Quantity quantiles linear regression

We show that the definition of the θth sample quantile as the solution to a minimization problem introduced by Koenker and Bassett (Econometrica 46(1):33–50, 1978) can be easily extended to obtain an analogous definition for the θth sample quantity quantile widely investigated and applied in the Italian literature. The key point is the use of the first-moment distribution of the variable instead of its distribution function. By means of this definition we introduce a linear regression model for quantity quantiles and analyze some properties of the residuals. In Sect. 4 we show a brief application of the methodology proposed. This research was partially supported by Fondo d’Ateneo per la Ricerca anno 2005—Università degli Studi di Milano-Bicocca. The paper is the result of the common work of the authors; in particular M. Zenga has written Sects. 1 and 5 while P. Radaelli has written the remaining sections.     

Evolution and decomposition of income inequality in Italy, 1991–2004

The aggregate measures of inequality do not display any significant trend in the concentration of equivalent income among the Italian households in the early 2000s. Yet some sizeable shifts in the income distribution seem to suggest that the relative positions of groups of households have changed on the income scale. Through a decomposition analysis of Gini index by income source we find that in the more recent years the income from self-employment is the main disequalizing factor. The decomposition by social groups provides the evidence that it is the group of self-employed and managers who have gained more ground on the income scale. This work has been debated by the three Authors under the coordination of Claudio Quintano. Rosalia Castellano has written Sect. 1, while Andrea Regoli has written Sects. 2 to 6.     

A test of concordance based on Gini’s mean difference

A new rank correlation index, which can be used to measure the extent of concordance or discordance between two rankings, is proposed. This index is based on Gini’s mean difference computed on the totals ranks corresponding to each unit and it turns out to be a special case of a more general measure of the agreement of m rankings. The proposed index can be used in a test for the independence of two criteria used to rank the units of a sample, against their concordance/discordance. It can then be regarded as a competitor of other classical methods, such as Kendall’s tau. The exact distribution of the proposed test-statistic under the null hypothesis of independence is studied and its expectation and variance are determined; moreover, the asymptotic distribution of the test-statistic is derived. Finally, the implementation of the proposed test and its performance are discussed. Both the authors contributed equally to this work; however, the actual writing of the paper was as follows: Sects. 2 and 3 are due to C. G. Borroni, Sects. 1 and 4 are due to M. Zenga.     

Estimates based on preliminary data from a specific subsample and from respondents not included in the subsample

Various approaches to obtaining estimates based on preliminary data are outlined. A case is then considered which frequently arises when selecting a subsample of units, the information for which is collected within a deadline that allows preliminary estimates to be produced. At the moment when these estimates have to be produced it often occurs that, although the collection of data on subsample units is still not complete, information is available on a set of units which does not belong to the sample selected for the production of the preliminary estimates. An estimation method is proposed which allows all the data available on a given date to be used to the full-and the expression of the expectation and variance are derived. The proposal is based on two-phase sampling theory and on the hypothesis that the response mechanism is the result of random processes whose parameters can be suitably estimated. An empirical analysis of the performance of the estimator on the Italian Survey on building permits concludes the work. The Sects. 1,2,3,4 and the technical appendixes have been developed by Giorgio Alleva and Piero Demetrio Falorsi; Sect. 5 has been done by Fabio Bacchini and Roberto Iannaccone. Piero Demetrio Falorsi is chief statisticians at Italian National Institute of Statistics (ISTAT); Giorgio Alleva is Professor of Statistics at University “La Sapienza” of Rome, Fabio Bacchini and Roberto Iannaccone are researchers at ISTAT.     

A fuzzy logic approach to poverty analysis based on the Gini and Bonferroni inequality indices

In the poverty analysis framework, a great deal of attention has been paid to the poverty measurement in terms of monetary variables, such as income or consumption. In this context, a relevant open problem is connected with the distinction between poor and non-poor. In fact, the concept of poverty is rather vague and cannot be defined in a clear way. In this respect, following a fuzzy logic approach, some new poverty measures are proposed. In particular, the fuzzy extension of two existing poverty measures based on the Gini and Bonferroni inequality indices is provided. Some synthetic and real applications are given in order to show how the proposed poverty measures work.     

