efficiency analysis generating an efficient extreme point for an molp and some comparisons this paper starts with analyzing efficiency of an alternative in a multi objective problem by combination of concepts in data envelopment analysis dea and multiple objective linear programming molp we search a composite alternative to compare with a given alternative and assess its efficiency in an molp problem in addition to some results this leads us to produce some procedures for generating an initial efficient extreme point to an molp problem we compare our procedures with some other existing methods and exhibit some advantages of our methods in addition we consider some models of dea as molp problems and use them to illustrate some contents of the paper which also appears some analogies between these areas

estimation of noisy telegraph processes nonlinear filtering versus nonlinear smoothing corresp in the estimation problem of a two state stationary markov process with gaussian white noise added the optimal smoother is a two filter smoother in a special case the performance of the optimal nonlinear filter and smoother is evaluated analytically some asymptotic results are also derived

preference voting and project ranking using dea and cross evaluation cook and kress 1990 using data envelopment analysis dea as their starting point proposed a procedure to rank order the candidates in a preferential election notionally each candidate is permitted to choose the most favourable weights to be applied to his her standings first place second place etc votes in the usual dea manner with the additional assurance region restriction that the weight for a j place vote should be more than that for a j 1 amount we consider that this freedom to choose weights is essentially illusory when maximum discrimination between the candidates is sought in which case the weights used to evaluate and rank the candidates are as if imposed externally at the outset to avoid this we present an alternative procedure which retains cook and kress central idea but where as well as using each candidate s rating of him herself we now make use of each candidate s ratings of all the candidates we regard the so called cross evaluation matrix as the summary of a self and peer rating process in which the candidates seek to interpret the voters preferences as favourably for themselves relative to the other candidates as possible the problem then becomes one of establishing an overall rating for each candidate from these individual ratings for this for each candidate we use a weighted average of all the candidates ratings of that candidate where the weights themselves are in proportion to each candidate s overall rating the overall ratings are therefore proportional to the components of the principal left hand eigenvector of the cross evaluation matrix these ideas are then applied to the selection of r d projects to comprise an r d program thus indicating thier wider applicability

the power of optimization over randomization in designing experiments involving small samples random assignment typically seen as the standard in controlled trials aims to make experimental groups statistically equivalent before treatment however with a small sample which is a practical reality in many disciplines randomized groups are often too dissimilar to be useful we propose an approach based on discrete linear optimization to create groups whose discrepancy in their means and variances is several orders of magnitude smaller than with randomization we provide theoretical and computational evidence that groups created by optimization have exponentially lower discrepancy than those created by randomization and that this allows for more powerful statistical inference

polyhedral cone ratio dea models with an illustrative application to large commercial banks abstract polyhedral cone ratio data envelopment analysis models generalizing the ccr ratio model are developed for situations with a finite number of dmus and employing polyhedral cones of virtual multipliers they provide improved definitions of efficiency over ccr models whose input output data and or numbers of dmus are inadequate to capture aspects or restrictions which should be involved the focus here is on the sum form for cones which easily provides for capturing exogenous expert opinion as well as mathematical reduction to the old form with its very powerful software transformation from the usual intersection form to it and vice versa is explicitly given thereby the advantages of either or both are available the theory is illustrated with two dimensional examples and by real banking examples for motivation

fuzzy multiattribute grey related analysis using dea qualitative input is encountered in many real decision making domains often such domains include tradeoffs among multiple attributes and estimates of parameters are often expressed with some degree of uncertainty grey related analysis has been proposed as a means to use interval fuzzy representation of data when dealing with multiple criteria data model parameters that can involve uncertainty include both performances of alternatives on attributes as well as attribute weights dea is proposed as an objective way to derive weights this paper presents a grey related fuzzy set methodology incorporating data envelopment analysis as a way to more objectively rank alternatives the purpose is to demonstrate the method the focus is on identifying alternatives performing the most efficiently with respect to the decision maker s preference the method is demonstrated on a multiattribute siting problem simulation is applied to validate model efficiency

detecting random walks on graphs with heterogeneous sensors we consider the problem of detecting a random walk on a graph based on observations of the graph nodes when visited by the walk each node of the graph observes a signal of elevated mean which we assume can be different across different nodes outside of the path of the walk and also in its absence nodes measure only noise assuming the neyman pearson setting our goal then is to characterize detection performance by computing the error exponent for the probability of a miss under a constraint on the probability of false alarm since the exact computation of the error exponent is known to be difficult equivalent to the computation of the lyapunov exponent we approximate its value by finding a tractable lower bound the bound reveals an interesting detectability condition the walk is detectable whenever the entropy of the walk is smaller than one half of the expected signal to noise ratio we derive the bound by extending the notion of markov types to gauss markov types these are sequences of the state observation pairs with a given number of node to node transition counts and the same average signal values across nodes computed from the measurements made during the times the random walk visited each node s respective location the lower bound has an intuitive interpretation among all gauss markov types that are asymptotically feasible in the absence of the walk the bound finds the most typical one under the presence of the walk finally we show by a sequence of judicious problem reformulations that computing the bound reduces to solving a convex optimization problem which is a result of in its interest own right

