets and are shown to exhibit more stable rankings and decreased sensitivity to parameter settings

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

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

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 over representation of observations in subsets of a dea technology abstract this paper proposes a test for whether data are over represented in a given production zone i e a subset of a production possibility set which has been estimated using the non parametric data envelopment analysis dea approach a binomial test is used that relates the number of observations inside such a zone to a discrete probability weighted relative volume of that zone a monte carlo simulation illustrates the performance of the proposed test statistic and provides good estimation of both facet probabilities and the assumed common inefficiency distribution in a three dimensional input space potential applications include tests for whether benchmark units dominate more or less observations than expected

nearest neighbor clustering a baseline method for consistent clustering with arbitrary objective functions clustering is often formulated as a discrete optimization problem the objective is to find among all partitions of the data set the best one according to some quality measure however in the statistical setting where we assume that the finite data set has been sampled from some underlying space the goal is not to find the best partition of the given sample but to approximate the true partition of the underlying space we argue that the discrete optimization approach usually does not achieve this goal and instead can lead to inconsistency we construct examples which provably have this behavior as in the case of supervised learning the cure is to restrict the size of the function classes under consideration for appropriate small function classes we can prove very general consistency theorems for clustering optimization schemes as one particular algorithm for clustering with a restricted function space we introduce nearest neighbor clustering similar to the k nearest neighbor classifier in supervised learning this algorithm can be seen as a general baseline algorithm to minimize arbitrary clustering objective functions we prove that it is statistically consistent for all commonly used clustering objective functions

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

a hybrid clustering method for identifying high density clusters abstract a hybrid method for clustering multivariate observations is proposed which combines elements of the k means and the single linkage clustering techniques one purpose of the proposed method is to discover the high density clusters given a random sample of size n from some underlying population a high density cluster at level c in a population with density f is defined as a maximal connected set of points x with f x c this clustering procedure is practicable for very large numbers of observations and is shown to be consistent under certain regularity conditions in one dimension

rate of escape of some chaotic julia sets we give a formula for the rates of escape for julia sets with preperiodic critical points and forc endomorphisms of the interval with non flat pre periodic critical points outside the basin of attracting periodic 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

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

characterization stability and convergence of hierarchical clustering methods we study hierarchical clustering schemes under an axiomatic view we show that within this framework one can prove a theorem analogous to one of kleinberg 2002 in which one obtains an existence and uniqueness theorem instead of a non existence result we explore further properties of this unique scheme stability and convergence are established we represent dendrograms as ultrametric spaces and use tools from metric geometry namely the gromov hausdorff distance to quantify the degree to which perturbations in the input metric space affect the result of hierarchical methods

the dip test of unimodality the dip test measures multimodality in a sample by the maximum difference over all sample points between the empirical distribution function and the unimodal distribution function that minimizes that maximum difference the uniform distribution is the asymptotically least favorable unimodal distribution and the distribution of the test statistic is determined asymptotically and empirically when sampling from the uniform

procedures for the identification of multiple outliers in linear models abstract we consider the problem of identifying and testing multiple outliers in linear models the available outlier identification methods often do not succeed in detecting multiple outliers because they are affected by the observations they are supposed to identify we introduce two test procedures for the detection of multiple outliers that appear to be less sensitive to this problem both procedures attempt to separate the data into a set of clean data points and a set of points that contain the potential outliers the potential outliers are then tested to see how extreme they are relative to the clean subset using an appropriately scaled version of the prediction error the procedures are illustrated and compared to various existing methods using several data sets known to contain multiple outliers also the performances of both procedures are investigated by a monte carlo study the data sets and the monte carlo indicate that both procedures are effective in the detection of multiple outliers

a krein space approach to symmetric ordinary differential operators with an indefinite weight function on considere les proprietes spectrales du probleme differentiel l f 1 n p 0 f n n 1 n 1 p 1 f n 1 n 1 p n f rf sur un intervalle fini ou infini a b avec des coefficients reels localement sommables 1 p 0 p 1 p n r sous l hypothese que p 0 0 et que la fonction poids r change de signe sur a b

bounds on the non real spectrum of differential operators with indefinite weights ordinary and partial differential operators with an indefinite weight function can be viewed as bounded perturbations of non negative operators in krein spaces under the assumption that 0 and infty are not singular critical points of the unperturbed operator it is shown that a bounded additive perturbation leads to an operator whose non real spectrum is contained in a compact set and with definite type real spectrum outside this set the main results are quantitative estimates for this set which are applied to sturm liouville and second order elliptic partial differential operators with indefinite weights on unbounded domains

singular sturm liouville problems the friedrichs extension and comparison of eigenvalues a new characterization of singular self adjoint boundary conditions for sturm liouville problems is given these are an exact parallel of the regular case they are given explicitly in terms of principal and non principal solutions the special nature of the friedrichs extension is clearly apparent and highlighted inequalities among the eigenvalues of different boundary conditions separated and coupled are obtained most of all e want to stress the method of proof it is based on a very elementary transformation which transforms any singular non oscillatory limit circle endpoint into a regular one