Fuzzy measures of the incidence of relative poverty and deprivation: a multi-dimensional perspective

In this paper we present a methodology for the study of multi-dimensional aspects of poverty and deprivation. The conventional poor/non-poor dichotomy is replaced by defining poverty as a matter of degree, determined by the place of the individual in the income distribution. The fuzzy poverty measure proposed is in fact also expressible in terms of the generalised Gini measure. The same methodology facilitates the inclusion of other dimensions of deprivation into the analysis: by appropriately weighting indicators of deprivation to reflect their dispersion and correlation, we can construct measures of non-monetary deprivation in its various dimensions. These indicators illuminate the extent to which purely monetary indicators are insufficient in themselves in capturing the prevalence of deprivation. An important contribution of the paper is to identify rules for the aggregation of fuzzy sets appropriate for the study of poverty and deprivation. In particular, we define a ‘composite’ fuzzy set operator which takes into account whether the sets being aggregated are of a ‘similar’ or a ‘dissimilar’ type. These rules allow us to meaningfully combine income and the diverse non-income deprivation indices at the micro-level and construct what we have termed ‘intensive’ and ‘extensive’ indicators of deprivation. We note that mathematically the same approach can be carried over to the study of persistence of poverty and deprivation over time.     

A Clipped Gaussian Geo-Classification model for poverty mapping

The importance of discrete spatial models cannot be overemphasized, especially when measuring living standards. The battery of measurements is generally categorical with nearer geo-referenced observations featuring stronger dependencies. This study presents a Clipped Gaussian Geo-Classification (CGG-C) model for spatially-dependent ordered data, and compares its performance with existing methods to classify household poverty using Ghana living standards survey (GLSS 6) data. Bayesian inference was performed on data sampled by MCMC. Model evaluation was based on measures of classification and prediction accuracy. Spatial associations, given some household features, were quantified, and a poverty classification map for Ghana was developed. Overall, the results of estimation showed that many of the statistically significant covariates were generally strongly related with the ordered response variable. Households at specific locations tended to uniformly experience specific levels of poverty, thus, providing an empirical spatial character of poverty in Ghana. A comparative analysis of validation results showed that the CGG-C model (with 14.2% misclassification rate) outperformed the Cumulative Probit (CP) model with misclassification rate of 17.4%. This approach to poverty analysis is relevant for policy design and the implementation of cost-effective programmes to reduce category and site-specific poverty incidence, and monitor changes in both category and geographical trends thereof.KEYWORDS: Ordered responses, spatial correlation, Bayesian estimation via MCMC, Gaussian random fields, poverty classification     

Firm size distributions and stochastic growth models: a comparison between ICT and Mechanical Italian Companies

In this paper we analyze the relationship between the distribution of firm size and stochastic processes of growth. Three main models have been suggested by Gibrat (1931), Kalecki (1945) and Champernowne (1973). The first two lead to lognormal distribution and the last to Pareto distribution. We fitted lognormal and Pareto distribution to two Italian sectors: ICT and mechanical. For ICT we found that lognormal distribution must be rejected and Pareto fits reasonably well to the last 30% of largest companies. For mechanical sector we can not reject lognormal distribution. Furthermore, we perform some experiments to corroborate the theoretical models. By means of transition matrices we found that ICT shows features very close to Gibrats and Champernownes models, while Kaleckis model strongly fits to mechanical.JEL Classification: L00, L25, D21Correspondence to: Luigi GrossiThis research was partially supported by grants from Ministero dellIstruzione, dellUniversitá e della Ricerca (MIUR). Despite being the results of a joint work, Sects. 1, 4, 8 and 10 should be attributed to Ganugi, Sects. 3, 6, and 7 to Grossi and Sects. 2, 5, and 9 to Crosato.     

A Dynamic Latent Model for Poverty Measurement

The main purpose of this paper is the longitudinal analysis of the poverty phenomenon. By interpreting poverty as a latent variable, we are able to resort to the statistical methodology developed for latent structure analysis. In particular, we propose to use the mixture latent Markov model which allows us to achieve two goals: (i) a time-invariant classification of households into homogenous groups, representing different levels of poverty; (ii) the dynamic analysis of the poverty phenomenon which highlights the distinction between transitory and permanent poverty situations. Furthermore, we exploit the flexibility provided by the model in order to achieve the measurement of poverty in a multidisciplinary framework, using several socio-economic indicators as covariates and identifying the main relevant factors which influence permanent and transitory poverty. The analysis of the longitudinal data of the Survey on Households Income and Wealth of the Bank of Italy provides the identification of two groups of households which are characterized by different dynamic features. Moreover, the inclusion of socio-economic covariates such as level of education, employment status, geographical area and residence size of the household head shows a direct association with permanent poverty.     

Estimating the Parameters of Stochastic Volatility Models Using Option Price Data

This article describes a maximum likelihood method for estimating the parameters of the standard square-root stochastic volatility model and a variant of the model that includes jumps in equity prices. The model is fitted to data on the S&P 500 Index and the prices of vanilla options written on the index, for the period 1990 to 2011. The method is able to estimate both the parameters of the physical measure (associated with the index) and the parameters of the risk-neutral measure (associated with the options), including the volatility and jump risk premia. The estimation is implemented using a particle filter whose efficacy is demonstrated under simulation. The computational load of this estimation method, which previously has been prohibitive, is managed by the effective use of parallel computing using graphics processing units (GPUs). The empirical results indicate that the parameters of the models are reliably estimated and consistent with values reported in previous work. In particular, both the volatility risk premium and the jump risk premium are found to be significant.     

