论自然地震预测、预报的可能性——写在5．12汶川地震2周年之际

我国是一个地震多发的国家,防震减灾已成为我国的基本国策。目前自然地震的研究和预测存在着两种不同的理念和四种预测方法。坚持对地震中短期和临震宏观、微观异常现象与地质结构、构造相结合进行地应力规律研究,实现有效预测和预报自然地震将成为可能。     

Goodness‐of‐Fit Test for Monotone Functions

Abstract. In this article, we develop a test for the null hypothesis that a real‐valued function belongs to a given parametric set against the non‐parametric alternative that it is monotone, say decreasing. The method is described in a general model that covers the monotone density model, the monotone regression and the right‐censoring model with monotone hazard rate. The criterion for testing is an ‐distance between a Grenander‐type non‐parametric estimator and a parametric estimator computed under the null hypothesis. A normalized version of this distance is shown to have an asymptotic normal distribution under the null, whence a test can be developed. Moreover, a bootstrap procedure is shown to be consistent to calibrate the test.     

Goodness‐of‐Fit Tests for Bivariate and Multivariate Skew‐Normal Distributions

Abstract. Goodness‐of‐fit tests are proposed for the skew‐normal law in arbitrary dimension. In the bivariate case the proposed tests utilize the fact that the moment‐generating function of the skew‐normal variable is quite simple and satisfies a partial differential equation of the first order. This differential equation is estimated from the sample and the test statistic is constructed as an L ₂ ‐type distance measure incorporating this estimate. Extension of the procedure to dimension greater than two is suggested whereas an effective bootstrap procedure is used to study the behaviour of the new method with real and simulated data.     

Prediction of long memory processes on same-realisation

For the class of stationary Gaussian long memory processes, we study some properties of the least-squares predictor of _Xn+1$X_{n+1}$ based on (_Xn,…,_X1)$(X_n,\dots ,X_1)$. The predictor is obtained by projecting _Xn+1$X_{n+1}$ onto the finite past and the coefficients of the predictor are estimated on the same realisation. First we prove moment bounds for the inverse of the empirical covariance matrix. Then we deduce an asymptotic expression of the mean-squared error. In particular we give a relation between the number of terms used to estimate the coefficients and the number of past terms used for prediction, which ensures the L²$L^2$- sense convergence of the predictor. Finally we prove a central limit theorem when our predictor converges to the best linear predictor based on all the past.     

How does the DerSimonian and Laird procedure for random effects meta-analysis compare with its more efficient but harder to compute counterparts?

The procedure suggested by DerSimonian and Laird is the simplest and most commonly used method for fitting the random effects model for meta-analysis. Here it is shown that, unless all studies are of similar size, this is inefficient when estimating the between-study variance, but is remarkably efficient when estimating the treatment effect. If formal inference is restricted to statements about the treatment effect, and the sample size is large, there is little point in implementing more sophisticated methodology. However, it is further demonstrated, for a simple special case, that use of the profile likelihood results in actual coverage probabilities for 95% confidence intervals that are closer to nominal levels for smaller sample sizes. Alternative methods for making inferences for the treatment effect may therefore be preferable if the sample size is small, but the DerSimonian and Laird procedure retains its usefulness for larger samples.     

数据窥查效应、可靠性检验与平稳Bootstrap模拟——兼论技术交易规则与沪深300指数的预测

数据窥查效应是金融学研究中的一种常见现象,虽然很早就引起了学者们的关注,但由于研究方法的限制,目前国内还没有关于数据窥查效应的系统研究。为此,针对数据窥察效应,借助平稳Bootstrap模拟,探讨可靠性检验的统计学原理和计算步骤。构建了2 000多个模型,采用递归最小二乘的估计方法,研究是否可以利用技术交易规则预测沪深300指数的走势,并进一步探讨可靠性检验P值的动态演变过程,验证理论分析的结论,进而通过增加用于预测的样本长度来有效克服数据窥查效应。对平稳Bootstrap模拟区组选择的探讨表明,同时选择多个区组长度进行实证分析可以使结论更加稳健。     

