Tests for departure from normality in the case of linear stochastic processes

Summary In this paper the asymptotic distributions of the third and the fourth sampling moments of a discrete-parameter linear process are derived together with the asymptotic distributions of the sampling skewness and the excess of kurtosis. The knowledge of these distributions allows us, in the case of “large” samples, to test the departure from normality, a problem which can be regarded as important in various practical applications, but which cannot be treated with the aid of classical tests based on the assumption that the sample values are independent. Some numerical examples illustrate the applications of the proposed tests in practice.

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Zusammenfassung In diesem Beitrage sind die asymptotischen Stichprobenverteilungen der dritten und vierten Momente eines linearen stochastischen Prozesses und auch die asymptotischen Stichprobenverteilungen der Schiefe und des Exzesses der Kurtosis hergeleitet. Die Kenntnis dieser Verteilungen erlaubt für “gro?e” Stichproben die Abweichung der Proze?verteilung von der Normalverteilung zu prüfen, ein Problem, das in vielen F?llen der praktischen Anwendungen wichtig ist, aber mit den klassischen Testen, welche die Unabh?ngigkeit der Stichprobenwerte annehmen, nicht behandelt werden kann. Die praktische Anwendung der vorgelegten Methode ist mit einigen numerischen Beispielen illustriert.

     

Variance estimation in the change analysis of a linear regression model

We study a “direct test” of Chu and White (1992) proposed for detecting changes in the trend of a linear regression model. The power of this test strongly depends on a suitable estimation of the variance of the error variables involved. We discuss various types of variance estimators and derive their asymptotic properties under the null-hypothesis of “no change” as well as under the alternative of “a change in linear trend”. A small simulation study illustrates the estimators' finite sample behaviour.     

Verbesserung des nicht-randomisierten exakten Testes von R.A. Fisher

Summary The so-called Exact Test of R. A. Fisher for comparing two probabilitiesp ₁ andp ₂ in a Fourfold-Table with small cell frequencies is known as a UMPU-Test. But in practice the test is used in a nonrandomized, often tabulated version. Given a certain level of significanceα it is shown: the critical region of this nonrandomized test, referred to as “Fisher 1”, can be enlarged considerably. For instance for all sample-size-sums up to 20 andα=0.01 the total number of points in the critical regions of “Fisher 1” is 552 whereas the analogous number of the new version “Fisher 2” is 788. The size of tables for “Fisher 2” can be reduced considerably because the main parts of the critical regions can be described by the aid of some Chi-square-test versions. In particular Yates’ continuity-correction turns out to be always conservative in the above mentioned region relative to “Fisher 2” whereas this is not strictly true relative to “Fisher 1”.      

Are day traders bias free?—evidence from internet stock message boards

This study addresses the issue whether day traders’ recommendations on stocks are biasfree. We test whether on average day traders’ “Hold” sentiment is skewed and different from a neutral opinion. Posted messages and mature text classifier technology provide a novel approach to analyze the content of these “Hold” sentiment postings among day traders. Findings indicate that the self-disclosed “Hold” sentiment conveys an optimistic opinion and significantly differs from neutral. These results help both investors and researchers to better understand day traders’ psychology and behaviors when they recommend stocks. The paper also provides insight into the construction of future online sentiment indexes based on stock message boards.     

Determining of threat perceptions affecting direction of the US defense expenditures by using ordinal regression models

The article examines whether the US threat perceptions defined in terms of federal government national defense outlays in billions of constant (FY 2000) dollars change along with periodical changes in international politics between 1945 and 2007. Three different models affecting direction of the US defense expenditures are developed. The first model are estimated by using five link functions even though results of only two of them, complementary log–log and cauchit, are presented. As complementary log–log produced the best results, others models are predicted by using only this function. The parameter estimates of complementary log–log function for the first model indicate that four of these variables (Ford, Carter, Reagan and Bush Sr.) out of eleven are significant in the category of presidents. “Truman Docrtrine/Cominform”, “Korean War”, “Vietnam War”, and “Invasion of Iraq” also seem to be the important independent variables on empirical grounds for the first model. While “Party”, “Invasion of Iraq”, “Vietnam War”, “Korean War”, and “Cuban Missile Crisis” constitute the important independent variables on empirical grounds for the second model, “Korean War”, “Vietnam War”, “Invasion of Iraq”, “Truman Docrtrine/Cominform”, “The Cold War and New World Order”, and “Cuban Missile Crisis” are important independent variables on empirical grounds for the third model. Estimations based on these three models therefore suggest that aforementioned independent variables do indeed have effect on the US defense expenditures.     

