Approximations of the eigenvalues of the covariance matrix of a first-order autoregressive process

This paper provides explicit estimates of the eigenvalues of the covariance matrix of an autoregressive process of order one. Also explicit error bounds are established in closed form. Typically, such an error bound is given by $\text{ε}{}_{\mathrm{k}}\text{= (}\text{4}\text{(n+1)}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{ρ}{}^2\text{sin}\text{(}\text{kπ}\text{(n+1)}\text{)}$, so that the approximations improve as the size of the matrix increases. In other words, the accuracy of the approximations increases as direct computations become more costly.     

Empirical comparisons of some tests of separate families of hypotheses

Summary This paper is devoted to a comparison of the asymptotic tests of separate families of hypotheses proposed byCox [1961, 1962] and byAtkinson [1970]. The adequacy of the asymptotic results for finite samples is investigated and some conclusions reached. An examination of the terms which differentiate the two procedures is made. Empirical simulated results are discussed for cases involving the exponential, the lognormal and the Weibull distributions.

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Zusammenfassung In dieser Arbeit wird ein Vergleich angestellt zwischen den Vorschlägen vonCox [1961, 1962] undAtkinson [1970] über asymptotische Tests separierter Familien von Hypothesen. Die Angemessenheit der asymptotischen Resultate für endliche Proben wird untersucht und einige Folgerungen gezogen. Eine Prüfung der Terme, die die beiden Verfahren differenzieren, wird vorgenommen. Empirisch simultierte Resultate werden distribuiert für Fälle mit exponential, lognormal und Weibull Verteilungen.

     

Application of a double bootstrap to investigation of determinants of technical efficiency of farms in Central Europe

The paper provides one of the first applications of the double bootstrap procedure (Simar and Wilson 2007) in a two-stage estimation of the effect of environmental variables on non-parametric estimates of technical efficiency. This procedure enables consistent inference within models explaining efficiency scores, while simultaneously producing standard errors and confidence intervals for these efficiency scores. The application is to 88 livestock and 256 crop farms in the Czech Republic, split into individual and corporate.

Evaluation of inequivalent projections of Hadamard matrices of order 24

Screening designs are useful for situations where a large number of factors (q) is examined but only few (k) of these are expected to be important. It is of practical interest for a given k to know all the inequivalent projections of the design into the k dimensions. In this paper we give all the (combinatorially) inequivalent projections of inequivalent Hadamard matrices of order 24 into k=3,4 and 5 dimensions, as well as their frequencies. Then, we sort these projections according to their generalized resolution, generalized aberration and centered L₂-discrepancy measure of uniformity. Then, we study the hidden projection properties of these designs as they are introduced by Wang and Wu (1995). The hidden projection property suggests that complex aliasing allows some interactions to be estimated without making additional runs.     

Properties of nonlinear transformations of fractionally integrated processes

This paper shows that the properties of nonlinear transformations of a fractionally integrated process strongly depend on whether the initial series is stationary or not. Transforming a stationary Gaussian I(d) process with d>0 leads to a long-memory process with the same or a smaller long-memory parameter depending on the Hermite rank of the transformation. Any nonlinear transformation of an antipersistent Gaussian I(d) process is I(0)). For non-stationary I(d) processes, every polynomial transformation is non-stationary and exhibits a stochastic trend in mean and in variance. In particular, the square of a non-stationary Gaussian I(d) process still has long memory with parameter d, whereas the square of a stationary Gaussian I(d) process shows less dependence than the initial process. Simulation results for other transformations are also discussed.     

Characterizations of distributions via linearity of regression of generalized order statistics

Let X (r, n, m, k), 1 r n, denote generalized order statistics based on an absolutely continuous distribution function F. We characterize all distribution functions F for which the following linearity of regression holds E(X(r+l,n,m,k) | X(r,n,m,k))=aX(r,n,m,k)+b.We show that only exponential, Pareto and power distributions satisfy this equation. Using this result one can obtain characterizations of exponential, Pareto and power distributions in terms of sequential order statistics, Pfeifers records and progressive type II censored order statistics. Received July 2001/Revised August 2002     

Effect of outliers on the estimation of parameters

Summary The estimation of parameter in the type of distributionf(x)=b x ^{–1 /b} exp (–x ^b (/b),x>0, is considered, when several outliers of the type , ,r=1,2, ...,k, are present in the data. The estimates of as well as of 's are put in the closed form. Special cases, Weibull, Gamma and Exponential are considered for the case of single outlier. Actual estimates are calculated from the generated samples of size 2 and 3 for the Weibull and Exponential.     