Maximum likelihood estimation of ARFIMA models with a Box-Cox transformation

In this paper we study the interaction between the estimation of the fractional differencing parameter d of ARFIMA models and the common practice of instantaneous transformation of the observed time series. At this aim, we first discuss the effect of a nonlinear transformation of the data on the identification of the process and on the estimate of d. Thus, we propose a joint estimation of the Box-Cox parameter and d by means of a modified normalized version of the Whittle likelihood. Then, the variance and covariance matrix of the parameters estimates is obtained. Finally, a Monte Carlo study is performed in order to check the behaviour of the proposed estimators in finite samples.The paper is the result of a joint research of the two authors. As far as it concerns this version of the work, A. DElia wrote Sects. 2, 3, 4, while D. Piccolo wrote Sects. 1, 5, 6.     

Poverty as a System: Human Contestability Approach to Poverty Measurement

Since Sen's (1976) paper on poverty measurement, a substantial literature, both theoretical and empirical, has emerged. There have been several recent efforts to drive poverty measures based on different approaches and axioms. These poverty indices are based on head count ratio, poverty gaps and distribution of income. These are very narrow in approach and suffer from several drawbacks. However, the purpose of the present paper is to introduce a new poverty measure based on a holistic and system modelling approach. Based on Chopra's human contestability (Chopra, 2003, 2007) approach to poverty, this new approach to measuring poverty has been developed using a structure equation model based on Kanji's business excellence model (Kanji, 2002) to create the proposed poverty model. We construct a latent variable structural equation model to measure the contestability excellence within certain boundaries of the societal system. It will provide us with a measurement of poverty in a society or community in terms of human contestability. A higher human contestability index will indicate the lower poverty within the society. Strengths and weakness as of various components will also indicate that a characteristic of the individual requires extra society or government support to remove poverty. However, there remains considerable disagreement on the best way to achieve this.     

A marginal regression model for multivariate failure time data with a surviving fraction

A marginal regression approach for correlated censored survival data has become a widely used statistical method. Examples of this approach in survival analysis include from the early work by Wei et al. (J Am Stat Assoc 84:1065–1073, 1989) to more recent work by Spiekerman and Lin (J Am Stat Assoc 93:1164–1175, 1998). This approach is particularly useful if a covariate’s population average effect is of primary interest and the correlation structure is not of interest or cannot be appropriately specified due to lack of sufficient information. In this paper, we consider a semiparametric marginal proportional hazard mixture cure model for clustered survival data with a surviving or “cure” fraction. Unlike the clustered data in previous work, the latent binary cure statuses of patients in one cluster tend to be correlated in addition to the possible correlated failure times among the patients in the cluster who are not cured. The complexity of specifying appropriate correlation structures for the data becomes even worse if the potential correlation between cure statuses and the failure times in the cluster has to be considered, and thus a marginal regression approach is particularly attractive. We formulate a semiparametric marginal proportional hazards mixture cure model. Estimates are obtained using an EM algorithm and expressions for the variance–covariance are derived using sandwich estimators. Simulation studies are conducted to assess finite sample properties of the proposed model. The marginal model is applied to a multi-institutional study of local recurrences of tonsil cancer patients who received radiation therapy. It reveals new findings that are not available from previous analyses of this study that ignored the potential correlation between patients within the same institution.     

Recursive computation for repeated measures models with patterned variance matrices

A convenient recursive computational method for repeated measures analysis, provided by McGilchrist and Cullis (1990), has been extended by the authors to heterogeneous error structures and also to the repeated measures model with random coefficients. The approach is outlined briefly in this paper. A computing program for the approach has been written and used to obtain results for simulated data having various error structures. A summary of the results is given. The computing program together with some subroutines is available from the authors.     

Wavelets in statistics: A review

The field of nonparametric function estimation has broadened its appeal in recent years with an array of new tools for statistical analysis. In particular, theoretical and applied research on the field of wavelets has had noticeable influence on statistical topics such as nonparametric regression, nonparametric density estimation, nonparametric discrimination and many other related topics. This is a survey article that attempts to synthetize a broad variety of work on wavelets in statistics and includes some recent developments in nonparametric curve estimation that have been omitted from review articles and books on the subject. After a short introduction to wavelet theory, wavelets are treated in the familiar context of estimation of «smooth» functions. Both «linear» and «nonlinear» wavelet estimation methods are discussed and cross-validation methods for choosing the smoothing parameters are addressed. Finally, some areas of related research are mentioned, such as hypothesis testing, model selection, hazard rate estimation for censored data, and nonparametric change-point problems. The closing section formulates some promising research directions relating to wavelets in statistics.     

