Karl Pearson and the Establishment of Mathematical Statistics

At the end of the nineteenth century, the content and practice of statistics underwent a series of transitions that led to its emergence as a highly specialised mathematical discipline. These intellectual and later institutional changes were, in part, brought about by a mathematical-statistical translation of Charles Darwin's redefinition of the biological species as something that could be viewed in terms of populations. Karl Pearson and W.F.R. Weldon's mathematical reconceptualisation of Darwinian biological variation and "statistical" population of species in the 1890s provided the framework within which a major paradigmatic shift occurred in statistical techniques and theory. Weldon's work on the shore crab in Naples and Plymouth from 1892 to 1895 not only brought them into the forefront of ideas of speciation and provided the impetus to Pearson's earliest statistical innovations, but it also led to Pearson shifting his professional interests from having had an established career as a mathematical physicist to developing one as a biometrician. The innovative statistical work Pearson undertook with Weldon in 1892 and later with Francis Galton in 1894 enabled him to lay the foundations of modern mathematical statistics. While Pearson's diverse publications, his establishment of four laboratories and the creation of new academic departments underscore the plurality of his work, the main focus of his life-long career was in the establishment and promulgation of his statistical methodology.     

CENTRAL LIMIT THEORMS IN C[0,1] FOR A CLASS OF ESTIMATORS OF A DISTRIBUTION FUNCTION

As non–parametric estimates of an unknown distribution function (d.f.) F based on i.i.d. observations X ₁ X_n with this d.f.

are used, where H _n is a sequence of d.f.'s converging weakly to the unit mass at zero. Under regularity conditions on F and the sequence ( H _n) it is shown that √_n( F _n– F ) and √_n( R _n – F ) in C [0,1] converge in distribution to a process G with G( t ) = W° ( F ( t )), where W ° is a Brownian bridge in C [0,1]. Further the a.s. uniform convergence of R., is considered and some examples are given.     

Validation and measurement invariance of the multidimensional qualitative job insecurity scale

This contribution introduces the Multidimensional Qualitative Job Insecurity Scale (MQJIS). Drawing from the qualitative job insecurity literature and addressing some of other scales’ limitations, a multidimensional model is proposed and investigated by means of confirmatory factor analysis and multilevel confirmatory factor analysis. Study 1 aims to explore the psychometric properties and factorial structure of MQJIS in an Italian sample of blue-collar workers (N?=?583), showing that a model with one higher-order factor (i.e., qualitative job insecurity) and four dimensions (i.e., social relationships, employment conditions, working conditions, and work content) shows a good fit to the data and good reliability indices. Study 2 aims to investigate MQJIS measurement invariance across several groups, based on country of origin, age, and gender. Results on a sample of Belgian and Italian workers (N?=?710) show that MQJIS met the criteria for uniqueness invariance across genders and scalar invariance across countries and age groups. Significance, implications, and future directions stemming from the initial validation and the confirmed measurement invariance of this scale are discussed.

     

The deterministic shift extension and the affine dynamic Nelson–Siegel model

The affine dynamic Nelson–Siegel model links the affine class of models with the Nelson–Siegel interpolation scheme of the yield curve. Its parameters are interpreted as the latent factors of the spot rate process driven by an affine diffusion. Using an appropriate specification of this diffusion, the yields become in form of the Nelson–Siegel model but an adjustment term is introduced. In this paper, the model is extended using a deterministic shift extension so as to perfectly fit the term structure and reduce the correction term. This enhancement allows to simulate the yield curve and the spot rate process consistently with the market data used for the calibration of the model. A numerical example discusses the calibration results of the original model and the proposed extension.     

Persistence of shocks on seasonal processes

The paper addresses the issue of measuring the persistence of shocks on seasonally integrated processes observed at quarterly intervals. We show that the amplitude of the limiting cycle described by the cumulated impulse response function provides a parametric measure of persistence and that Cochrane's normalized variance ratio can correspondingly be extended as a non-parametric counterpart. For illustrative purposes the latter is applied to the Italian GDP and to the output of the agricultural sector.     