中国区域经济增长路径的差异性研究——基于ACF检验的新证据

运用考虑结构变化的自相关函数（ACF）方法,利用子样本抽样和稳态自助法抽样,依据相对最优的原理构建了ACF的最优置信区间,使用1953—2008年中国省市自治区数据,对中国区域经济增长路径的实际特征进行了经验分析。研究的结论表明,中国区域经济增长的转移动态路径具有显著的差异性,区域经济增长均呈现出非线性振荡的转移特征,对数线性化的新古典索罗增长模型并不能刻画出中国区域经济转移动态特征。     

基于copula回归模型的损失预测

在非寿险损失预测的广义线性模型中,通常假设损失次数与损失强度相互独立,事实上二者之间往往存在一定的相依关系,可通过copula函数来刻画.在损失已经发生的条件下,假设损失次数服从零截断泊松分布,损失强度服从伽玛分布,可以建立损失次数与损失强度相互依赖的copula回归模型.把损失强度的分布扩展到逆高斯分布,并将此模型应用于一组车险保单数据进行实证研究.结果表明:该模型不但在损失预测方面优于独立假设下的广义线性模型,而且也优于损失强度服从伽马分布假设下的copula回归模型.     

A comparison of bootstrap approaches for estimating uncertainty of parameters in linear mixed‐effects models

A version of the nonparametric bootstrap, which resamples the entire subjects from original data, called the case bootstrap, has been increasingly used for estimating uncertainty of parameters in mixed‐effects models. It is usually applied to obtain more robust estimates of the parameters and more realistic confidence intervals (CIs). Alternative bootstrap methods, such as residual bootstrap and parametric bootstrap that resample both random effects and residuals, have been proposed to better take into account the hierarchical structure of multi‐level and longitudinal data. However, few studies have been performed to compare these different approaches. In this study, we used simulation to evaluate bootstrap methods proposed for linear mixed‐effect models. We also compared the results obtained by maximum likelihood (ML) and restricted maximum likelihood (REML). Our simulation studies evidenced the good performance of the case bootstrap as well as the bootstraps of both random effects and residuals. On the other hand, the bootstrap methods that resample only the residuals and the bootstraps combining case and residuals performed poorly. REML and ML provided similar bootstrap estimates of uncertainty, but there was slightly more bias and poorer coverage rate for variance parameters with ML in the sparse design. We applied the proposed methods to a real dataset from a study investigating the natural evolution of Parkinson's disease and were able to confirm that the methods provide plausible estimates of uncertainty. Given that most real‐life datasets tend to exhibit heterogeneity in sampling schedules, the residual bootstraps would be expected to perform better than the case bootstrap. Copyright © 2013 John Wiley & Sons, Ltd.     

Usual and Shortest Confidence Intervals on Odds Ratios from Logistic Regression

Based on the large-sample normal distribution of the sample log odds ratio and its asymptotic variance from maximum likelihood logistic regression, shortest 95% confidence intervals for the odds ratio are developed. Although the usual confidence interval on the odds ratio is unbiased, the shortest interval is not. That is, while covering the true odds ratio with the stated probability, the shortest interval covers some values below the true odds ratio with higher probability. The upper and lower limits of the shortest interval are shifted to the left of those of the usual interval, with greater shifts in the upper limits. With the log odds model γ + Xβ, in which X is binary, simulation studies showed that the approximate average percent difference in length is 7.4% for n (sample size) = 100, and 3.8% for n = 200. Precise estimates of the covering probabilities of the two types of intervals were obtained from simulation studies, and are compared graphically. For odds ratio estimates greater (less) than one, shortest intervals are more (less) likely to include one than are the usual intervals. The usual intervals are likelihood-based and the shortest intervals are not. The usual intervals have minimum expected length among the class of unbiased intervals. Shortest intervals do not provide important advantages over the usual intervals, which we recommend for practical use.