A negative binomial thinning-based bivariate INAR(1) process

This article considers a bivariate INAR(1) process based on an extension of the negative binomial thinning operator by prespecifying the distribution of the innovations. The dependence is introduced through the innovation components. The existence, uniqueness, strict stationarity, ergodicity, and some probabilistic properties of the process are derived. The estimation methods of conditional least squares and conditional maximum likelihood are considered. Some numerical results of the estimates are presented by simulation study. An application to crime data set is provided.     

RECENT DEVELOPMENTS IN COUNT DATA MODELLING: THEORY AND APPLICATION

Abstract. This paper deals with statistical methods for modelling individual behavior when the endogenous variable is a nonnegative integer. Examples are the number of children, the number of job changes or the number of shopping trips in a given period. Several approaches—Poisson, robust Poisson, negative binomial (NEGBIN), NEGBIN _k , hurdle Poisson, truncated-at-zero Poisson—are discussed with a focus on specification, estimation, and testing. An application to labor mobility data illustrates the gain obtained by carefully taking into account the specific structure of the data.     

Bounds for the difference between median and mean of beta and negative binomial distributions

Summary We obtain bounds for the difference between the median and mean of the beta and negative binomial distributions using elementary methods.     

Bounds for the median of the negative binomial distribution

Summary Bounds are obtained for the median of the negative binomial distribution which are valid for all possible parameter values of the distribution when the median is defined as inf {x: P(X≤x)≥1/2}.     

A School-Level Gravity Model of Student Migration Flows to Higher Education Institutions

This paper presents a gravity model of student migration flows to higher education institutions (HEIs) in Ireland. The analysis is performed on a novel dataset containing detailed information on a range of ‘push’ and ‘pull’ factors, allowing one to estimate the effects of a number of important school-level characteristics on these flows. This is achieved by estimating and comparing a fixed-effects Poisson model and two conditional fixed-effects negative binomial models and selecting the best model on the basis of the Akaike information criterion (AIC). The preferred negative binomial model accounts for over-dispersion in the student flow data and allows for estimation of the parameter coefficients of the HEI-invariant characteristics. The analysis suggests that while geography plays a very important role in explaining student flows, so too do a range of school-level characteristics. Furthermore, it is found that distance has a differential impact across HEIs and HEI types with important implications for policy-makers and HEI managers.     

Mixed random systematic sampling designs

In this paper, an alternative sampling procedure that is a mixture of simple random sampling and systematic sampling is proposed. It results in uniform inclusion probabilities for all individual units and positive inclusion probabilities for all pairs of units. As a result, the proposed sampling procedure enables us to estimate the population mean unbiasedly using the ordinary sample mean, and to provide an unbiased estimator of its sampling variance. It is also found that the suggested sampling procedure performs well especially when the size of simple random sample is small. Received August 2001     

Locally D- and c-optimal designs for Poisson and negative binomial regression models

The research on optimal experimental designs for nonlinear regression models is of great interest because these models are used to characterize chemical, biological or agricultural phenomena. Much of them involve an exponential decay. In this paper, locally D- and c-optimal designs are derived analytically for Poisson and negative binomial regression models.     

Mean square error estimation in multi-stage sampling

Summary: Suppose for a homogeneous linear unbiased function of the sampled first stage unit (fsu)-values taken as an estimator of a survey population total, the sampling variance is expressed as a homogeneous quadratic function of the fsu-values. When the fsu-values are not ascertainable but unbiased estimators for them are separately available through sampling in later stages and substituted into the estimator, Raj (1968) gave a simple variance estimator formula for this multi-stage estimator of the population total. He requires that the variances of the estimated fsu-values in sampling at later stages and their unbiased estimators are available in certain `simple forms'. For the same set-up Rao (1975) derived an alternative variance estimator when the later stage sampling variances have more ‘complex forms’. Here we pursue with Raj's (1968) simple forms to derive a few alternative variance and mean square error estimators when the condition of homogeneity or unbiasedness in the original estimator of the total is relaxed and the variance of the original estimator is not expressed as a quadratic form.  We illustrate a particular three-stage sampling strategy and present a simulation-based numerical exercise showing the relative efficacies of two alternative variance estimators. Received: 19 February 1999     

Disciplinary sanctions in English Premiership Football: Is there a racial dimension?

This paper assesses the evidence for a racial difference in both the dispensation of formal disciplinary sanctions and in the number of fouls called by referees in professional football. The study uses a unique dataset comprising player match-level information drawn from five recent seasons of the English Premiership. These data were merged with data from other sources to identify, among other things, the racial affiliation of the player across four separate categories (viz., white, black, mixed race, and Asian). No systematic evidence of an unfair treatment of players from the non-white minority groups in respect of either the receipt of disciplinary cards or in the number of penalised fouls called by referees was detected.     

Cumulative and CUB Models for Rating Data: A Comparative Analysis

Ordinal measurements as ratings, preference and evaluation data are very common in applied disciplines, and their analysis requires a proper modelling approach for interpretation, classification and prediction of response patterns. This work proposes a comparative discussion between two statistical frameworks that serve these goals: the established class of cumulative models and a class of mixtures of discrete random variables, denoted as CUB models, whose peculiar feature is the specification of an uncertainty component to deal with indecision and heterogeneity. After surveying their definition and main features, we compare the performances of the selected paradigms by means of simulation experiments and selected case studies. The paper is tailored to enrich the understanding of the two approaches by running an extensive and comparative analysis of results, relative advantages and limitations, also at graphical level. In conclusion, a summarising review of the key issues of the alternative strategies and some final remarks are given, aimed to support a unifying setting.     