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

a statistical model of cluster stability in the current paper we present a method for assessing cluster stability this method combined with a clustering algorithm yields an estimate of the data partition namely the number of clusters we adopt the cluster stability standpoint where clusters are imagined as islands of high density in a sea of low density explicitly a cluster is associated with its high density core our approach offers to evaluate the goodness of a cluster by the similarity amongst the entire cluster and its core we propose to measure this resemblance by two sample tests or by probability distances between appropriate probability distributions the distances are calculated on clustered samples drawn from the source population according to two different distributions the first law is the underlying set distribution the second law is constructed so that it represents the clusters cores here a variant of the k nearest neighbor density estimation is applied so that items belonging to cores have a much higher chance to be selected as the sample distribution is unknown a distribution free two sample test is required to examine the mentioned correspondence for constructing such a test we use distance functions built on negative definite kernels in practice outliers in the samples and limitations of the clustering algorithm heavily contribute to the noise level as a result of this shortcoming the distance values have to be determined for many pairs of samples and therefore an empirical distance s distribution is obtained the distribution is dependent on the examined number of clusters to prevent this property for biasing the results we normalize the distances it is conjectured that the true number of clusters yields the most concentrated normalized distribution to measure the concentration we use the sample mean and the sample 25th percentile the paper exhibits the good performance of the proposed method on synthetic and real world data

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

consistency of cheeger and ratio graph cuts this paper establishes the consistency of a family of graph cut based algorithms for clustering of data clouds we consider point clouds obtained as samples of a ground truth measure we investigate approaches to clustering based on minimizing objective functionals defined on proximity graphs of the given sample our focus is on functionals based on graph cuts like the cheeger and ratio cuts we show that minimizers of these cuts converge as the sample size increases to a minimizer of a corresponding continuum cut which partitions the ground truth measure moreover we obtain sharp conditions on how the connectivity radius can be scaled with respect to the number of sample points for the consistency to hold we provide results for two way and for multiway cuts furthermore we provide numerical experiments that illustrate the results and explore the optimality of scaling in dimension two

optimal construction of k nearest neighbor graphs for identifying noisy clusters we study clustering algorithms based on neighborhood graphs on a random sample of data points the question we ask is how such a graph should be constructed in order to obtain optimal clustering results which type of neighborhood graph should one choose mutual k nearest neighbor or symmetric k nearest neighbor what is the optimal parameter k in our setting clusters are defined as connected components of the t level set of the underlying probability distribution clusters are said to be identified in the neighborhood graph if connected components in the graph correspond to the true underlying clusters using techniques from random geometric graph theory we prove bounds on the probability that clusters are identified successfully both in a noise free and in a noisy setting those bounds lead to several conclusions first k has to be chosen surprisingly high rather of the order n than of the order logn to maximize the probability of cluster identification secondly the major difference between the mutual and the symmetric k nearest neighbor graph occurs when one attempts to detect the most significant cluster only

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

continuity properties of entropy on donne une borne superieure sur le defaut en semicontinuite superieure des entropies topologiques et metriques d une auto application c r d une variete c r r 1

estimates on the non real eigenvalues of regular indefinite sturm liouville problems regular sturm liouville problems with indefinite weight functions may possess finitely many non real eigenvalues in this paper we prove explicit bounds on the real and imaginary parts of these eigenvalues in terms of the coefficients of the differential expression

fully adaptive density based clustering the clusters of a distribution are often defined by the connected components of a density level set however this definition depends on the user specified level we address this issue by proposing a simple generic algorithm which uses an almost arbitrary level set estimator to estimate the smallest level at which there are more than one connected components in the case where this algorithm is fed with histogram based level set estimates we provide a finite sample analysis which is then used to show that the algorithm consistently estimates both the smallest level and the corresponding connected components we further establish rates of convergence for the two estimation problems and last but not least we present a simple yet adaptive strategy for determining the width parameter of the involved density estimator in a data depending way

consistent procedures for cluster tree estimation and pruning for a density f on mathbb r d a high density cluster is any connected component of x f x geq lambda for some lambda 0 the set of all high density clusters forms a hierarchy called the cluster tree of f we present two procedures for estimating the cluster tree given samples from f the first is a robust variant of the single linkage algorithm for hierarchical clustering the second is based on the k nearest neighbor graph of the samples we give finite sample convergence rates for these algorithms which also imply consistency and we derive lower bounds on the sample complexity of cluster tree estimation finally we study a tree pruning procedure that guarantees under milder conditions than usual to remove clusters that are spurious while recovering those that are salient

consistency of single linkage for high density clusters abstract high density clusters are defined on a population with density f in r dimensions to be the maximal connected sets of form x f x c single linkage clustering is evaluated for consistency in detecting such high density clusters other standard hierarchical techniques such as average and complete linkage are hopelessly inconsistent for these clusters the asymptotic consistency of single linkage closely depends on the percolation problem of broadbent and hammersley if small spheres are removed at random from a solid at which density of spheres will water begin to flow through the solid if there is a single critical density such that no flow takes place below a certain density and flow occurs through a single connected set above that density then single linkage is consistent in separating high density clusters by disjoint single linkage clusters that include a positive fraction of sample points in the respective clusters and pass arbitrarily close to all points in the respective clusters

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

non real eigenvalues of indefinite sturm liouville problems abstract the present paper deals with non real eigenvalues of regular indefinite sturm liouville problems a priori bounds and sufficient conditions of the existence for non real eigenvalues are obtained under mild integrable conditions of coefficients

complex analytic dynamics on the riemann sphere dichotomie dynamique de fatou et julia points periodiques consequences du theoreme de montel l ensemble de julia est la fermeture de l ensemble des points periodiques repulseurs resultats classiques sur l ensemble de fatou classification de sullivan de l ensemble de fatou une condition pour le developpement sur l ensemble de julia la dynamique des polynomes l ensemble de mandelbrot et le travail de douady et hubbard le theoreme d application de riemann mesurable et la dynamique analytique

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