On Some Nonparametric Tests of Dispersion

Let X and Y be random variables with distribution functions F and G and medians ζand η, respectively. X will be said to be more dispersed about the median than Y if F(x+ζ) – F(–x+ζ) G (x+η) – G (–x+η)for all x > O, with sharp inequality holding for some positive x. Asymptotically nonparametric tests for the hypothesis that F (x+ζ) = G (x+η) against alternatives of the above type (for ζ and η unknown), provided F(x+ζ) (but not necessarily G (x+η)) is symmetric and Fand G have bounded densities, are constructed from a subclass Of SUKHATME'S modified generalized U - statistics [12]. One simple test of this subclass turns out to be the MANN-WHITNEY test as performed on the |X_i–ζ| and | Y_j–η| where ζ and η are the corresponding sample medians. Consistency and PITMAN efficiencies of some of the tests proposed are discussed under two families of alternatives in which the Y's differ from the X's through departure from symmetry as well as by being more (less) dispersed: a model of “heterogeneous response” and the wellknown gross error model. The usual scale alternatives are also studied and the relationship of our tests to those previously given in the literature is pointed out.     

Fourier inversion and the Hausdorff distance

This paper continues research done by F.H. Ruymgaart and the author. For a function f on R ^d we consider its Fourier transform F f and the functions f_M (M>0) derived from F f by the formula f_M(x) =( F( ε_M · F f ))(− x );, where the ε_M are suitable integrable functions tending to 1 pointwise as M →∞. It was shown earlier that, relative to a metric d _H , analogous to the Hausdorff distance between closed sets, one has d _H (f_M, f) = O( M ^−½) for all f in a certain class. We now show that, for such f , the estimate O( M ^−½) is optimal if and only if f has a discontinuity point.     

Karl Pearson in Russian Contexts

The confluence of statistics and probability into mathematical statistics in the Russian Empire through the interaction, 1910–1917, of A.A. Chuprov and A.A. Markov was influenced by the writings of the English Biometric School, especially those of Karl Pearson. The appearance of the Russian-language exposition of Pearsonian ideas by E. E. Slutsky in 1912 was instrumental in this confluence. Slutsky's predecessors in such writings (Lakhtin, Orzhentskii, and Leontovich) were variously of mathematical, political economy, and biological backgrounds. Work emanating from the interpolational nature of Pearson's system of frequency curves was continued subsequently through the work of Markov, Bernstein, Romanovsky, and Kravchuk (Krawtchouk), who laid a solid probabilistic foundation. The correlational nature in the interpolational early work of Chebyshev, and work of the English Biometric School in the guise of linear least-squares fitting exposited as the main component of Slutsky's book, was developed in population as well as sample context by Chuprov. He also championed the expectation operation in providing exact relations between sample and population moments, in direct interaction with Karl Pearson. Romanovsky emerges as the most adaptive and modern mathematical statistician.     

Consistent estimation in the presence of incidental parameters

Summary Let (X,A) be a measurable space andP _ϑη |A (ϑη) ∈ Θ x H, ∥A, (θ, η) ∈ Θ×H, a parametrized family of probability measures (for short:p-measures). This paper is concerned with the problem of consistently estimatingθ from realizations governed by , where η^u ∈ H, v ∈ ℕ, are unknown.     

Exploring the antecedents of born-global companies’ international development

In recent years the emergence of so-called born-global firms -firms which start their international activities from their start up- has challenged traditional theoretical assumptions about the incremental process of internationalization, giving birth to the development of a new stream of studies. In order to give a contribution to this area of studies, the purpose of this paper is to empirically test a model to explain how well some factors are able to explain the level of international development of born global companies. A mail survey was conducted within a sample of born-global Italian companies, belonging to the most representative industries for the Italian economy (metal products and machinery equipment; furniture; chemicals and food). Findings support the validity of a model including five significant predictors: uncertainty and dynamism in the firm’s industry, operating in niche-based industries, markets’ and segments’ knowledge held by the founder/managers, product innovation and firms’ innovativeness, access to networks. Findings are discussed and managerial implications are drawn.     