On the active approach of stochastic linear programming

Summary The problem of statistical distribution of the optimal objective function under the so-called active approach of stochastic linear programming is investigated here from two interrelated aspects. First, the active approach is viewed as a method of decomposition. Second, some results on the asymptotic form of distribution of extreme values are utilized to derive the asymptotic form of the distribution of the maximand under the active approach. Research done under the partial support of the U.S. National Science Foundation Grant No. 420-04-62 at the Department of Economics, Iowa State University. Some of the work related to this paper may be found in the following references:Sengupta, J. K., G. Tintner, andC. Millham: “On Some Theorems of Stochastic Linear Programming”. Management Science, Vol. 10, October 1963, pp. 143–159.Sengupta, J. K.: “The stability of truncated solutions of stochastic linear programming”. Econometrica, Vol. 34, January 1966. pp. 77–104.Sengupta, J. K.: “On the stability of solution under recursive programming”. Metrika 1966.Sengupta, J. K. andT. Kumar: “An application of sensitivity analysis to a linear programming problem”. Unternehmensforschung, Vol. 9, 1965.     

Asymptotic efficiencies of spacings tests for goodness of fit

Tests based on higher-order orm-step spacings have been considered in the literature for the goodness of fit problem. This paper studies the asymptotic distribution theory for such tests based on non-overlappingm-step spacings whenm, the length of the step, also increases with the sample sizen, to inifinity. By utilizing the asymptotic distributions under a sequence of close alternatives and studying their relative efficiencies, we try to answer a central question about the choice ofm in relation ton. Efficiency comparisons are made with tests based on overlappingm-step spacings, as well as corresponding chi-square tests.     

Testing whetherF is more IFR thanG

A distributionF is said to be “more IFR” than another distributionG ifG ⁻¹ F is convex. WhenF(0) =G(0) = 0, the problem of testingH ₀ :F(x) =G (θx) for someθ > 0 andx ⩾ 0, against the alternativeH _A:F is more IFR thanG, is considered in this paper. Both cases, whenG is completely specified (one-sample case) and when it is not specified but a random sample form it is available (two-sample case) are considered. The proposed tests are based onU-statistics. The asymptotic relative efficiency of the tests are compared with several other tests and the test statistics remain asymptotically normal under certain dependency assumptions. Research supported in part by a grant from the US Air Force Office of Scientific Research.     

Social Distance,Respondent Cooperation and Item Nonresponse in Sex Survey

This paper examines the ways in which the number of item nonresponses is determined by social distance and/or interview rapport, with a focus on responses of “refusal” and “don’t know”, implying the respondent’s lack of willingness and ability to provide substantive responses to sensitive questions. The data analyzed were from 39 self- administered questions concerning sexual attitudes and behaviors in the 2002 Taiwan Social Change Survey for module “Family and Changing Gender Role”. Poisson Regression in 2-level Hierarchical Linear Model was employed to enhance the accuracy of the analysis of the accumulation of “don’t know” and “refusal” responses. The results showed that respondent cooperation significantly decreased the number of both “don’t know” and “refusal” replies. The decrease was not conditioned by any kind of social distance. Age and education distances have respectively negative and positive effect on the number of “don’t know” and “refusal” answers. The married–married interview produced more “don’t know” and “refusal” than other paired interview types. The larger the ethnicity distance is, the more “refusal” appears. The substantial findings imply that the effects of social-distance and rapport (respondent cooperation) on the number of item nonresponses deserve more attention in research on survey methodology. The divergent findings on gender-distance effect and marital-status effect, however, call for replication studies in the future.     

Competitive market equilibrium under asymmetric information

This paper studies the existence of a competitive market equilibrium under asymmetric information. There are two agents involved in the trading of the risky assets: an “informed” trader and an “ordinary” trader. The market is competitive and the ordinary agent can infer the insider information from the price dynamics of the risky assets. The insider information is considered to be the total supply of the risky assets. The definition of market equilibrium is based on the law of supply-demand as described by a rational expectations equilibrium of the Grossman and Stiglitz (Am Econ Rev 70:393–408, 1980) model. We show that equilibrium can be attained by linear dynamics of an admissible price process of the risky assets for a given linear supply dynamics.      

