Elfving’s method for <Emphasis Type="Italic">m</Emphasis>-dimensional models

Elfvings method is a well known graphical procedure for obtaining c-optimal designs. Although the method is valid for any dimension it is rarely used for more than two parameters. Its usefulness seems to be constrained by the difficulty on the construction of the Elfving set. In this paper a computational procedure for finding c-optimal designs using Elfvings method for more than two dimensions is provided. It is suitable for any model, achieving an efficient performance for three or four dimensional models. The procedure can be implemented in most programming languages.Acknowledgments. The authors would like to thank Dr. Torsney for his helpful comments. This research was supported by a grant from JCyL SA004/01.     

A nonsymmetric sequential test

A one-sided testing problem based on an i.i.d. sample of observations is considered. The usual one-sided sequential probability ratio test would be based on a random walk derived from these observations. Here we propose a sequential test where the random walk is replaced by Lindleys random walk which starts anew at zero as soon as it becomes negative. We derive the asymptotics of the expected sample size and the error probabilities of this sequential test. We discuss the advantages of this test for certain nonsymmetric situations.Acknowledgement. The authors thank the referee for helpful comments and suggestions. Their research was supported by the German Research Foundation (DFG) and the Russian Foundation for Basic Research (RFBR).     

Visualizing Efficiency and Reference Relations in Data Envelopment Analysis with an Application to the Branches of a German Bank

The interest in Data Envelopment Analysis (DEA) as a method for analyzing the productivity of homogeneous Decision Making Units (DMUs) has significantly increased in recent years. One of the main goals of DEA is to measure for each DMU its production efficiency relative to the other DMUs under analysis. Apart from a relative efficiency score, DEA also provides reference DMUs for inefficient DMUs. An inefficient DMU has, in general, more than one reference DMU, and an efficient DMU may be a reference unit for a large number of inefficient DMUs. These reference and efficiency relations describe a net which connects efficient and inefficient DMUs. We visualize this net by applying Sammons mapping. Such a visualization provides a very compact representation of the respective reference and efficiency relations and it helps to identify for an inefficient DMU efficient DMUs respectively DMUs with a high efficiency score which have a similar structure and can therefore be used as models. Furthermore, it can also be applied to visualize potential outliers in a very efficient way.JEL Classification: C14, C61, D24, M2     

A note on the projection properties of Hadamard matrices obtained by the first Payley construction

We show that the projections on four factors of an arbitrary orthogonal array of strength 2 allow the estimation of main effects and two-factor interactions when all other effects are assumed to be zero, if those projections satisfy the bounds given by Weils theorem. The only exceptions are the Hadamard matrices of orders 16 and 24. A consequence is again the estimability of main effects and two-factor interactions for the projections on four factors of the first Payley construction for arbitrary run size.     

An alternative direct proof of Gibbard’s random dictatorship theorem

We present an alternative proof of the Gibbards random dictatorship theorem with ex post Pareto optimality. Gibbard(1977) showed that when the number of alternatives is finite and larger than two, and individual preferences are linear (strict), a strategy-proof decision scheme (a probabilistic analogue of a social choice function or a voting rule) is a convex combination of decision schemes which are, in his terms, either unilateral or duple. As a corollary of this theorem (credited to H. Sonnenschein) he showed that a decision scheme which is strategy-proof and satisfies ex post Pareto optimality is randomly dictatorial. We call this corollary the Gibbards random dictatorship theorem. We present a proof of this theorem which is direct and follows closely the original Gibbards approach. Focusing attention to the case with ex post Pareto optimality our proof is more simple and intuitive than the original Gibbards proof.Received: 15 October 2001, Accepted: 23 May 2003, JEL Classification: D71, D72Yasuhito Tanaka: The author is grateful to an anonymous referee and the Associate editor of this journal for very helpful comments and suggestions. And this research has been supported by a grant from the Zengin Foundation for Studies on Economics and Finance in Japan.     