Variation diminishing property of densities of uniform generalized order statistics

Let f _*,r , r ≥ 1, denote the density function of rth uniform generalized order statistics as defined by Kamps (1995) or Cramer and Kamps (2003). We prove the following variation diminishing property: the number of zeros in (0,1) of any linear combination does not exceed the number of sign changes in the sequence (a ₁, . . . ,a _r ). This result is applied to study monotonicity and convexity properties of f _*,r .     

Exploring the financial consequences of the servitization of manufacturing

Commentators suggest that to survive in developed economies manufacturing firms have to move up the value chain, innovating and creating ever more sophisticated products and services, so they do not have to compete on the basis of cost. While this strategy is proving increasingly popular with policy makers and academics there is limited empirical evidence to explore the extent to which it is being adopted in practice. And if so, what the impact of this servitization of manufacturing might be. This paper seeks to fill a gap in the literature by presenting empirical evidence on the range and extent of servitization. Data are drawn from the OSIRIS database on 10,028 firms incorporated in 25 different countries. The paper presents an analysis of these data which suggests that: [i] manufacturing firms in developed economies are adopting a range of servitization strategies—12 separate approaches to servitization are identified; [ii] these 12 categories can be used to extend the traditional three options for servitization—product oriented Product–Service Systems, use oriented Product–Service Systems and result oriented Product–Service Systems, by adding two new categories “integration oriented Product–Service Systems” and “service oriented Product–Service Systems”; [iii] while the manufacturing firms that have servitized are larger than traditional manufacturing firms in terms of sales revenues, at the aggregate level they also generate lower profits as a % of sales; [iv] these findings are moderated by firm size (measured in terms of numbers of employees). In smaller firms servitization appears to pay off while in larger firms it proves more problematic; and [v] there are some hidden risks associated with servitization—the sample contains a greater proportion of bankrupt servitized firms than would be expected.

Asymptotic normality of linear functions of concomitants of order statistics

Let T( ) be a linear function of concomitants of order statistics, whereT (·) denotes a statistical functional depending on some distribution function (df)F and is an estimator ofF. Under an auxiliary model approach we consider statistics of the form , where denotes a weighted empirical df and a finite population df (t denotes a triangular array). The results can be used to estimate income inequality in finite populations and especially when the survey is based on some design. The paper was written when the author was working at the Statistical Research Unit, Statistics Sweden, Stockholm, Sweden The research was supported by the Joint Committé of the Nordic Social Research Council.     

Tests of significance for the mean of a finite lot

Let ξ₁, ξ₂, ξ₃, ... be independent identically distributed random variables each with normal distribution with mean μ and variance σ². Tests for the process mean μ are well-known elements of statistical analysis: the Gauß test under known process variance σ², Student’st-test under unknown process variance σ². Let the process be partitioned in lots (ξ₁, ..., ξ _N ), (ξ _N+1, ..., ξ_2N ), ... of sizeN. Consider (ξ₁, ..., ξ _N ) as a stochastic representative of this lot sequence and let the lot be characterized by the lot mean $\frac{1}{N}\sum\limits_{i = 1}^N {\xi _i } $ . The lot mean can be considered as a parameter of the joint conditional distribution function of the lot variables under $\frac{1}{N}\sum\limits_{i = 1}^N {\xi _i } = z$ . The present paper investigates the analogies of the Gauß test and Student’st-test for the lot situation, i.e. tests of significance for the lot meanz under known and unknown process variance σ². This approach is of special interest for the statistical control of product quality in situations where the quality of a lot of items 1, 2, ...,N with quality characteristics ξ₁, ξ₂, ..., ξ _N is identified with the lot average $\frac{1}{N}\sum\limits_{i = 1}^N {\xi _i } = z$ .     

