Book review

W.G.Cochran: Sampling Techniques, 3rd. Ed. John Wiley & Sons, New York-Santa Barbara-London-Sydney-Toronto 1977. 428 S., £ 12.50; $21.50.

H.Toutenburg: Vorhersage in linearen Modellen. Akademie-Verlag, Berlin 1975, VIII, 176b S., 3 Tab., 28,– M.

O.Kallenberg: Random Measure. Akademie-Verlag, Berlin 1975; Academic Press, London 1976. 104 pp., 28,– M.     

Global convergence of the log-concave MLE when the true distribution is geometric

Let X₁, …, X_n be i.i.d. from a discrete probability mass function (pmf) p. In Balabdaoui et al. [(2013), ‘Asymptotic Distribution of the Discrete Log-Concave mle and Some Applications’, JRSS-B, in press], the pointwise limit distribution of the log-concave maximum-likelihood estimator (MLE) was derived in both the well- and misspecified settings. In the well-specified setting, the geometric distribution was excluded, classified as being degenerate. In this article, we establish the global asymptotic theory of the log-concave MLE of a geometric pmf in all ?_q distances for q∈{1, 2, …}∪{∞}. We also show how these asymptotic results could be used in testing whether a pmf is geometric.     

Convergence Rate of Wavelet Expansions of Gaussian Random Processes

This article characterizes uniform convergence rate for general classes of wavelet expansions of stationary Gaussian random processes. The convergence in probability is considered.     

Recent and classical goodness-of-fit tests for the Poisson distribution

We give a critical synopsis of classical and recent tests for Poissonity, our emphasis being on procedures which are consistent against general alternatives. Two classes of weighted Cramér–von Mises type test statistics, based on the empirical probability generating function process, are studied in more detail. Both of them generalize already known test statistics by introducing a weighting parameter, thus providing more flexibility with regard to power against specific alternatives. In both cases, we prove convergence in distribution of the statistics under the null hypothesis in the setting of a triangular array of rowwise independent and identically distributed random variables as well as consistency of the corresponding test against general alternatives. Therefore, a sound theoretical basis is provided for the parametric bootstrap procedure, which is applied to obtain critical values in a large-scale simulation study. Each of the tests considered in this study, when implemented via the parametric bootstrap method, maintains a nominal level of significance very closely, even for small sample sizes. The procedures are applied to four well-known data sets.     

V aR 之下厚尾分布的最优资产组合的收敛性

主要研究在V aR 风险度量之下, 收益具有厚尾性质的资产的投资组合问题. 证明了基于 尾部分布二阶展开的最优投资组合收敛于基于尾部分布一阶展开的最优投资组合. 因此, 对于 V aR 风险度量之下的最优投资组合问题, 如果要求的风险承受水平充分低, 则只需要利用尾 部分布的一阶展开代替厚尾部分布进行近似计算, 就可以达到满意的精度, 从而不需要进行复 杂的高阶运算.     

China’s GDP: Examining provincial disparities (1952–1998)

Accompanying rapid economic growth in China, there have been provincial disparities. This article presents and analyzes the evolution of Chinas provincial GDP per capita disparity between 1952 and 1998. First, an examination of some basic indicators of disparity is carried out, and a test for unconditional convergence is performed to explore the dispersion features. Then, a more comprehensive regression analysis, allowing insights into the evidence of conditional convergence and highlighting the main determinants of growth in two main periods of the recent history of China (i.e., prereform and postreform) is presented. Finally, a discussion and conclusion are provided.     

Technology spillover and regional convergence process: a statistical analysis of the Italian case

Recent literature broadly highlight the importance of modelling technological innovation effects on economic growth. This paper develops a methodology that allows to measure technology contribution to economic convergence; the choice of a regional framework also allows to underline interregional knowledge transmission as a the major channel of technological progress. Moreover, the specification of a dynamic growth model enables to evaluate both the regional convergence and the effect of innovation on long-run labour productivity without resorting to any technology index measurement. We contribute to the methodological literature also by comparing different dynamic panel data estimation procedures and by detecting both the presence of small sample bias and the existence of a nearly unit root autoregressive process in labour productivity series. The results of an empirical analysis on Italian regions show how most of innovation resources derives from relevant spillover mechanisms. Furthermore, technology spillover intensity seems to be strongly affected by geography and productive structure of regions.Financial support by Fondazione Cassa di Risparmio di Rimini and Uniturim S.p.A. is gratefully acknowledged.     

初等概率论中的收敛性注记

通过介绍初等概率论中的四种收敛性 ,揭示了它们之间的相互关系     

Degeneracy in the Maximum Likelihood Estimation of Univariate Gaussian Mixtures for Grouped Data and Behaviour of the EM Algorithm

Abstract.  In the context of the univariate Gaussian mixture with grouped data, it is shown that the global maximum of the likelihood may correspond to a situation where a Dirac lies in any non-empty interval. Existence of a domain of attraction near such a maximizer is discussed and we establish that the expectation-maximization (EM) iterates move extremely slowly inside this domain. These theoretical results are illustrated both by some Monte-Carlo experiments and by a real data set. To help practitioners identify and discard these potentially dangerous degenerate maximizers, a specific stopping rule for EM is proposed.     

长三角的产业集聚及其省区特征、同构绩效——一个基于长三角产业集聚演化的视角

产业集聚是长三角产业发展的重要特征.文章根据影响产业集聚的一般因素,结合长三角区域经济发展实际,研究了长三角产业集聚的动力机制、空间演化路径和集聚绩效.文章认为,产业的集聚动力在于地区的竞争优势,新经济地理学理论中产业集聚的影响因素则加深和放大了地区的产业集聚过程;长三角的历史沿革、区位优势和中国转轨经济的体制改革特征决定了长三角省区经济空间演化的特征是产业同构;这种以产业同构为主要内容的长三角产业集聚并没有表现为省区经济之间的"重复建设"或者是"恶性竞争",基于在世界经济格局中廉价劳动力比较分工优势的长三角的产业集聚引起的外部性、市场扩大效应和价格指数效应成为区域产业同构具有正面绩效的支撑因素,但地区的工业化进程对相关产业的绩效存在影响.文章的实证研究支持上述结论.