The Use of Indices in Surveys

The paper deals with some new indices for ordinal data that arise from sample surveys. Their aim is to measure the degree of concentration to the “positive” or “negative” answers in a given question. The properties of these indices are examined. Moreover, methods for constructing confidence limits for the indices are discussed and their performance is evaluated through an extensive simulation study. Finally, the values of the indices defined and their confidence intervals are calculated for an example with real data. This revised version was published online in June 2006 with corrections to the Cover Date.     

Performance persistence of fixed income mutual funds

The “winner-winner, winner-loser, gone” methodology allows tests for short-term performance persistence for government and corporate fixed income mutual funds from 1990 to 1999. Persistence occurs when “winner” (loser) funds remain “winner” (loser) funds. If intermediate-term (long-term) bond returns are higher than long-term (intermediate-term) bond returns for successive years, the z-statistic is positive. Persistence is negative in the opposite case, and the pattern holds for longer lag periods. Statistical significance and consistency between the sign of persistence and bond returns indicates persistent returns on bond funds, but the nature of persistence is driven by changes in interest rates. The authors would like to acknowledge the research assistance of Michael Serra and Michael Wieczorek. This research was supported in part by the McDonough School of Business and the Capital Markets Research Center at Georgetown University.     

Do components of smooth tests of fit have diagnostic properties?

Smooth goodness of fit tests were introduced by Neyman (1937). They can be regarded as a compromise between globally consistent (“omnibus”) tests of fit and procedures having high power in the direction of a specific alternative. It is commonly believed that components of smooth tests like, e.g., skewness and kurtosis measures in the context of testing for normality, have special diagnostic properties in case of rejection of a hypothesisH ₀ in the sense that they constitute direct measures of the kind of departure fromH ₀. Recent years, however, have witnessed a complete change of attitude towards the diagnostic capabilities of skewness and kurtosis measures in connection with normality testing. In this paper, we argue that any component of any smooth test of fit is strictly non-diagnostic when used conventionally. However, a proper rescaling of components does indeed achieve the desired “directed diagnosis”.     

A family of measures of uncertainty involving utilities: Definition,properties, applications and statistical inferences

Consider an experiment involving the observation of a discrete random variable, or quantitative classification process. When, in addition to the probability of each value or class we know its “utility” (or, more precisely, we can quantify the “nature” of each value or class), the “uncertainty corresponding to the utilities” may be evaluated. In this paper, we are first going to introduce a family of Measures of Uncertainty involving Utilities and several properties of this family are studied. Then, some immediate applications are discussed: the definition of criteria for Comparing Experiments in Statistical Decision problems, and the quantification of the Inequality with respect to an economical attribute or the Industrial Concentration. Finally, we will analyze the asymptotic behaviour of the measures in simple random sampling, and some related problems. This work was partially supported by the Comisión Asesora de Investigación Científica Técnica (CAICYT) under the contract PB85-0401.     

Impact of relational norms, supplier development and trust on supplier performance

Supplier relationship management and supplier development initiatives assume a fundamental role in enterprise supply chain management. An important aspect of effective supplier relationship management is the role of trust. This paper seeks to understand whether supplier relationship management or supplier development initiative should be emphasized as a firm strives to achieve superior supplier performance. The analysis and discussion draws upon sourcing strategy literature and is based on empirical survey-data of mid to upper level managers with responsibility for supply management initiatives in their respective organizations in Denmark and in the USA. It examines the interrelationships among “relational norms”, “trust”, “supplier development initiatives” and ensuing “supplier performance”. The data analysis shows that firms must emphasize relation and trust building activities before investing in supplier development initiative. Supplier perception audits must be routinely performed to gauge the level of trust and strength of relational norms.     

One optional observation inflates α by $${100/\sqrt{n}}$$ per cent

For one-sample level α tests ψ _m based on independent observations X ₁, . . . , X _m , we prove an asymptotic formula for the actual level of the test rejecting if at least one of the tests ψ _n , . . . , ψ _n+k would reject. For k = 1 and usual tests at usual levels α, the result is approximately summarized by the title of this paper. Our method of proof, relying on some second order asymptotic statistics as developed by Pfanzagl and Wefelmeyer, might also be useful for proper sequential analysis. A simple and elementary alternative proof is given for k = 1 in the special case of the Gauss test.     

