ADF模式中漂移项和趋势项检验量分布与Bootstrap检验研究

在推导ADF检验模式下趋势项和漂移项伪t检验量极限分布基础上,提出修正的系数检验量。研究表明,它们与DF检验模式下检验量具有相同的极限分布;构造漂移项和趋势项检验的Bootstrap实现方法并证明了有效性。将蒙特卡洛模拟技术与临界值检验方法进行对比,结果表明Bootstrap方法能够明显降低检验的水平扭曲,在检验功效方面也有一定优势。模拟也显示临界值检验的局限性和Bootstrap方法的稳健性。     

空间面板杜宾模型的Bootstrap Wald-COMFAC检验研究

将共同因子约束(COMFAC)的Wald检验问题引入到空间面板模型中,讨论空间面板杜宾模型与空间面板误差模型的识别问题。蒙特卡洛模拟表明:在有限样本下,基于渐近临界值的Wald检验有着良好的检验功效,但存在着较为严重的尺度扭曲。进一步采用残差Bootstrap方法,在不损失检验功效的前提下,能够显著地降低检验的尺度扭曲。因此,残差Bootstrap方法是更为有效的检验方法。     

线性回归模型Bootstrap LM-Lag检验有效性研究

基于OLS估计残差,将Bootstrap方法用于空间滞后相关LM-Lag检验。在不同的误差结构和空间权重矩阵条件下,比较Bootstrap LM-Lag检验和渐近检验的水平扭曲和功效。通过Monte Carlo实验表明,当误差项不服从经典正态分布假设时,LM-Lag渐近检验存在严重的水平扭曲,Bootstrap检验能够有效地校正水平扭曲,并且Bootstrap LM-Lag检验的功效与渐近检验近似;无论误差项是否服从正态分布,从水平扭曲和功效角度看,线性回归模型Bootstrap LM-Lag检验有效。     

局部线性趋势模型单位根检验量分布与Bootstrap检验

本文引入局部趋势概念,研究数据生成和检验式都含有趋势单位根过程中伪t检验量的分布,结果表明该分布为标准正态分布与第四种DF分布的混合体,并揭示了向这两类分布转化的条件.为摆脱伪t检验量受到特定参数约束而不能用于实证分析的困境,本文提出了Bootstrap检验方法,并从理论上证明该方法可用于水平检验和功效研究,埃奇沃思展开进一步证实该方法能够降低水平扭曲.蒙特卡洛模拟结果显示,Bootstrap检验量具有最高检验正确率,检验功效在一定条件下也能与标准正态分布的检验结果相媲美,说明Bootstrap方法可以用于此类模型的单位根检验.     

空间误差分量模型的Bootstrap LM检验

空间误差分量模型(Spatial Error Components,SEC)传统的空间相关性LM检验存在严重的水平扭曲和较低的检验功效,导致检验统计量失效.文章将Bootstrap方法应用于SEC模型的空间相关性LM检验,提高检验统计量的有效性.Monte Carlo模拟实验表明,Bootstrap LM检验的水平受误差项分布、空间权重矩阵和样本量影响较小,并且远优于渐近LM检验,具有理想的检验水平;渐近LM检验和Bootstrap LM检验的功效均随着空间相关性的增强,及样本量的增大而增大,但Bootstrap LM检验在各种情形下均具有更高的检验功效,尤其是样本量较小时.简言之,Bootstrap LM检验是SEC模型更为优越的空间相关性检验方法.     

概化理论方差分量置信区间估计Bootstrap方法比较

使用Monte Carlo模拟技术生成多项分布数据,比较四种Bootstrap方法估计概化理论方差分量置信区间的性能,四种Bootstrap方法分别是Bootstrap-PC、Bootstrap-t、Bootstrap-BCa和Bootstrap-ABC方法.结果表明:(1)从整体上看,四种Bootstrap方法估计方差分量置信区间的包含率,校正的Bootstrap方法要优于未校正的Bootstrap方法;(2)校正的Bootstrap-PC和Bootstrap-t方法相当,校正的Bootstrap-BCa与Bootstrap-ABC方法相当,校正的Bootstrap-BCa和Bootstrap-ABC方法要优于校正的Bootstrap-PC和Bootstrap-t方法.     

空间经济计量滞后模型Bootstrap Moran检验功效的模拟分析

 当误差项不服从独立同分布时,利用Moran’s I统计量的渐近检验,无法有效判断空间经济计量滞后模型2SLS估计残差间存在空间关系与否。本文采用两种基于残差的Bootstrap方法,诊断空间经济计量滞后模型残差中的空间相关关系。大量Monte Carlo模拟结果显示,从功效角度看,无论误差项服从独立同分布与否,与渐近检验相比,Bootstrap Moran检验都具有更好的有限样本性质,能够更有效地进行空间相关性检验。尤其是,在样本量较小和空间衔接密度较高情况下,Bootstrap Moran检验的功效显著大于渐近检验。     

Bootstrap平均数假设检验样本容量探讨

Bootstrap方法是一种有放回的再抽样方法,可用于平均数假设检验的估计.采用蒙特卡洛数据模拟技术,模拟正态分布数据.设计研究程序,探讨在不同的样本量和再抽样次数不同情况下,Bootstrap方法在平均数假设检验中应用,所适宜的样本容量,将一类错误率作为对比条件.结果表明,跨越三种比较条件,只有当样本量大于等于5且模拟次数大于等于1000次时,才能得到满足条件的一类错误率,即表明使用Bootstrap方法才会取得较好的效果.     