Do institutions affect the matching process of disabled people? The Italian case

The aim of this paper is to investigate whether the various Italian regions’ efficiency in providing employment for disabled people under Law 12 March n.68 1999, “Regulation on the right to work of disabled people” (Law 68/99) can be affected by their institutional quality. For this reason, a Stochastic Frontier Approach is used for estimating the regional matching function, where the flow of disabled people who found a job is produced by the combination of unemployment and vacancies. The matching equation is estimated using regional data from ISFOL, from 2006 to 2011. Results show the presence of a territorial dualism with regard to the matching process. The Southern regions of Italy have the lowest efficiency scores due to their lower institutional quality. The empirical analysis confirms that a good institutional quality is able to reduce the inefficiency of the matching process of disabled people. Therefore, it requires the implementation of policies aimed at improving the level of institutions, particularly in Southern Italy, in order to improve the efficiency of Law 68/99.

     

Impact of Karl Pearson's Work on Statistical Developments in India

Karl Pearson's work greatly inspired P. C. Mahalanobis's interest in statistics, who was at the centre of modern statistical developments in India. Mahalanobis learned statistics on his own, reading Pearson's articles and his journal, and encouraged others to study Pearson's papers. Pearson was a Honorary Fellow of the Indian Statistical Institute, which has been a leading statistical training and research center in India. The statistical revolution that Pearson brought also facilitated the training and research of many Indian statisticians.     

Variance components models for survival data

Extensions of the Cox proportional hazards model for survival data are studied where allowance is made for unobserved heterogeneity and for correlation between the life times of several individuals. The extended models are frailty models inspired by Y ashin et al. (1995). Estimation is carried out using the EM algorithm. Inference is discussed and potential applications are outlined, in particular to statistical research in human genetics using twin data or adoption data, aimed at separating the effects of genetic and environmental factors on mortality.     

Minimax robust designs for field experiments

Experimental designs for field experiments are useful in planning agricultural experiments, environmental studies, etc. Optimal designs depend on the spatial correlation structures of field plots. Without knowing the correlation structures exactly in practice, we can study robust designs. Various neighborhoods of covariance matrices are introduced and discussed. Minimax robust design criteria are proposed, and useful results are derived. The generalized least squares estimator is often more efficient than the least squares estimator if the spatial correlation structure belongs to a small neighborhood of a covariance matrix. Examples are given to compare robust designs with optimal designs. The work was partially supported by research grants from the Natural Science and Engineering Research Council of Canada.     

Patterns of corporate governance and technical efficiency in Italian manufacturing

The purpose of this paper is to analyse the relationship between the corporate governance system and technical efficiency in Italian manufacturing. We use a non‐parametric frontier technique (DEA) to derive technical efficiency measures for a sample of Italian firms taken from nine manufacturing industries. These measures are then related to the characteristics of the corporate governance system. Two of these characteristics turn out to have a positive impact on technical efficiency: the percentage of the company shares owned by the largest shareholder and the fact that a firm belongs to a pyramidal group. Interestingly, a trade‐off emerges between these influences, in the sense that one is stronger in industries where the other is weaker. Copyright © 2007 John Wiley & Sons, Ltd.     