The Economic Convergence Performance of Central and Eastern European Countries

A critical discussion of a comparative growth analysis about Central and Eastern European (CEE) countries is performed. The main conclusion is that there was economic convergence for most CEE accession candidates, but not between them and Western Europe. Results do justify a separation into first and second-wave accession countries, but also undermine differences in Central and Eastern Europe between accession and non-accession countries.This paper critically examines theories and empirical studies for three types of convergence, namely , and club convergence. Each can be in absolute terms or conditional to the long-term equilibrium (steady state) for each country.Empirical results are provided for all types of convergence from 1996 to 2000, both with population-weighted and non-weighted data. The analysis is performed for differently framed country subgroups considering even Western Europe for better comparability. Once absolute convergence is found through a unit root test about a standard deviation time series of cross-sectional income per capita, the regression coefficient for initial income per capita with the average growth over the sample period as dependent variable ( convergence) establishes the speed of this process. The same method applies to the conditional version by using the distance of the income from the corresponding steady state instead of the level of GDP. Then Markov chain probability matrixes (club convergence) provide information about the past behaviour of the whole cross-sectional income distribution over time, but also about intra-mobility of single countries.     

Nonparametric discrimination of time series data

A normality assumption is usually made for the discrimination between two stationary time series processes. A nonparametric approach is desirable whenever there is doubt concerning the validity of this normality assumption. In this paper a nonparametric approach is suggested based on kernel density estimation firstly on (p+1) sample autocorrelations and secondly on (p+1) consecutive observations. A numerical comparison is made between Fishers linear discrimination based on sample autocorrelations and kernel density discrimination for AR and MA processes with and without Gaussian noise. The methods are applied to some seismological data.     

Seat allocation distributions and seat biases of stationary apportionment methods for proportional representation

In a proportional representation system, apportionment methods are used to round the vote proportion of a party to an integer number of seats in parliament. Assuming uniformly distributed vote proportions, we derive the seat allocation distributions for stationary divisor methods. An important characteristic of apportionment methods are seat biases, that is, expected differences between actual seat numbers and ideal shares of seats, when the parties are ordered from largest to smallest. We obtain seat bias formulas for the stationary divisor methods and for the quota method of greatest remainders.Acknowledgement. We thank Friedrich Pukelsheim for many fruitful discussions.Received March 2004     

The Impact of Respondent and Interviewer Characteristics on the Number of “No Opinion” Answers

In this article we analyse the number of no opinion answers to attitude items. We argue that that number can be considered as a count variable that should be analysed using Poisson regression or negative binomial regression. Since we're interested in the effect of both respondent and interviewer characteristics on the number of no opinion's we use multilevel analysis that takes into account the hierarchical structure of the data. As a consequence multilevel Poisson regression and multilevel negative binomial regression are applied. Our analysis shows that answering no opinion is related to some sociodemographic respondent characteristics. In addition we find a significant interviewer effect, but we are not able to explain that effect in terms of interviewer variables.     

Construction of D-optimal s 1 × s 2 × s 3 factorial designs using graph theory

In this paper, the maximum determinant of the associated 0-1 matrix in D-Optimal saturated main effect plans for 3× s_2 × s_3 factorials, is derived by the use of Graph theory and Combinatorics. The present work is related to a problem suggested by Chatterjee and Narasimhan (2002). Using the theoretical results, we also give the designs for s₃≥s₂ + 1. This research was supported by the State Scholarships Foundation of Greece.     

Probability theory in fuzzy sample spaces

This paper tries to develop a neat and comprehensive probability theory for sample spaces where the events are fuzzy subsets of The investigations are focussed on the discussion how to equip those sample spaces with suitable -algebras and metrics. In the end we can point out a unified concept of random elements in the sample spaces under consideration which is linked with compatible metrics to express random errors. The result is supported by presenting a strong law of large numbers, a central limit theorem and a Glivenko-Cantelli theorem for these kinds of random elements, formulated simultaneously w.r.t. the selected metrics. As a by-product the line of reasoning, which is followed within the paper, enables us to generalize as well as to bring together already known results and concepts from literature.Acknowledgement. The author would like to thank the participants of the 23rd Linz Seminar on Fuzzy Set Theory for the intensive discussion of the paper. Especially he is indebted to Professors Diamond and Höhle whose remarks have helped to get deeper insights into the subject. Additionally, the author is grateful to one anonymous referee for careful reading and valuable proposals which have led to an improvement of the first draft.This paper was presented at the 23rd Linz Seminar on Fuzzy Set Theory, Linz, Austria, February 5–9, 2002.