Measuring the Reliability of Qualitative Text Analysis Data

This paper reports a new tool for assessing thereliability of text interpretationsheretofore unavailable to qualitative research.It responds to a combination of twochallenges, the problem of assessing the reliabilityof multiple interpretations – asolution to this problem was anticipated earlier(Krippendorff, 1992) but not fullydeveloped – and the problem of identifying unitsof analysis within a continuum of textand similar representations (Krippendorff, 1995).The paper sketches the family of-coefficients, which this paper extends, andthen describes its new arrival.A computational example is included in the Appendix.     

Implementation and orderings of public information

We explore the relationship between public information and implementable outcomes in an environment characterized by random endowments and private information. We show that if public signals carry no information about private types, then an exact relationship holds: a more informative public signal structure, in the sense of Blackwell, induces a smaller set of ex-ante implementable social choice functions. This holds for a large set of implementation standards, including Nash implementation, and Bayesian incentive compatibility. The result extends the notion, dating to Hirshleifer (1971), that public information can have negative value to an endowment economy under uncertainty.Received: 23 September 2003, Accepted: 30 July 2004, JEL Classification: D80Colin M. Campbell: I thank two referees and seminar participants at the 2002 meetings of the Society for Economic Design, at the 2003 Winter Meetings of the Econometric Society, and at Yale University for helpful input.     

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).     

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.     

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.     

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.     

A statistical treatment of the problem of division

The problem of division is one of the most important problems in the emergence of probability. It has been long considered solved from a probabilistic viewpoint. However, we do not find the solution satisfactory. In this study, the problem is recasted as a statistical problem. The outcomes of matches of the game are considered as an infinitely exchangeable random sequence and predictors/estimators are constructed in light of de Finetti representation theorem. Bounds of the estimators are derived over wide classes of priors (mixing distributions). We find that, although conservative, the classical solutions are justifiable by our analysis while the plug-in estimates are too optimistic for the winning player.Acknowledgement. The authors would like to thank the referees for the insightful and informative suggestions and, particularly, for referring us to important references.Supported by NSC-88-2118-M-259-009.Supported in part by NSC 89-2118-M-259-012.Received August 2002     

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.     

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.     

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     

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.