Multivariate outlier detection in incomplete survey data: the epidemic algorithm and transformed rank correlations

Summary.  As a part of the EUREDIT project new methods to detect multivariate outliers in incomplete survey data have been developed. These methods are the first to work with sampling weights and to be able to cope with missing values. Two of these methods are presented here. The epidemic algorithm simulates the propagation of a disease through a population and uses extreme infection times to find outlying observations. Transformed rank correlations are robust estimates of the centre and the scatter of the data. They use a geometric transformation that is based on the rank correlation matrix. The estimates are used to define a Mahalanobis distance that reveals outliers. The two methods are applied to a small data set and to one of the evaluation data sets of the EUREDIT project.     

Multicriteria decision support in local energy planning: An evaluation of alternative scenarios for the Sustainable Energy Action Plan

One of the major challenges for the implementation of local energy planning is the successful development of a Sustainable Energy Action Plan (SEAP) by the local authorities (especially within the framework of their participation to the Covenant of Mayors’ initiative). This aspect constitutes a decision making problem, since the local authorities have to identify the best fields of actions and opportunities for reaching their long-term CO₂ reduction target. However, the already available methods and tools do not offer an integrated framework for the SEAPs’ development and especially the selection of sustainable Renewable Energy Sources (RES) and Rational Use of Energy (RUE) technologies. In this context, the aim of this paper is to present a participatory supportive framework for the implementation of local energy planning. At the first level, the proposed approach incorporates the development of alternative Scenarios of Actions (using knowledge-based process, participatory approach and aspiration level). At the second level, a direct and transparent multicriteria decision support is introduced, in order to evaluate the feasible Scenarios. It includes the application of a multicriteria ordinal regression approach and an extreme ranking analysis method for the estimation of the best and worst possible ranking position of each Scenario. The results from the pilot appraisal of the methodological approach to a “real” problem are presented and discussed. The adopted approach contributes to the selection of the most appropriate combination of RES/RUE actions, supporting in this way the local authorities to the development of their SEAP.     

Integrated framework for robustness analysis using ratio-based efficiency model with application to evaluation of Polish airports

We consider a problem of evaluating efficiency of Decision Making Units (DMUs) based on their deterministic performance on multiple consumed inputs and multiple produced outputs. We apply a ratio-based efficiency measure, and account for the Decision Maker׳s preference information representable with linear constraints involving input/output weights. We analyze the set of all feasible weights to answer various robustness concerns by deriving: (1) extreme efficiency scores and (2) extreme efficiency ranks for each DMU, (3) possible and necessary efficiency preference relations for pairs of DMUs, (4) efficiency distribution, (5) efficiency rank acceptability indices, and (6) pairwise efficiency outranking indices. The proposed hybrid approach combines and extends previous results from Ratio-based Efficiency Analysis and the SMAA-D method. The practical managerial implications are derived from the complementary character of accounted perspectives on DMUs׳ efficiencies. We present an innovative open-source software implementing an integrated framework for robustness analysis using a ratio-based efficiency model on the diviz platform. The proposed approach is applied to a real-world problem of evaluating efficiency of Polish airports. We consider four inputs related to the capacities of a terminal, runways, and an apron, and to the airport׳s catchment area, and two outputs concerning passenger traffic and number of aircraft movements. We present how the results can be affected by integrating the weight constraints and eliminating outlier DMUs.     

A Theory of Rational Choice under Ignorance

This paper contributes to a theory of rational choice for decision-makers with incomplete preferences due to partial ignorance, whose beliefs are representable as sets of acceptable priors. We focus on the limiting case of `Complete Ignorance' which can be viewed as reduced form of the general case of partial ignorance. Rationality is conceptualized in terms of a `Principle of Preference-Basedness', according to which rational choice should be isomorphic to asserted preference. The main result characterizes axiomatically a new choice-rule called `Simultaneous Expected Utility Maximization'. It can be interpreted as agreement in a bargaining game (Kalai-Smorodinsky solution) whose players correspond to the (extremal) `acceptable priors' among which the decision maker has suspended judgment. An essential but non-standard feature of Simultaneous Expected Utility choices is their dependence on the entire choice set. This is justified by the conception of optimality as compromise rather than as superiority in pairwise comparisons.     