Firms’ innovation performance and the role of the metropolitan location. Evidence from the European periphery

ABSTRACT

This paper assesses the role of metropolitan location in explaining firms’ innovation performance while accounting for other internal and external determinants of innovation. Using micro-level dataset and controlling for firm-specific, sector-specific and region-specific features, we identify a nuanced effect of location within metropolitan areas on the innovative performance of companies The results prove to vary for the different measures of innovation output of firms and in particular there is no metropolitan advantage detected for binary self-declared measures of innovations. The advantage is detected for the count-based quantity of innovation measures which is shown to critically depend on the higher performance of metropolitan-based firms in patenting and licencing. The interlinkages between location and firm-size matter and the results are asymmetric with particular benefits arising for micro-firms in their patenting and licencing.     

Test of Bernoulli success probability in inverse sampling for nearer alternatives using adaptive allocation

This paper provides a test procedure for the problem of testing Bernoulli success probability in the case of costly trials when an inverse sampling is carried out. The proposed test is based on a two population adaptive sampling scheme used in clinical trials. Some exact and asymptotic results related to the test are studied. The proposed procedure is applicable where the alternatives are not too far from the null hypothetical value.     

ON THE DISTRIBUTION OF ORDER STATISTICS FOR A RANDOM SAMPLE SIZE

The distributions of the life lengths of a parallel and of a series system with a random number of components have been studied in reliability theory. In this paper we obtain the distributions of the i'th order statistics and the range, assuming the sample size to be random, with a generalized negative binomial, a generalized Poisson and a generalized logarithmic series distribution. The results of Raghunandanan and Patil (1972) follow immediately from our results.     

Location determinants of high-growth firms

County-level location patterns of INC5000 companies provide one map of American entrepreneurship and innovativeness, and understanding the local factors associated with these firms’ emergence is important for stimulating regional economic growth and innovation. We draw on the knowledge spillover theory of entrepreneurship to motivate our regression model, and augment this theory with additional regional features that have been found to be important in the firm location literature. Zero-inflated negative binomial regressions indicate that these firms exist in counties with larger average establishment size, higher educational attainment and more natural amenities. Income growth, a mix of higher paying industries, and more banks per capita are associated with a smaller presence of these types of firms, all else equal. We conclude that the local conditions favouring high-growth firms are likely to be different from those favouring new firms in general, and that these conditions differ significantly in urban and rural areas and by industrial sectors.     

Statistical Problems in Ancient Numismatics

In antiquity coins were struck by placing a heated coin blank between two dies and hitting the upper die with a heavy blow of a hammer. When a die wore off, a new one was engraved. So dies intended to be the same show small differences that may be observed on extant coins as "the varieties". Numismatists collect statistics of die varieties in as large a sample as possible of extant coins of a single issue they can find to study. From these statistics they want to estimate the number of dies used in producing the coin issue. To do this they need a parametric stochastic model describing how coins survive and become part of the sample. Several models are tried and tested against the data of two large samples, one of them new. (Few large samples exist). Estimators are reviewed and some related statistical problems studied.     

On the application of the Minkowski-Farkas theorem to sampling designs

In the paper, we consider the following problem: Let {π_k} be a sequence satisfying 0π_kΣ1 (k=1,…, N) and π=n.Tben, is there an unordered sampling design such that, for each k=1,…N, the inclusion probability of unit k is equal to π? It is shown that it can be solved by the straightforward application of the Minkowski-Farkas theorem.     

Compromised imputation in survey sampling

In this paper, a compromised imputation procedure has been suggested. The estimator of mean obtained from compromised imputation remains better than the estimators obtained from ratio method of imputation and mean method of imputation. An idea to form “Warm Deck Method” of imputation has also been suggested. Received: July 1998     

ON THE DISTRIBUTIONS OF ORDER STATISTICS FOR A RANDOM SAMPLE SIZE*

The probability distribution of the i –th and j–th order statistics and of the range R of a sample of size n, taken from a population with probability density function f (x) have been obtained when the sample size n is a random variable N and has: (i) a generalized Poisson distribution; and (ii) a generalized negative bonimial distribution. Specific results are then obtained; (a) when f (x) is uniform over (0,1); and (b) when f(x) is exponential. All the results for N, being a Poisson, binomial and negative binomial rv follow as special cases.     

Estimating systematic continuous-time trends in recidivism using a non-Gaussian panel data model

We model panel data of crime careers of juveniles from a Dutch Judicial Juvenile Institution. The data are decomposed into a systematic and an individual-specific component, of which the systematic component reflects the general time-varying conditions including the criminological climate. Within a model-based analysis, we treat (1) shared effects of each group with the same systematic conditions, (2) strongly non-Gaussian features of the individual time series, (3) unobserved common systematic conditions, (4) changing recidivism probabilities in continuous time and (5) missing observations. We adopt a non-Gaussian multivariate state-space model that deals with all these issues simultaneously. The parameters of the model are estimated by Monte Carlo maximum likelihood methods. This paper illustrates the methods empirically. We compare continuous time trends and standard discrete-time stochastic trend specifications. We find interesting common time variation in the recidivism behaviour of the juveniles during a period of 13 years, while taking account of significant heterogeneity determined by personality characteristics and initial crime records.     

Trend and Comparative Analysis of Inequality of Social Opportunity

This article sets out a new method for the analysis of inequality of social opportunity. The shortcomings of the previous concepts and measures attempting to assess the degree of openness of the mobility process independently of marginal effects are displayed. The suggested new approach refers to relative opportunity distributions of individuals according to their social origin. Starting from the premise that these distributions underlying the observed allocation of social positions are continuous, it is assumed that it is possible to compare them using straight lines. The various slopes of the lines represent inequality of social opportunity coefficients which permit trend and comparative analysis of the mobility process net results.