Characterizing systems of distributions by quantile measures

Modelling an empirical distribution by means of a simple theoretical distribution is an interesting issue in applied statistics. A reasonable first step in this modelling process is to demand that measures for location, dispersion, skewness and kurtosis for the two distributions coincide. Up to now, the four measures used hereby were based on moments.
In this paper measures are considered which are based on quantiles. Of course, the four values of these quantile measures do not uniquely determine the modelling distribution. They do, however, within specific systems of distributions, like Pearson's or Johnson's; they share this property with the four moment-based measures.
This opens the possibility of modelling an empirical distribution—within a specific system—by means of quantile measures. Since moment-based measures are sensitive to outliers, this approach may lead to a better fit. Further, tests of fit—e.g. a test for normality—may be constructed based on quantile measures. In view of the robustness property, these tests may achieve higher power than the classical moment-based tests.
For both applications the limiting joint distribution of quantile measures will be needed; they are derived here as well.     

Simulating non‐normal distributions with specified L‐moments and L‐correlations

This paper derives a procedure for simulating continuous non‐normal distributions with specified L‐moments and L‐correlations in the context of power method polynomials of order three. It is demonstrated that the proposed procedure has computational advantages over the traditional product‐moment procedure in terms of solving for intermediate correlations. Simulation results also demonstrate that the proposed L‐moment‐based procedure is an attractive alternative to the traditional procedure when distributions with more severe departures from normality are considered. Specifically, estimates of L‐skew and L‐kurtosis are superior to the conventional estimates of skew and kurtosis in terms of both relative bias and relative standard error. Further, the L‐correlation also demonstrated to be less biased and more stable than the Pearson correlation. It is also shown how the proposed L‐moment‐based procedure can be extended to the larger class of power method distributions associated with polynomials of order five.     

Moment convergence of M‐estimators

This study extends the rate of convergence theorem of M‐estimators presented by van der Vaart and Wellner (weak convergence and empirical processes: with applications to statistics, Springer‐Verlag, Newyork, 1996) who gave a result of the form r  to a result of the form sup_nE | r , for any p≥1. This result is useful for deriving the moment convergence of the rescaled residual. An application to maximum likelihood estimators is discussed.     

Nonparametric estimation of variance, skewness and kurtosis of the distribution of a statistic by jackknife and bootstrap techniques

While jackknife and bootstrap estimates of the variance of a statistic are well–known, the author extends these nonparametric maximum likelihood techniques to the estimation of skewness and kurtosis. In addition to the usual negative jackknife also a positive jackknife as proposed by BERAN (1984) receives interest in this work. The performance of the methods is investigated by a Monte Carlo study for Kendall's tau in various situations likely to occur in practice. Possible applications of these developments are discussed.     

Economic cohesion and development of the European Union's regions and member states - A methodological proposal to measure and identify the degree of regional economic cohesion

The EU cohesion policy seeks to mitigate imbalances between countries and regions and enhance greater economic development of the whole Union. However, notwithstanding its efforts and certain progress on this issue, territorial disparities still represent an open challenge for the European Union, which requires improving the cohesion policy, particularly regarding its measurement, in order to allocate resources more efficiently.This article aims to propose an innovative methodology to measure and identify the degree of cohesion of both EU NUTS-2 regions and member states in economic terms. To this end we first selected the main indicators which would better explain GDP per capita growth by applying factor analysis; and second, we measure the degree of cohesion as the relationship between economic development and its potential attributable to the inequalities detected in the selected set of indicators. To ensure the robustness of this research, we compared the results obtained by applying the Gini, Atkinson, and Theil indexes. Finally, the Economic Cohesion Index (ECI) has been elaborated in order to identify regions that, regardless of their economic development, still present a very low level of cohesion within the group in which it is compared.The main findings indicate that the 27 EU countries are quite cohesive. On the contrary, from the regional perspective, the study shows important imbalances between economic development and its potential that mainly affect the regions of Greece, Spain, and Italy, where Greece is the leading country among less developed regions and Spain and Italy among more developed.     

