世界経済・社会統計 = World development indicators

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

can be formulated in terms of basis functions and discuss the dif culties in posterior simulations due to interdependence of these functions. Such interdependence affects the ef ciency of the sampling algorithms to draw from posterior distribution of the tree structures. Different strategies that are suggested in the literature for dealing with the sampling problem are discussed, and a detailed example using binary classi cation is presented to illustrate the Bayesian analysis. To alleviate the problems that arise in tree models, Chapter 7 introduces partition models. The partition models can be considered a generalization of tree models, and they allow for sampling from the posterior distributions of the tree structure. As noted by the authors, these models suffer from lack of interpretability in high dimensions. The authors present one-dimensional partition models whose analysis provides a general framework for the changepoint problems. Multidimensional partition models, where partitions are de ned by Dirichlet tessellations, are considered, and Bayesian inference for classi cation problems is discussed. Disease mapping models are presented as an application of partition models for spatial problems. Chapter 8 is a short chapter describing Bayesian nearest-neighbor modeling. The nearest-neighbor classi cation algorithm, which is used commonly in pattern recognition, is given a probabilistic formulation by introducing a parameter that controls the degree of association between the neighboring classes. In Chapter 9 the authors generalize the single-response case to multipleresponse models where the observed response is a collection of values. The chapter focuses on regression models and does not consider classi cation models such as the multivariate probit models. Multivariate Bayesian regression framework is introduced where basis functions can be determined from the data using methods of Chapter 3. A generalization is considered using seemingly unrelated regression (SUR) models and their Bayesian analysis is presented. Prior speci cation for basis function matrix are discussed, and computational details of the MCMC methods are given for both models. The book has a comprehensive bibliography, and each chapter (except Chap. 1) has a section on further reading. There are two appendixes at the end. Appendix B gives a summary of posterior inference results that are helpful for some of the development in the text. In summary, this book presents recent developments in Bayesian nonlinear modeling and provides a complete treatment of regression and classi cation problems by emphasizing a data-driven approach in determining appropriate models. Its in-depth coverage of implementation issues and detailed discussion of pros and cons of different modeling strategies make it attractive for many researchers. It de nitely makes my list of recommended texts in Bayesian statistics.

Resampling Methods for Dependent Data

This paper attempts to estimate the environmental Kuznets curve (EKC) in the case of France by taking the role of nuclear energy in electricity production into account. We adopt the autoregressive distributed lag (ARDL) approach to cointegration as the estimation method. Additionally, we examine the stability of the estimated models and investigate the Granger causality relationships between the variables in the system. The results from our estimation provide evidence supporting the EKC hypothesis and the estimated models are shown to be stable over the sample period. The uni-direction running from other variables to CO2 emissions are confirmed from the casualty tests. Specifically, the uni-directional causality relationship running from nuclear energy to CO2 emissions statistically provides evidence on the important role of nuclear energy in reducing CO2 emissions.

Empirical Study on the Environmental Kuznets Curve for CO2 in France: The Role of Nuclear Energy

Asset prices and central bank policy.

Identification of independent structural shocks in the presence of multiple Gaussian components

In this article, we describe the command xtpurt, which implements the heteroskedasticity-robust panel unit-root tests suggested in Herwartz and Siedenburg (2008, Computational Statistics and Data A...

Panel Unit-root Tests for Heteroskedastic Panels:

Structural vector autoregressive (SVAR) models are frequently applied to trace the contemporaneous linkages among (macroeconomic) variables back to an interplay of orthogonal structural shocks. Under Gaussianity the structural parameters are unidentified without additional (often external and not data-based) information. In contrast, the often reasonable assumption of heteroskedastic and/or non-Gaussian model disturbances offers the possibility to identify unique structural shocks. We describe the R package svars which implements statistical identification techniques that can be both heteroskedasticity-based or independence-based. Moreover, it includes a rich variety of analysis tools that are well known in the SVAR literature. Next to a comprehensive review of the theoretical background, we provide a detailed description of the associated R functions. Furthermore, a macroeconomic application serves as a step-by-step guide on how to apply these functions to the identification and interpretation of structural VAR models.

svars: An R Package for Data-Driven Identification in Multivariate Time Series Analysis

Time‐varying volatility and linear trends are common features of several macroeconomic time series. Recent articles have proposed panel unit root tests (PURTs) that are pivotal in the presence of volatility shifts, excluding linear trends, however. This article proposes a new PURT that works well for data that is both heteroskedastic and trending. Under the null hypothesis, the test statistic has a limiting Gaussian distribution. We derive the local asymptotic power to underpin the consistency of the test statistic. Simulation results reveal that the test performs well in small samples. As an empirical illustration, we examine the stationarity of energy use per capita in OECD economies. While the series are in general difference stationary, they could also be considered as trend stationary for specific time spans.

/pdf/heteroskedasticity-robust-unit-root-testing-for-trending-qq26ey82zj.pdf

Heteroskedasticity‐Robust Unit Root Testing for Trending Panels

https://onlinelibrary.wiley.com/doi/pdf/10.1111/ecin.13035

Data-driven identification in SVARs—When and how can statistical characteristics be used to unravel causal relationships?

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