Sampling studies on a test against trend in binomial data

Summary A series of 375 “Monte-Carlo” realizations were performed on a number of groupings of 100 samples each fromt distinct binomial populations (t=3, 4, 5, 7, 9) in order to obtain estimates of the power function of theV andX ² index of dispersion tests in detection of a “trend” in the binomial probabilities.     

Consistency and its converse: an introduction

This essay is a didactic introduction to the literature on the “consistency principle” and its “converse”. An allocation rule is consistent if for each problem in its domain of definition and each alternative that it chooses for it, then for the “reduced problem” obtained by imagining the departure of an arbitrary subgroup of the agents with their “components of the alternative” and reassessing the options open to the remaining agents, it chooses the restriction of the alternative to that subgroup. Converse consistency pertains to the opposite operation. It allows us to deduce that a rule chooses an alternative for a problem from the knowledge that for each two-agent subgroup, it chooses its restriction to the subgroup for the associated reduced problem this subgroup faces. We present two lemmas that have played a critical role in helping understand the implications of these properties in a great variety of models, the Elevator Lemma and the Bracing Lemma. We describe several applications. Finally, we illustrate the versatility of consistency and of its converse by means of a sample of characterizations based on them.     

Analysing the lobby-effect of port competitiveness’ determinants: a stochastic frontier approach

Building upon a formerly performed study on port competitiveness, this article discusses the use of a stochastic frontier model as an interesting novel use to test, identify and correct respondents’ bias by applying it to competitiveness analysis based on perceptions of senior executives. Measuring the importance of competition determinants of seaports, conventionally analyzed using a SWOT-analysis based on (transport) infrastructure as a prime requirement for port activity growth, is an important issue to port management. However, it seems that the “institutional” environment of a seaport is also critical in obtaining a competitive advantage. In Haezendonck et al. (2000 and 2001) those port specific advantages and disadvantages were identified using factor analysis and L1-regression on the perceptions of 75 respondents, all senior executives and experts, through a survey. As regards the results of this study, critiques were formulated on the use of perceptions, often biased due to the political lobbying potential of the results. Since respondents often see independent studies as an opportunity to obtain more or early government subsidies, attract new investment projects or at least highlight the attention on their specific problems and demands, they were prone to underestimating the positive impact of the key success factors of the studied seaport compared to its main rivals, in this case major seaports in the so-called Hamburg–Le Havre competitive range. The purpose of this article is to test the assumption that respondents significantly underestimate the positive impact of port specific advantages and to see which of the respondent subgroups within the 75 respondents sample are more responsible than others for this underestimation. In addition, we argue and demonstrate that the use of a stochastic frontier method is appropriate for this matter. Each of 25 considered competition determinants of the original study is decomposed into a noise and “efficiency” term, based on the Bayesian stochastic frontier model (BSFM). In this article, we find evidence that BSFM could be used to test the “lobby-effect” or underestimation of the real effect of determinants, that terminal operators as a subgroup of respondents, are more likely to underestimate the key success factors than the subgroup of port experts and that those determinants that are directly related to government action show more underestimation than competitiveness determinants that result from private investments.     

The Qualitative and Quantitative Models for Performance Measurement Systems: The Agile Service Development

A decision model for selection using analytic hierarchy process (AHP), however, they did not consider interdependence property but consider independence property among alternatives or criteria. It could become inadequate in measurement of actual performance of the decision process. In order to reduce the decision gap, this paper considers when independence among different elements of a system assumption is violated and takes into account the degree of the interdependence among them. The fuzzy analytic network process (FANP) approach with agile theory is developed to apply in analyzing the new service development in the wholesale center. The FANP could not only offer a hierarchy framework more efficiency and accuracy but also improve human judgment on the importance of requirements involving imprecise and vague. The technique has proved useful for comparing the importance among the determinants of agile for new service development in decision maker’s mind, including agile cost, time, robustness and scope. The empirical result points out that “Diverse designs” of new service development is the best choice for the wholesale center, following as “Service extended” and “Technological core”.