On classes of estimators of the variance function of a linear estimator

Summary The variance function of a linear estimator can be expressed into a quadratic form. The present paper presents classes of estimators of this quadratic form along the lines implicitly suggested byHorvitz andThompson [1952] while formulating the classes of linear estimators. Accordingly it is noted that there exist nine principal classes of estimators out of which one principal class is examined in detail. Furthermore to illustrate the theory an example is considered where the expression for a unique estimator variance of the best estimator in theT ₁ class is derived.     

Dynamics of the Standard of Living in St Petersburg during Five Years of Economic Reform

The monitoring of changing living conditions in St Petersburg was started in 1989. In 1993 the Finance and Economics Committee of the Government of St Petersburg and a team of researchers from the Institute of Sociology at the Russian Academy of Sciences began collaborating in a study of the levels of socio-economic differentiation among the population and the priorities in city budget policies. A telephone survey scheme was designed based on representative samples (1000–2500 respondents) of the adult population (18 years and over) and controlled by city district distribution, sex, age, social status and housing. This scheme was implemented regularly with 2–3 month intervals between surveys. It was also undertaken for the purpose of reviewing the general orientation of social politics, decisions on budget priorities, new urgent needs and goals, and the diagnosis and short-term prognosis of trends and policy moves. Detailed and structured information on the living standards of the St Petersburg population is available from the computerized data-base, reports, and from the city's daily newspaper Nevskoe vremya. The studies have demonstrated that economic differentiation in St Petersburg has grown significantly as a result of current reforms (from a 1 to 4 ratio before 1990 to 1 to 10 by the end of 1996). Analysis of the economic characteristics of the population of St Petersburg has revealed that over the course of the past five years there has been rapid differentiation along new lines. At present, wealth and poverty, rather than shared social and professional attributes, tend to unite or separate people. The level of family and personal income determines consumer behaviour, lifestyle, values, cultural attitudes and even individuals' self-perception. La surveillance des changements des conditions de vie à Saint Pétersbourg a commencé en 1989. En 1993 le Comité de l'Economie et des Finances du Gouvernement de Saint Pétersbourg et une équipe de chercheurs de l'Institut de Sociologie de l'Académie des Sciences de Russie commencèrent une étude collaborative des niveaux de différenciation socio-économique dans la population et des priorités de la politique budgétaire de la ville. Un sondage téléphonique fut proposé, fondé sur une section représentative (1000 à 2500 personnes) de la population adulte (de 18 ans et plus) et contrôllée par la distribution des quartiers de la ville, par sexe, âge, statut social et logement. Ce projet fut mis en exécution régulièrement, avec 2 ou 3 mois d'intervalle entre les sondages. Il fut aussi entrepris dans le but d'examiner l'orientation générale des politiques sociales, des décisions quant aux priorités budgétaires, les nouveaux besoins et buts urgents, et le diagnosis et prognosis à court terme des tendances et changements de politique. L'information détaillée structurée concernant les niveaux de vie de la population de Saint Pétersbourg peut être obtenue dans le compte-rendu de la base des donnés sur l'ordinateur et dans le quotidien de la ville, Nevskoe Vremya. Les recherches ont démontré que le différenciation économique à Saint Pétersbourg a considérablement augmentéà la suite des réformes actuelles (d'une proportion de 1 à 4 avant 1990 à une proportion de 1 à 10 à la fin de 1996). L'analyse des caractéristiques économiques de la population de Saint Péterbourg a révélé qu'il y a eu une rapide différenciation d'un type nouveau au cours des cinq dernières années. A présent ce sont la richesse et la pauvreté, plutôt que les attributs sociaux et professionnels communs, qui ont tendance à unir ou à séparer les gens. Le niveau de revenu personnel et familial détermine le comportment des consommateurs, le style de vie, sens des valeurs, attitudes culturelles et même la perception d'eux-mêmes qu'ont les individus.     

Market entry of firms with different legal forms: an empirical test of the influence of institutional factors

Drawing upon institutional theory we develop a conceptual model and investigate the determinants of market entry for worker cooperatives, publicly traded and limited-liability companies. Our results show that formal institutional conditions (i.e., mercantile legislation) influence the start-up choice of entrepreneurs regarding the legal form of their new venture. In addition, we take into account the influence of informal institutional conditions (i.e., local corporate culture) on the market entry rate of firms with different legal structures. Findings show that, while market entry is sensitive to the general economic climate, entry rates of firms with a different legal structure respond differently to the same economic conditions.