Industry convergence as a strategy for achieving sustainable development of agricultural complex: The case of Sandun‐Lanli in China

The purpose of the paper is to conceptualize and provide empirical evidence for the adoption of industry convergence strategy to sustainably develop the agricultural complex (AC) as a form of multifunctional agriculture in the Chinese context, which aims to achieve environmental sustainability in agricultural production and promotion of farmers' income and employment opportunities. A longitudinal single‐case study method was adopted. Thirty‐six face‐to‐face interviews were carried out with key respondents from various levels and types of government agencies, the Wu‐Sheng Company, and village collectives; participative observations were conducted during the fieldwork between 2016 and 2019. We found sustainability is embedded in and achieved through the industry convergence strategies of AC in the rural area of China. We are the first to formally define AC, propose the four‐stage industry convergence strategies of Wu‐Sheng in the process of developing the AC, and build connection between the AC and sustainable development. The case provides important, rich insights into the AC, industry convergence, and agricultural land use policy and therefore has enormous implications for agricultural companies as well as governments.     

Local Powers of Optimal One‐sample and Multi‐sample Tests for the Concentration of Fisher‐von Mises‐Langevin Distributions

One‐sample and multi‐sample tests on the concentration parameter of Fisher‐von Mises‐Langevin distributions on (hyper‐)spheres have been well studied in the literature. However, only little is known about their behaviour under local alternatives, which is due to complications inherent to the curved nature of the parameter space. The aim of the present paper therefore consists in filling that gap by having recourse to the Le Cam methodology, which has recently been adapted from the linear to the spherical setup. We obtain explicit expressions of the powers for the most efficient one‐ and multi‐sample tests. As a nice by‐product, we are also able to write down the powers (against local Fisher‐von Mises‐Langevin alternatives) of the celebrated Rayleigh test of uniformity. A Monte Carlo simulation study confirms our theoretical findings and shows the empirical powers of the above‐mentioned procedures.     

Stationary-Increment Variance-Gamma and t Models: Simulation and Parameter Estimation

We detail a method of simulating data from long range dependent processes with variance-gamma or t distributed increments, test various estimation procedures [method of moments (MOM), product-density maximum likelihood (PMLE), non-standard minimum χ² and empirical characteristic function estimation] on the data, and assess the performance of each. The investigation is motivated by the apparent poor performance of the MOM technique using real data ( Tjetjep & Seneta, 2006 ); and the need to assess the performance of PMLE for our dependent data models. In the simulations considered the product-density method performs favourably.     

On Quantile‐based Asymmetric Family of Distributions: Properties and Inference

In this paper, we provide a detailed study of a general family of asymmetric densities. In the general framework, we establish expressions for important characteristics of the distributions and discuss estimation of the parameters via method‐of‐moments as well as maximum likelihood estimation. Asymptotic normality results for the estimators are provided. The results under the general framework are then applied to some specific examples of asymmetric densities. The use of the asymmetric densities is illustrated in a real‐data analysis.     

Pro‐competitive Effect of Trade and Non‐decreasing Price‐Cost Margins*

This study surveys the empirical evidence on the pro‐competitive effect of international trade and analyses the determinants of price‐cost margins for OECD countries between 1970 and 2003. The main objective was to focus on the quantification of the impact of imports on margins, and understand why, despite trade liberalization, price‐cost margins have not fallen overall. On average, imports would have contributed to a large decrease of five percentage points in the price‐cost margins. However, these effects seem to have been partially counterbalanced by the impacts of financial deepening and disinflation.     

