Asymptotically valid single-stage multiple-comparison procedures

We establish general conditions for the asymptotic validity of single-stage multiple-comparison procedures (MCPs) under the following general framework. There is a finite number of independent alternatives to compare, where each alternative can represent, e.g., a population, treatment, system or stochastic process. Associated with each alternative is an unknown parameter to be estimated, and the goal is to compare the alternatives in terms of the parameters. We establish the MCPs’ asymptotic validity, which occurs as the sample size of each alternative grows large, under two assumptions. First, for each alternative, the estimator of its parameter satisfies a central limit theorem (CLT). Second, we have a consistent estimator of the variance parameter appearing in the CLT. Our framework encompasses comparing means (or other moments) of independent (not necessarily normal) populations, functions of means, quantiles, steady-state means of stochastic processes, and optimal solutions of stochastic approximation by the Kiefer–Wolfowitz algorithm. The MCPs we consider are multiple comparisons with the best, all pairwise comparisons, all contrasts, and all linear combinations, and they allow for unknown and unequal variance parameters and unequal sample sizes across alternatives.     

On the statistical inference of a machine-generated autoregressive AR(1) model

We have obtained the asymptotic bias and the limiting distribution for the Yule–Walker estimator of the autoregressive parameter under a considerably weaker assumption than that of independence in the noise sequence. Among other things, these suggest robustness of the classical results and throw some light on the use of simulations based on pseudorandom numbers in verifying these results.     

Improved local polynomial estimation in time series regression

We propose a modification of local polynomial estimation which improves the efficiency of the conventional method when the observation errors are correlated. The procedure is based on a pre-transformation of the data as a generalization of the pre-whitening procedure introduced by Xiao et al. [(2003), ‘More Efficient Local Polynomial Estimation in Nonparametric Regression with Autocorrelated Errors’, Journal of the American Statistical Association, 98, 980–992]. While these authors assumed a linear process representation for the error process, we avoid any structural assumption. We further allow the regressors and the errors to be dependent. More importantly, we show that the inclusion of both leading and lagged variables in the approximation of the error terms outperforms the best approximation based on lagged variables only. Establishing its asymptotic distribution, we show that the proposed estimator is more efficient than the standard local polynomial estimator. As a by-product we prove a suitable version of a central limit theorem which allows us to improve the asymptotic normality result for local polynomial estimators by Masry and Fan [(1997), ‘Local Polynomial Estimation of Regression Functions for Mixing Processes’, Scandinavian Journal of Statistics, 24, 165–179]. A simulation study confirms the efficiency of our estimator on finite samples. An application to climate data also shows that our new method leads to an estimator with decreased variability.     

Estimation of the limit variance for sums under a new weak dependence condition

We prove a self-normalized central limit theorem for a mixing class of processes introduced in Kacem M, Loisel S, Maume-Deschamps V. [Some mixing properties of conditionally independent processes. Commun Statist Theory Methods. 2016;45:1241–1259]. This class is larger than more classical strongly mixing processes and thus our result is more general than [Peligrad M, Shao QM. Estimation of the variance of partial sums for ρ-mixing random variables. J Multivar Anal. 1995;52:140–157; Shi S. Estimation of the variance for strongly mixing sequences. Appl Math J Chinese Univ. 2000;15(1):45–54] ones. The fact that some conditionally independent processes satisfy this kind of mixing properties motivated our study. We investigate the weak consistency as well as the asymptotic normality of the estimator of the variance that we propose.     

Dependent Lindeberg central limit theorem for the fidis of empirical processes of cluster functionals

Drees H. and Rootzén H. [Limit theorems for empirical processes of cluster functionals (EPCF). Ann Stat. 2010;38(4):2145–2186] have proven central limit theorems (CLTs) for EPCF built from β-mixing processes. However, this family of β-mixing processes is quite restrictive. We expand some of those results, for the finite-dimensional marginal distributions (fidis), to a more general dependent processes family, known as weakly dependent processes in the sense of Doukhan P. and Louhichi S. [A new weak dependence condition and applications to moment inequalities. Stoch. Proc. Appl. 1999;84:313–342]. In this context, the CLT for the fidis of EPCF is sufficient in some applications. For instance, we prove the convergence without mixing conditions of the extremogram estimator, including a small example with simulation of the extremogram of a weakly dependent random process but nonmixing, in order to confirm the efficacy of our result.     

Central limit theorem for the variable bandwidth kernel density estimators

In this paper we study the ideal variable bandwidth kernel density estimator introduced by McKay (1993a, b) and Jones et al. (1994) and the plug-in practical version of the variable bandwidth kernel estimator with two sequences of bandwidths as in Giné and Sang (2013). Based on the bias and variance analysis of the ideal and plug-in variable bandwidth kernel density estimators, we study the central limit theorems for each of them. The simulation study confirms the central limit theorem and demonstrates the advantage of the plug-in variable bandwidth kernel method over the classical kernel method.     

Generalized Mann–Whitney Type Tests for Microarray Experiments

New statistical procedures are introduced to analyse typical microRNA expression data sets. For each separate microRNA expression, the null hypothesis to be tested is that there is no difference between the distributions of the expression in different groups. The test statistics are then constructed having certain type of alternatives in mind. To avoid strong (parametric) distributional assumptions, the alternatives are formulated using probabilities of different orders of pairs or triples of observations coming from different groups, and the test statistics are then constructed using corresponding several‐sample U‐statistics, natural estimates of these probabilities. Classical several‐sample rank test statistics, such as the Kruskal–Wallis and Jonckheere–Terpstra tests, are special cases in our approach. Also, as the number of variables (microRNAs) is huge, we confront a serious simultaneous testing problem. Different approaches to control the family‐wise error rate or the false discovery rate are shortly discussed, and it is shown how the Chen–Stein theorem can be used to show that family‐wise error rate can be controlled for cluster‐dependent microRNAs under weak assumptions. The theory is illustrated with an analysis of real data, a microRNA expression data set on Finnish (aggressive and non‐aggressive) prostate cancer patients and their controls.     

On the Estimation of Integrated Volatility With Jumps and Microstructure Noise

In this article, we propose a nonparametric procedure to estimate the integrated volatility of an Itô semimartingale in the presence of jumps and microstructure noise. The estimator is based on a combination of the preaveraging method and threshold technique, which serves to remove microstructure noise and jumps, respectively. The estimator is shown to work for both finite and infinite activity jumps. Furthermore, asymptotic properties of the proposed estimator, such as consistency and a central limit theorem, are established. Simulations results are given to evaluate the performance of the proposed method in comparison with other alternative methods.     

基于宏观经济结构视角下的我国碳交易和碳金融关系研究

碳交易不仅是一个经济问题,它同时还是一个政治问题。因此,考察碳交易和碳金融不仅要从动态的角度来进行,更要从战略资源、战略商品的高度来看待碳交易。文章在明晰碳交易相关概念的基础上,首先对碳交易秩序进行分析,然后把碳金融放在宏观经济结构的背景下,而非仅仅对碳交易提供金融服务的背景下,对碳交易和现代金融业进行阐述,从而找到现代金融业和碳交易之间的框架结构以及应采取的措施。总体而言,应在保护碳排放权的产权利益的基础上,以全国集中的碳交易所为中心,引导银行、证券、基金、保险、信托等各方面金融机构,依据市场信号自行设计符合碳交易市场的金融产品。     

择一定理与二层多目标规划的最优性条件

使用关于集值映射的择一定理,在锥一次类凸背景下,对二层多目标规划的最优性条件进行讨论,获得了几个必要条件和充分条件。