Robust modal estimation and variable selection for single-index varying-coefficient models

In this article, we present a new efficient iteration estimation approach based on local modal regression for single-index varying-coefficient models. The resulted estimators are shown to be robust with regardless of outliers and error distributions. The asymptotic properties of the estimators are established under some regularity conditions and a practical modified EM algorithm is proposed for the new method. Moreover, to achieve sparse estimator when there exists irrelevant variables in the index parameters, a variable selection procedure based on SCAD penalty is developed to select significant parametric covariates and the well-known oracle properties are also derived. Finally, some numerical examples with various distributed errors and a real data analysis are conducted to illustrate the validity and feasibility of our proposed method.     

A robustness framework for monitoring real options under uncertainty

This paper presents a problem structuring methodology to assess real option decisions in the face of unpredictability. Based on principles of robustness analysis and scenario planning, we demonstrate how decision-aiding can facilitate participation in projects setting and achieve effective decision making through the use of real options reasoning. We argue that robustness heuristics developed in earlier studies can be practical proxies for real options performance, hence indicators of efficient flexible planning. The developed framework also highlights how to integrate real options solutions in firms’ strategic plans and operating actions. The use of the methodology in a location decision application is provided for illustration.     

On influence diagnostic in univariate elliptical linear regression models

We discuss in this paper the assessment of local influence in univariate elliptical linear regression models. This class includes all symmetric continuous distributions, such as normal, Student-t, Pearson VII, exponential power and logistic, among others. We derive the appropriate matrices for assessing the local influence on the parameter estimates and on predictions by considering as influence measures the likelihood displacement and a distance based on the Pearson residual. Two examples with real data are given for illustration.     

An illustration of dynamic network DEA in commercial banking including robustness tests

The main motivation of this article is to illustrate dynamic network data envelopment analysis (DN-DEA) in commercial banking with emphasis on testing robustness. To this end, sixteen foreign banks in China are benchmarked against thirty-two domestic banks for the post-2007 period that follows major reforms. When network and dynamic dimensions are brought together, a more comprehensive analysis of the period 2008–2010 is enabled where divisional and between-period interactions are reflected in efficiency estimates. Weighted, variable returns-to-scale, non-oriented dynamic network slacks-based measure is used within the framework of the intermediation approach to bank behavior. A bank network (i.e., a decision-making unit, DMU) is conceptualized as comprised of two divisions or sub-DMUs, namely, interest-bearing operations and non-interest operations linked by number of referrals. Undesirable outputs from sub-DMUs 1 and 2 (non-performing loans, and proportion of fruitless referrals, respectively) are treated as carry-overs that impact the efficiency of the following periods. Under robustness testing, the illustrative application discusses discrimination by efficiency estimates, dimensionality of the performance model, stability of estimates through re-sampling (leave-one-out method), and sensitivity of results to divisional weights and returns-to-scale assumptions. The results based on Chinese commercial banks are illustrative in nature because of simulated data used on two of the variables.     

Estimation of the means of the bivariate normal using moving extreme ranked set sampling with concomitant variable

The estimation of the means of the bivariate normal distribution, based on a sample obtained using a modification of the moving extreme ranked set sampling technique (MERSS) is considered. The modification involves using a concomitant random variable. Nonparametric-type methods as well as the maximum likelihood estimation are considered. The estimators obtained are compared to their counterparts based on simple random sampling (SRS). It appears that the suggested estimators are more efficient. Also, MERSS with concomitant variable is easier to use in practice than the usual ranked set sampling (RSS) with concomitant variable. The issue of robustness of the procedure is addressed. Real trees data set is used for illustration.     

Trimmed and Outer Means and Their Variances

Some properties of trimmed and outer means for the normal situation are considered; in particular, the mean of the outer half of the sample has the same variance as the mean of the inner half. An inequality involving variances of unbiased estimators of location and their complements is derived and some of its consequences are examined.