a value efficiency approach to incorporating preference information in data envelopment analysis we develop a procedure and the requisite theory for incorporating preference information in a novel way in the efficiency analysis of decision making units the efficiency of deci sion making units is defined in the spirit of data envelopment analysis dea complemented with decision maker s preference information concerning the desirable structure of inputs and outputs our procedure begins by aiding the decision maker in searching for the most preferred combination of inputs and outputs of decision making units for short most preferred solution which are efficient in dea then assuming that the decision maker s most preferred solution maximizes his her underlying unknown value function we approximate the indifference contour of the value function at this point with its possible tangent hyperplanes value efficiency scores are then calculated for each decision making unit comparing the inefficient units to units having the same value as the most preferred solution the resulting value efficiency scores are optimistic approximations of the true scores the procedure and the resulting efficiency scores are immediately applicable to solving practical problems

performance evaluation an integrated method using data envelopment analysis and fuzzy preference relations in a multi attribute decision making madm context the decision maker needs to provide his preferences over a set of decision alternatives and constructs a preference relation and then use the derived priority vector of the preference to rank various alternatives this paper proposes an integrated approach to rate decision alternatives using data envelopment analysis and preference relations this proposed approach includes three stages first pairwise efficiency scores are computed using two dea models the ccr model and the proposed cross evaluation dea model second the pairwise efficiency scores are then utilized to construct the fuzzy preference relation and the consistent fuzzy preference relation third by use of the row wise summation technique we yield a priority vector which is used for ranking decision making units dmus for the case of a single output and a single input the preference relation can be directly obtained from the original sample data the proposed approach is validated by two numerical examples

matching on the fly sequential allocation with higher power and efficiency we propose a dynamic allocation procedure that increases power and efficiency when measuring an average treatment effect in fixed sample randomized trials with sequential allocation subjects arrive iteratively and are either randomized or paired via a matching criterion to a previously randomized subject and administered the alternate treatment we develop estimators for the average treatment effect that combine information from both the matched pairs and unmatched subjects as well as an exact test simulations illustrate the method s higher efficiency and power over several competing allocation procedures in both simulations and in data from a clinical trial

structural comparison of data envelopment analysis and multiple objective linear programming the concept of efficiency as it applies to decision making units dmus solutions alternatives plays an important role both in data envelopment analysis dea and multiple objective linear programming molp despite this and other apparent similarities dea and molp research has developed separately we show that structurally the dea formulation to identify efficient units is quite similar to the molp model based on the reference point or the reference direction approach to generate efficient solutions dea and molp should not be seen as substitutes but rather as complements we show that they cross fertilize each other molp provides interesting extensions to dea and dea provides new areas of application to molp

a hybrid genetic algorithm for multiobjective problems with activity analysis based local search the objective of this research was the development of a method that integrated an activity analysis model of profits from production with a biophysical model and included the capacity for optimization over multiple objectives we specified a hybrid genetic algorithm using activity analysis as a local search method and nsga ii for calculation of the multiple objective pareto optimal set we describe a parallel computing approach to computation of the genetic algorithm and apply the algorithm to evaluation of an input tax to regulate pollution from agricultural production

asymptotic theory of rerandomization in treatment control experiments although complete randomization ensures covariate balance on average the chance of observing significant differences between treatment and control covariate distributions increases with many covariates rerandomization discards randomizations that do not satisfy a predetermined covariate balance criterion generally resulting in better covariate balance and more precise estimates of causal effects previous theory has derived finite sample theory for rerandomization under the assumptions of equal treatment group sizes gaussian covariate and outcome distributions or additive causal effects but not for the general sampling distribution of the difference in means estimator for the average causal effect we develop asymptotic theory for rerandomization without these assumptions which reveals a non gaussian asymptotic distribution for this estimator specifically a linear combination of a gaussian random variable and truncated gaussian random variables this distribution follows because rerandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals we demonstrate that compared with complete randomization rerandomization reduces the asymptotic quantile ranges of the difference in means estimator moreover our work constructs accurate large sample confidence intervals for the average causal effect