Emergence of Political Unionism in Economies of British Colonial Origin: The Cases of Jamaica and Trinidad

Abstract . What were the circumstances under which political unionism has emerged in economies of British colonial origin, such as Jamaica and Trinidad? The hypothesis tested is that the political activities of trade unions in such economies played a role in the process of economic development, helping to achieve political independence and then economic growth. But at that stage political unionism is found to be incompatible with needed acceleration of growth rates. A significant deterioration in economic and social conditions produced a crisis and the unions traded support for the parties for some control over economic and social policy. This gave the political leaders the power they needed to negotiate for independence but, in Jamaica, it changed the focus and character of the labor movement.     

Exact bahadur efficiencies of tests for superadditivity of the mean function of a non-homogeneous poisson process

Consider a non-homogeneous Poisson process,N(t), with mean value functionΛ(t) and intensity functionsΛ(t). A conditional test of the hypothesis that the process is homogeneous, versus alternatives for whichΛ(t) is superadditive, was proposed by Hollander and Proschan (1974). Proposing a new test for superadditivity ofΛ(t), Kochar and Ramallingam (1989) have observed the fact that the Pitman asymptotic relative efficiency of their test with respect to the Hollander-Proschan test is unity. In order to distinguish between these competing tests, we shall compute the exact Bahadur slopes of these tests for important alternatives and demonstrate that the new test has high Bahadur efficiencies relative to the test of Hollander and Proschan.     

Slow convergence of the number of near-maxima for Burr XII distributions

A near-maximum is an observation which falls within a distance a of the maximum observation in an independent and identically distributed sample of size n. Subject to some conditions on the tail thickness of the population distribution, the number K _n (a) of near-maxima is known to converge in probability to one or infinity, or in distribution to a shifted geometric law. In this paper we show that for all Burr XII distributions K _n (a) converges almost surely to unity, but this convergence property may not become clear under certain cases even for very large n. We explore the reason of such slow convergence by studying a distributional continuity between Burr XII and Weibull distributions. We have also given a theoretical explanation of slow convergence of K _n (a) for the Burr XII distributions by showing that the rate of convergence in terms of P{K _n (a) > 1} tending to zero changes very little with the sample size n. Illustrations of the limiting behaviour K _n (a) for the Burr XII and the Weibull distributions are given by simulations and real data. The study also raises an important issue that although the Burr XII provides overall better fit to a given data set than the Weibull distribution, cautions should be taken for the extrapolation of the upper tail behaviour in the case of slow convergence.      

Generic properties of the core and equilibria of pure exchange economies

We show that for an open dense set of markets with a continuum of traders the number of equilibrium allocations [which by the celebrated theorem of ^{Aumann (Econometrica. 1964, 32. 39–50)} coincide with the core allocations for such markets are finite. This presents a limiting case result that complements similar asymptotic theorems for cores of large economies proved by ^{Bewley (Econometrica 1973, 41, 425–454)}, and ^{Dierker (Journal of Mathematical Economics 1975, 2. 155–169)}. If we require that the measure on the space of agents be one with a finite number of atoms of equal weight, our reasoning recovers the classical results obtained by ^{Debreu (Econometrica. 1970. 38, 387–392)} for economies with a finite number of agents.     

Graphical Analysis of Capability of a Process Producing a Product Family

Statistical techniques are effective and powerful means of quantifying the variability of processes, analyzing this variability with reference to product requirements, and eliminating this variability in product manufacturing. Many process capability indices have been effectively and widely used to determine whether the quality of a process meets preset targets. However, conventional process capability indices cannot be applied to assess the entire process capability of a product family with nominal-the-best specifications. This work presents a novel process capability index (C_pp^T), which takes into account all family members. The index C_pp is a simple transformation from index C_pm, and C_pp^T provides additional, individual information concerning the accuracy and precision of a process. Vännman’s (δ, γ)-plot [Vännman and Deleryd, Quality and Reliability Engineering International 15(3): 213–217 (1999)] is revised to compare the process capabilities of family members under both 100% inspection and sampling plans. Examples are provided to demonstrate the method’s practical application.