Bootstrap confidence regions computed from autoregressions of arbitrary order

Given a linear time series, e.g. an autoregression of infinite order, we may construct a finite order approximation and use that as the basis for confidence regions. The sieve or autoregressive bootstrap, as this method is often called, is generally seen as a competitor with the better-understood block bootstrap approach. However, in the present paper we argue that, for linear time series, the sieve bootstrap has significantly better performance than blocking methods and offers a wider range of opportunities. In particular, since it does not corrupt second-order properties then it may be used in a double-bootstrap form, with the second bootstrap application being employed to calibrate a basic percentile method confidence interval. This approach confers second-order accuracy without the need to estimate variance. That offers substantial benefits, since variances of statistics based on time series can be difficult to estimate reliably, and—partly because of the relatively small amount of information contained in a dependent process—are notorious for causing problems when used to Studentize. Other advantages of the sieve bootstrap include considerably greater robustness against variations in the choice of the tuning parameter, here equal to the autoregressive order, and the fact that, in contradistinction to the case of the block bootstrap, the percentile t version of the sieve bootstrap may be based on the 'raw' estimator of standard error. In the process of establishing these properties we show that the sieve bootstrap is second order correct.     

Importance of interpolation when constructing double-bootstrap confidence intervals

We show that, in the context of double-bootstrap confidence intervals, linear interpolation at the second level of the double bootstrap can reduce the simulation error component of coverage error by an order of magnitude. Intervals that are indistinguishable in terms of coverage error with theoretical, infinite simulation, double-bootstrap confidence intervals may be obtained at substantially less computational expense than by using the standard Monte Carlo approximation method. The intervals retain the simplicity of uniform bootstrap sampling and require no special analysis or computational techniques. Interpolation at the first level of the double bootstrap is shown to have a relatively minor effect on the simulation error.     

激光反射式光电水位测量仪

本文介绍一种以激光作为测量光源,利用光敏电阻随光线强弱变化而阻值随之变化的特性,控制或门电路工作,并在数字电压表上显示水面高度的测量仪。     

基于灰色关联度的小样本预测模型

针对传统灰色预测模型无法处理以及难以寻找统计规律的小样本数据,通过对序列之间灰色关联度物理含义的分析,挖掘序列内部以及序列之间的数据变化规律,并在此基础上构建了一种新的灰色预测模型;应用该模型对中国2008年度的GDP进行预测,预测结果验证了该模型的有效性及实用性;该模型的提出为小样本数据提供了一种新的预测方法。     

基于核和灰度的双重异构数据序列预测建模方法研究

通过建立灰色异构数据"核"序列的DGM(1,1)模型,实现双重异构数据"核"的预测;以"核"为基础、以双重异构数据序列中较大的区间灰数信息域作为预测结果的信息域,构建基于区间灰数与实数的双重异构数据序列灰色预测模型,有效地将灰色预测模型建模对象从"同质数据"拓展至"双重异构数据"。研究成果对丰富灰色预测模型理论体系具有积极意义。     

Non-ergodic martingale estimating functions and related asymptotics

Well-known estimation methods such as conditional least squares, quasilikelihood and maximum likelihood (ML) can be unified via a single framework of martingale estimating functions (MEFs). Asymptotic distributions of estimates for ergodic processes use constant norm (e.g. square root of the sample size) for asymptotic normality. For certain non-ergodic-type applications, however, such as explosive autoregression and super-critical branching processes, one needs a random norm in order to get normal limit distributions. In this paper, we are concerned with non-ergodic processes and investigate limit distributions for a broad class of MEFs. Asymptotic optimality (within a certain class of non-ergodic MEFs) of the ML estimate is deduced via establishing a convolution theorem using a random norm. Applications to non-ergodic autoregressive processes, generalized autoregressive conditional heteroscedastic-type processes, and super-critical branching processes are discussed. Asymptotic optimality in terms of the maximum random limiting power regarding large sample tests is briefly discussed.     

Detection and Interpretation of a Multivariate Signal Using Combined Charts

A control procedure is presented in this article that is based on jointly using two separate control statistics in the detection and interpretation of signals in a multivariate normal process. The procedure detects the following three situations: (i) a mean vector shift without a shift in the covariance matrix; (ii) a shift in process variation (covariance matrix) without a mean vector shift; and (iii) both a simultaneous shift in the mean vector and covariance matrix as the result of a change in the parameters of some key process variables. It is shown that, following the occurrence of a signal on either of the separate control charts, the values from both of the corresponding signaling statistics can be decomposed into interpretable elements. Viewing the two decompositions together helps one to specifically identify the individual components and associated variables that are being affected. These components may include individual means or variances of the process variables as well as the correlations between or among variables. An industrial data set is used to illustrate the procedure.     

Testing non-nested log-linear models with pseudo estimator

As the number of random variables for the categorical data increases, the possible number of log-linear models which can be fitted to the data increases rapidly, so that various model selection methods are developed. However, we often found that some models chosen by different selection criteria do not coincide. In this paper, we propose a comparison method to test the final models which are non-nested. The statistic of Cox (1961, 1962) is applied to log-linear models for testing non-nested models, and the Kullback-Leibler measure of closeness (Pesaran 1987) is explored. In log-linear models, pseudo estimators for the expectation and the variance of Cox's statistic are not only derived but also shown to be consistent estimators.     

Improved deviance goodness of fit statistics for a gamma regression model

A gamma regression model with an exponential link function for the means Is considered. Moment properties of the deviance statistics based on maximum likelihood and weighted least squares fits are used to define modified deviance statistics which provide alternative global goodness of fit tests. The null distribution properties of the deviances and modified deviances are compared with those of the approximating chi-square distribution and It is shown that the use of the modified deviances gives much better control over the significance levels of the tests.     

On the robustness of the extreme deviate test for a single multivariate outlier against heavy-tailed distributions

In this paper we assess the sensitivity of the multivariate extreme deviate test for a single multivariate outlier to non-normality in the form of heavy tails. We find that the empirical significance levels can be markedly affected by even modest departures from multivariate normality. The effects are particularly severe when the sample size is large relative to the dimension. Finally, by way of example we demonstrate that certain graphical techniques may prove useful in identifying the source of rejection for the multivariate extreme deviate test.