Revisiting the Curvilinear Relation Between Job Insecurity and Work Withdrawal: The Moderating Role of Achievement Orientation and Risk Aversion

Although speculation of the curvilinear relations between job insecurity and job‐related behaviors is theoretically appealing, the empirical evidence has been sparse. The purpose of this study was to contribute to the literature on job insecurity and work withdrawal behaviors by reexamining their curvilinear relation, and the effects of achievement orientation and propensity for risk aversion on this U‐shaped relationship. Using samples with both secure and insecure job situations, we hypothesized that job insecurity could have both positive and negative effects on work withdrawal simultaneously; however, one of these effects could dominate the other at different levels of job insecurity. That is, a U shape would best describe such a relationship, since a moderate level of job insecurity would result in the lowest level of work withdrawal. Furthermore, we hypothesized that achievement orientation and propensity for risk aversion moderates this relationship in such a way that the curvilinear relationship is weaker (flattened curve) when the individual's achievement orientation is high, and that the curvilinear relationship is stronger (steep curve) when the individual's propensity for risk aversion is high. Results show that these hypotheses were supported; implications and limitations of the study are discussed. © 2014 Wiley Periodicals, Inc.     

A Path Construction for the Virtual Waiting Time of an M/G/1 Queue

Consider the M/G/1 queue, the finite dam M/G/1 with capacity T, and the impatient customer M/G/1 model, where customers become lost customers if their waiting time exceeds τ. In this note we prove that for all three models and each xe(0, r) the distribution of the number of downcrossings of the virtual waiting time process with level x during a busy cycle is identical. This implies the weaker statement that on [0, T) the distribution functions of the steady state distributions of the amount of unprocessed work (virtual waiting time) are proportional. A number of applications is given.     

Do alternative energy markets provide optimal alternative investment opportunities?

This paper investigates diversification opportunities for investors among different alternative energy markets. We sample six alternative energy markets namely World, Developed, Emerging, EU, BRIC and G7 with daily data ranging from January 2006 to December 2017. For estimations, we use wavelet multiple correlation and wavelet multiple cross correlation proposed by Polanco-Martínez and Fernández-Macho (2014) to find pairwise correlation at different investment horizons. Our work contributes in measuring integration level among alternative regional energy markets across different investment horizons. Our results highlight that World, Developed, Emerging, EU markets offer maximum diversification when included with either Emerging or BRIC energy markets in a portfolio. Furthermore, diversification benefits are more prominent under intra-week to monthly investment horizons for all portfolio combinations. We also rank different pairs of alternative markets based on their integration level which carry important implications for portfolio diversification and risk management.     

On generalized transforms of distribution functions

In this note we discuss the following problem. LetX andY to be two real valued independent r.v.'s with d.f.'sF and ?. Consider the d.f.F*? of the r.v.X oY, being o a binary operation among real numbers. We deal with the following equation: $$\mathcal{G}^1 (F * \phi ,s) = \mathcal{G}^2 (F,s)\square \mathcal{G}^3 (\phi ,s)\forall s \in S$$ where \(\mathcal{G}^1 ,\mathcal{G}^2 ,\mathcal{G}^3 \) are real or complex functionals, т another binary operation ands a parameter. We give a solution, that under stronger assumptions (Aczél 1966), is the only one, of the problem. Such a solution is obtained in two steps. First of all we give a solution in the very special case in whichX andY are degenerate r.v.'s. Secondly we extend the result to the general case under the following additional assumption: $$\begin{gathered} \mathcal{G}^1 (\alpha F + (1 - \alpha )\phi ,s) = H[\mathcal{G}^i (F,s),\mathcal{G}^i (\phi ,s);\alpha ] \hfill \\ \forall \alpha \in [0,1]i = 1,2,3 \hfill \\ \end{gathered} $$ .     

Public Managers’ Skills Development for Effective Performance Management: Empirical evidence from Italian local governments

Performance management has become an important element of the reform agenda of public sector around the world. However, scholars and practitioners highlight that many public administrations do not manage performance very well. A ‘litmus test’ of the success of a performance-based reform is observing whether public managers use performance information to make better-informed decisions. Having said that, the aim of this article is to see whether public managers of Italian local governments in the Apulia region (the South of Italy) use performance information after the last performance-based reform (Brunetta’s Reform: decree No. 150/09). The learning purpose is analysed and discussed. The research may suggest scholars, practitioners and policy makers the routes for developing performance utilization in difficult organizational contexts where performance management systems do not work.