On Families of Distributions with Shape Parameters

Univariate continuous distributions are one of the fundamental components on which statistical modelling, ancient and modern, frequentist and Bayesian, multi‐dimensional and complex, is based. In this article, I review and compare some of the main general techniques for providing families of typically unimodal distributions on with one or two, or possibly even three, shape parameters, controlling skewness and/or tailweight, in addition to their all‐important location and scale parameters. One important and useful family is comprised of the ‘skew‐symmetric’ distributions brought to prominence by Azzalini. As these are covered in considerable detail elsewhere in the literature, I focus more on their complements and competitors. Principal among these are distributions formed by transforming random variables, by what I call ‘transformation of scale’—including two‐piece distributions—and by probability integral transformation of non‐uniform random variables. I also treat briefly the issues of multi‐variate extension, of distributions on subsets of and of distributions on the circle. The review and comparison is not comprehensive, necessarily being selective and therefore somewhat personal. © 2014 The Authors. International Statistical Review © 2014 International Statistical Institute     

Estimation and testing of crossing‐points in fixed design regression

Many phenomena in the life sciences can be analyzed by using a fixed design regression model with a regression function m that exhibits a crossing‐point in the following sense: the regression function runs below or above its mean level, respectively, according as the input variable lies to the left or to the right of that crossing‐point, or vice versa. We propose a non‐parametric estimator and show weak and strong consistency as long as the crossing‐point is unique. It is defined as maximizing point arg max of a certain marked empirical process. For testing the hypothesis H₀ that the regression function m actually is constant (no crossing‐point), a decision rule is designed for the specific alternative H₁ that m possesses a crossing‐point. The pertaining test‐statistic is the ratio max/argmax of the maximum value and the maximizing point of the marked empirical process. Under the hypothesis the ratio converges in distribution to the corresponding ratio of a reflected Brownian bridge, for which we derive the distribution function. The test is consistent on the whole alternative and superior to the corresponding Kolmogorov–Smirnov test, which is based only on the maximal value max. Some practical examples of possible applications are given where a certain study about dental phobia is discussed in more detail.     

Repeated measures and longitudinal data analysis using higher‐order entropies

This paper implements the generalized maximum entropy (GME) method in longitudinal data setup to investigate the regression para meters and correlation among the repeated measurements. We derive the GME system using Shannon classical entropy as well as some higher‐order entropies assuming an autoregressive correlation structure. This method is illustrated using two simulated examples to study the effect of changing the support range and compare the performance of the GME approach with the classical estimation methods.     

The effect of regional factors in the development of eco‐innovations in the firm

This research addresses the study of the effect of regional factors in the development of eco‐innovations in the firm. We assume the hypothesis of regional heterogeneity, that is, geographical factors and the regional heterogeneity play an important role in determining the innovations in the firms. In this line, we will approach our study from the perspective of regional innovation systems (RISs). Therefore, our research question involves the evaluation of regional factors as determinants of eco‐innovation developing in the firm. To examine these questions, the PITEC database that covers the period 2011–2013 was used. Overall, 5,461 firms have been employed for the ordinal logit regression model. This research contributes to the studies of eco‐innovation, extending the investigation into drivers of eco‐innovation, and highlights the impact that RIS has on the eco‐innovative development in the firm. We find that regional interaction and regional characteristics are key elements for the development of eco‐innovation in firms. Thus, the density of companies in the region, the regional per capita income, and the existence of financing mechanisms are key elements for the eco‐innovative development in the firm.     

Non‐parametric Analysis of Gap Times for Multiple Event Data: An Overview

Multiple event data are frequently encountered in medical follow‐up, engineering and other applications when the multiple events are considered as the major outcomes. They may be repetitions of the same event (recurrent events) or may be events of different nature. Times between successive events (gap times) are often of direct interest in these applications. The stochastic‐ordering structure and within‐subject dependence of multiple events generate statistical challenges for analysing such data, including induced dependent censoring and non‐identifiability of marginal distributions. This paper provides an overview of a class of existing non‐parametric estimation methods for gap time distributions for various types of multiple event data, where sampling bias from induced dependent censoring is effectively adjusted. We discuss the statistical issues in gap time analysis, describe the estimation procedures and illustrate the methods with a comparative simulation study and a real application to an AIDS clinical trial. A comprehensive understanding of challenges and available methods for non‐parametric analysis can be useful because there is no existing standard approach to identifying an appropriate gap time method that can be used to address research question of interest. The methods discussed in this review would allow practitioners to effectively handle a variety of real‐world multiple event data.     