near optimal signal detection for finite state markov signals with application to magnetic resonance force microscopy detection of a finite state markov signal in additive white gaussian noise awgn can be done in an intuitive manner by applying an appropriate filter and using an energy detector one might not expect this heuristic approach to signal detection to be optimal however in this paper we show that for a certain type of finite state markov signal namely the discrete time dt random telegraph this filtered energy detector is approximately optimal under the following conditions of symmetric transition probabilities low signal to noise ratio snr long observation time and small probability of transition between two consecutive time instances when these last three conditions hold but the transition probabilities are not symmetric we show that a variant of the filtered energy detector is approximately optimal it is also shown under low snr conditions that the likelihood ratio test lrt for a finite state dt markov signal in awgn reduces to the matched filter statistic with the minimum mean squared error mmse predictor signal values used in place of the known signal values using this result we propose a general methodology for obtaining an approximation to the lrt of a finite state dt markov signal in awgn specifically instead of the conditional mean also mmse estimators affine estimators with lowest mean squared error are used this work is relevant to magnetic resonance force microscopy an emerging technology that uses ultrasensitive force sensing to detect magnetic resonance sensitivity down to the single spin level was demonstrated in a recent experiment

target setting in the general combined oriented ccr model using an interactive molp method the traditional data envelopment analysis dea model does not include a decision maker s dm preference structure while measuring relative efficiency with no or minimal input from the dm to incorporate dm s preference information in dea various techniques have been proposed an interesting method to incorporate preference information without necessary prior judgment is the use of an interactive decision making technique that encompasses both dea and multi objective linear programming molp in this paper we will use zionts wallenius z w method to reflecting the dm s preferences in the process of assessing efficiency in the general combined oriented ccr model a case study will conducted to illustrate how combined oriented efficiency analysis can be conducted using the molp method

a multiple criteria approach to data envelopment analysis in this paper we present a multiple criteria data envelopment analysis mcdea model which can be used to improve discriminating power of dea methods and also effectively yield more reasonable input and output weights without a priori information about the weights in the proposed model several different efficiency measures including classical dea efficiency are defined under the same constraints each measure serves as a criterion to be optimized efficiencies are then evaluated under the framework of multiple objective linear programming molp the method is illustrated through three examples in which data sets are taken from previous research on dea s discriminating power and weight restriction

optimal a priori balance in the design of controlled experiments summary we develop a unified theory of designs for controlled experiments that balance baseline covariates a priori before treatment and before randomization using the framework of minimax variance and a new method called kernel allocation we show that any notion of a priori balance must go hand in hand with a notion of structure since with no structure on the dependence of outcomes on baseline covariates complete randomization no special covariate balance is always minimax optimal restricting the structure of dependence either parametrically or non parametrically gives rise to certain covariate imbalance metrics and optimal designs this recovers many popular imbalance metrics and designs previously developed ad hoc including randomized block designs pairwise matched allocation and rerandomization we develop a new design method called kernel allocation based on the optimal design when structure is expressed by using kernels which can be parametric or non parametric relying on modern optimization methods kernel allocation which ensures nearly perfect covariate balance without biasing estimates under model misspecification offers sizable advantages in precision and power as demonstrated in a range of real and synthetic examples we provide strong theoretical guarantees on variance consistency and rates of convergence and develop special algorithms for design and hypothesis testing

the covariate adaptive biased coin design for balancing clinical trials in the presence of prognostic factors the present paper deals with sequential designs intended to balance the allocations of two competing treatments in the presence of prognostic factors after giving a theoretical framework on the optimality of balanced designs that can arise when covariates are taken into account we propose a new family of covariate adaptive randomized designs that represents higher order approximation to balance treatments both globally and also across covariates we derive the theoretical properties of the suggested designs in terms of loss of precision and predictability the performance of this proposal is illustrated through a simulation study and compared with those of other procedures suggested in the literature copyright 2011 oxford university press

a multiplier bound approach to assess relative efficiency in dea without slacks abstract in this paper we propose a new approach to deal with the non zero slacks in data envelopment analysis dea assessments that is based on restricting the multipliers in the dual multiplier formulation of the used dea model it guarantees strictly positive weights which ensures reference points on the pareto efficient frontier and consequently zero slacks we follow a two step procedure which after specifying some weight bounds results in an assurance region type model that will be used in the assessment of the efficiency the specification of these bounds is based on a selection criterion among the optimal solutions for the multipliers of the unbounded dea models that tries to avoid the extreme dissimilarity between the weights that is often found in dea applications the models developed do not have infeasibility problems and we do not have problems with the alternate optima in the choice of weights that is made to use our multiplier bound approach we do not need a priori information about substitutions between inputs and outputs and it is not required the existence of full dimensional efficient facets on the frontier either as is the case of other existing approaches that address this problem