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。     

基于K-S统计量的两个一维及多维总体相等性的Bootstrap检验

Prastgaard(1995)讨论了用Kolmogorov-Smimov统计量T1及相应的Bootstrap统计量T1来检验两总体的相等性.文章提出基于K-S统计量的新的统计量T2及相应的Bootstrap统计量T2,分别在一维及多维的情形下证明了它们在原假设下有相同的极限分布进行了大量的数值模拟,验证了上述统计量的正确性及优劣,给出了模拟的结果,并对此做了对比与分析.     

基于贝叶斯的Bootstrap置信区间

在许多领域中,Bootstrap成为一种数据处理的有效方法。很多情况下,模型中感兴趣的参数的置信区间难以构建,为了解决这一问题,文章提出了一个新的贝叶斯Bootstrap置信区间的估计量,并做了蒙特卡洛模拟比较,结果比经典区间估计方法和经典Bootstrap方法更优,并进行了实例分析。     

Bootstrap方法在证券投资基金风险测量中的应用

 Bootstrap method will largely improve the accuracy of risk measurement, which be used to calculate the value at risk of securities investment funds. The application of the Bootstrap method with GARCH-based risk measurement model, not only consider the fund’s data auto-correlation and the time-variable variance characteristic, but also very well simulate the distribution of the residual. The theoretical analysis and empirical analysis indicate that this flexible parameter-nonparametric mixed risk measurement model can improve estimation precision of VAR.     

Bootstrap confidence interval estimates of cpk: an introduction

The interpretation of C_pk:, a common measure of process capability and confidence limits for it, is based on the assumption that the process is normally distributed. The non-parametric but computer intensive method called Bootstrap is introduced and three Bootstrap confidence interval estimates for C^ are defined. An initial simulation of two processes (one normal and the other highly skewed) is presented and discussed     

Some blum-kiefer-rosenblatt type tests for the joint independence of variables

Testing the joint independence of variables has long been an interesting issue in statistical inferences. Blum, Kiefer and Rosenblatt (1961) suggested a test based on a sample distribution function. To overcome the sparseness of data points in high-dimensional space and deal with general cases, we in this paper suggest several extended versions of B-K-R tests via projection pursuit. Bootstrap method is applied to determine the critical values and for computational reason, an approximation derived by Number-theoretic method, for the bootstrap statistics is suggested. Several simulation experiments are performed and a real-life example is investigated.     

A new way of quantifying the symmetry of a random variable: Estimation and hypothesis testing

New measures of skewness for real-valued random variables are proposed. The measures are based on a functional representation of real-valued random variables. Specifically, the expected value of the transformed random variable can be used to characterize the distribution of the original variable. Firstly, estimators of the proposed skewness measures are analyzed. Secondly, asymptotic tests for symmetry are developed. The tests are consistent for both discrete and continuous distributions. Bootstrap versions improving the empirical results for moderated and small samples are provided. Some simulations illustrate the performance of the tests in comparison to other methods. The results show that our procedures are competitive and have some practical advantages.     

A Comparative Study of Model-based Tests of Independence for Ordinal Data Using the Bootstrap

When analyzing categorical data using loglinear models in sparse contingency tables, asymptotic results may fail. In this paper the empirical properties of three commonly used asymptotic tests of independence, based on the uniform association model for ordinal data, are investigated by means of Monte Carlo simulation. Five different bootstrapped tests of independence are presented and compared to the asymptotic tests. The comparisons are made with respect to both size and power properties of the tests. Results indicate that the asymptotic tests have poor size control. The test based on the estimated association parameter is severely conservative and the two chi-squared tests (Pearson, likelihood-ratio) are both liberal. The bootstrap tests that either use a parametric assumption or are based on non-pivotal test statistics do not perform better than the asymptotic tests in all situations. The bootstrap tests that are based on approximately pivotal statistics provide both adjustment of size and enhancement of power. These tests are therefore recommended for use in situations similar to those included in the simulation study.     

Bootstrap—An exploration

We review a few unusual aspects of Bootstrap and some of the recent theoretical as well as methodological advances. We discuss the handling of non-linearity by Bootstrap through a numerical example in Section  2. Application to the estimation of high-dimensional inverse covariance matrix is presented in Section  3 with emphasis on the Augmented Bootstrap and a Bayesian version of it. Another high dimensional example, namely, Random Forest and its offshoot random survival forest (Ishwaran et al. (2008)  [32]) are discussed in Section  4. Bootstrap for massive data, introduced by Kleiner et al. (2011) [35], is discussed in Section  4. In Section  5, we discuss some aspects of Bootstrap in the context of hypothesis testing in high-dimension.     

SADDLEPOINT METHODS FOR BOOTSTRAP CONFIDENCE BANDS IN NONPARAMETRIC REGRESSION

Bootstrap techniques have been used to construct confidence bands in nonparametric regression problems (Härdle & Bowman, 1988). Yet the required simulation is generally computationally intensive and therefore makes it difficult to conduct further investigations. In this paper, two saddlepoint methods are considered as alternatives to the naive simulation procedure. Some improvements to Härdle & Bowman's bootstrap method are suggested. The improvements are numerically verified using these efficient and accurate analytic methods.