Empirical bayesInterval estimates: An application to geographical epidemiology

Summary Empirical Bayes estimates have been advocated as an improvement for mapping rare diseases or health events aggregated in small areas. In particular different parametric approaches have been proposed for dealing with non-normal data, assuming that disease occurrencies follow non-homogeneous Poisson law, whose parameters are treated as random variables. This paper shows how to conduct a complete Empirical Bayes analysis under an exchangeable model in the context of Geographical Epidemiology. Three different approaches for defining confidence limits obtained using a parametric bootstrap are compared: method 1 relies only on the first and second moment of the bootstrapped posterior distributions; method 2 computes the centiles of the bootstrapped posteriors; method 3 equates to α the average of the probabilities derived from the estimated bootstrapped cumulative posterior distributions. The simple Poisson-Gamma formulation was used to model mortality data on Larynx Cancer in the Local Health Units of Tuscany (1980–82 males). Two areas of significant elevated risk are identified.     

Nonparametric estimation of the canonical measure for infinitely divisible distributions

Infinitely divisible distributions (i.d.d.'s) with a finite variance have a characteristic function of a particular form. The exponent is written in terms of the canonical or Kolmogorov measure. This paper considers a nonparametric estimate of the Kolmogorov measure based on the empirical characteristic function (e.c.f.) and a truncation. The weak convergence of this estimator is studied. The raw form of the estimator is a functional of the e.c.f., but to be useful in a finite sample it requires some additional smoothing. Thus smoothed estimators are considered. A dynamic data dependent method of truncation is given. A simulation study is undertaken to show how the Kolmogorov measure can be estimated, as well as giving an illustration of the numerical stability questions. It is also seen that a large sample size is needed.     

我国贫困人口的脆弱度与贫困动态

 在贫困脆弱性和贫困动态理论的逻辑归纳与阐述基础上，利用辽宁省重点贫困县调查样本数据，采用聚类分析、脆弱度分析以及敏感度分析等方法实际测度了贫困县贫困状态的分布情况和脆弱程度；从贫困动态的角度，对贫困户1997～2006年间的贫困发生频次、深度及持续时段进行了统计分析。研究发现，各个贫困县的贫困脆弱性程度存在一定的差异，且受多重致贫因素的影响呈现出一定的类型分布特征；贫困动态的分析在一定程度上支持了贫困脆弱度的结果；贫困时段分析与以往研究发现略有不同，呈现出“暂时贫困”和“长期贫困”二者“并重”的特征，而非“单一分布”的“偏态”， 真正有效率的扶贫救济制度应当准确地锁定在持续贫困的家庭上，政策相应地要具有差异性和弹性，这样才有可能快速及时的解决攻坚阶段的贫困问题。     

包含加法模型和混合模型的指数分析体系

统计指数体系分析方法的一个较大不足就是局限于乘法形式的经济方程式,然而经济现象之间的相互联系是多种多样的,目前的统计指数体系分析方法难以应用于形式多样的复杂经济现象的因素分析。本文把基于乘法方式的指数体系称之为指数体系的“乘法模型”,并以此为基础,将传统的只包含乘法关系的经济方程式加以扩展,将其推广到可以应用于加减运算的“加法模型”和包含全部四则运算的“混合模型”,建立了“广义指数分析模型”。该模型不仅保留了传统统计指数体系的基本结构和基本分析方法,还可以较大地提高统计指数分析的深度和广度,由此可以基本解决统计指数体系分析方法的局限性问题。     

Cultural tourism and temporary art exhibitions in Italy: a panel data analysis

The main aim of this work is to study the relationship between cultural tourism and temporary art exhibitions by means of a panel data analysis. In literature, the capability of cultural attractions, e.g. art exhibitions, of increasing the tourist flow has not been investigated yet and we start to fill this gap. Our data set consists of monthly observed variables on 52 Italian provinces over the period 2003–2007. Our response variable is the amount of hotel arrivals and the set of covariates includes the amount of visitors of temporary exhibitions of ancient, modern and contemporary art plus a set of variables that contribute to tourist arrivals, like the kind of destination, the attraction capability of each province and so on. Of particular interest is to discover the art sector that has the strongest influence on the tourist flow towards Italy by keeping into account both the temporal dynamic and the heterogeneity of the Italian provinces. To this aim, we discuss the static and dynamic error component regression models from both the theoretical and practical point of view. The estimated two-way fixed effects regression models suggest that all the three sectors contribute to the tourist flow but in a quite different fashion. On the basis of our analysis we derive some indications for the policy maker in the field of cultural tourism.