Exercise as a Means of Reducing Perceptions of Work‐Family Conflict: A Test of the Roles of Self‐Efficacy and Psychological Strain

Prior research suggests that exercise has positive benefits for individuals and the organizations they work for. Using the literature related to social cognitive theory and exercise, the present study hypothesizes and tests the effects of exercise on two directions of work‐family conflict: work interference with family (WIF) and family interference with work (FIW). Using a sample of 476 working adults, we found that exercise was both positively related to self‐efficacy for managing work‐family conflict and negatively related to reported psychological strain, which in turn were related to reductions in work‐family conflict. Model fit for the data support our contention that exercise indirectly influences work‐family conflict via its direct impact on increased self‐efficacy and reduced psychological strain. © 2014 Wiley Periodicals, Inc.     

Organization‐Based Self‐Esteem,Psychological Contract Fulfillment,and Perceived Employment Opportunities: A Test of Self‐Regulatory Theory

This study addresses organization‐based self‐esteem (OBSE) development by examining the role of perceptions of employer psychological contract fulfillment, and the self‐regulatory processes by which OBSE evolves and produces its effects. Self‐regulatory theory helps reveal why psychological contract fulfillment relates to OBSE, how OBSE mediates its effects, and the ways in which OBSE might interact with perceived employment opportunities to affect job satisfaction, performance, and turnover intentions. The results show that OBSE is related to and mediates the relationships between relational contract fulfillment and employee job satisfaction and performance, but OBSE is not related to transactional contract fulfillment. Nor does OBSE mediate the relationships between transactional contract fulfillment and the dependent variables. Perceived employment opportunities moderate the relationships of OBSE with job satisfaction and turnover intentions. This study concludes with recommendations of ways managers can increase their sensitivity to the types of messages they communicate to employees. © 2014 Wiley Periodicals, Inc.     

Why SMEs invest in environmental measures: sustainability evidence from small and medium‐sized printing firms

Why do SMEs invest in environmental measures? From the literature we know that most SMEs are rather slow in adopting these sustainable measures, but then the following question arises: why are other SMEs fast in this respect? From our research, it becomes clear that improving the working conditions is the most important reason why these fast‐going SMEs invest in environmental measures, as this probably improves their employees' motivation and performance. This explanation connects ‘planet’ and ‘people’ with each other, and does not exclude ‘profit’, which completes the traditional sustainability circle. Copyright © 2006 John Wiley & Sons, Ltd and ERP Environment.     

Regulating Work: Measuring the Scope and Burden of Occupational Licensure Among Low‐ and Moderate‐Income Occupations in the United States

This study examines the scope and burden of occupational licensing laws in the United States for 102 low‐ and moderate‐income occupations. Findings indicate that the licences studied require of aspiring workers, on average, $US209 in fees, one exam, and about nine months of education and training, plus minimum grade and age levels. Data also indicate striking disparities in requirements within and between occupations and within and between states. These inconsistencies likely reflect not the relative public health and safety risks of occupations, but instead the lobbying prowess of practitioners in securing laws to shut out competition.     

Asymptotic distributions of φ-divergences of hypothetical and observed frequencies on refined partitions

For a wide class of goodness-of-fit statistics based on φ-divergences between hypothetical cell probabilities and observed relative frequencies, the asymptotic normality is established under the assumption n / m _n →γ∈(0,∞), where n denotes sample size and m _n the number of cells. Related problems of asymptotic distributions of φ-divergence errors, and of φ-divergence deviations of histogram estimators from their expected values, are considered too.