半参数变系数回归模型的空间相关性检验

对半参数变系数回归模型,构造了新的空间相关性检验统计量,利用三阶矩 逼近方法导出了其检验 值的近似计算公式,蒙特卡罗模拟结果表明该统计量在检测空间相关性方面具有较高的准确性和可靠性。同时考察了误差项服从不同分布时的检验功效,体现出该检验方法的稳健性。进一步,我们还给出了检验统计量的Bootstrap方法以及检验水平的模拟效果。     

基于Bootstrap-DEA方法的苹果种植户生产效率及其影响因素分析

采用384份苹果种植户调查数据,运用Bootstrap-DEA方法,测算苹果种植户生产效率;运用Probit概率模型,分析苹果种植户特征对苹果生产效率的影响。结果表明:苹果种植户生产效率普遍较低,提升的空间较大。基于当前的技术水平,果园主要管理者受教育程度、家庭果园劳动力数量、主要管理者年龄、果园主要管理者参加培训的次数、雇工投入特征对苹果生产效率具有显著正向影响,肥料投入、灌溉投入对苹果生产效率具有显著负向影响。     

An evaluation of the bootstrap for model validation in mixture models

Bootstrapping has been used as a diagnostic tool for validating model results for a wide array of statistical models. Here we evaluate the use of the non-parametric bootstrap for model validation in mixture models. We show that the bootstrap is problematic for validating the results of class enumeration and demonstrating the stability of parameter estimates in both finite mixture and regression mixture models. In only 44% of simulations did bootstrapping detect the correct number of classes in at least 90% of the bootstrap samples for a finite mixture model without any model violations. For regression mixture models and cases with violated model assumptions, the performance was even worse. Consequently, we cannot recommend the non-parametric bootstrap for validating mixture models.

The cause of the problem is that when resampling is used influential individual observations have a high likelihood of being sampled many times. The presence of multiple replications of even moderately extreme observations is shown to lead to additional latent classes being extracted. To verify that these replications cause the problems we show that leave-k-out cross-validation where sub-samples taken without replacement does not suffer from the same problem.     

Bootstrap estimation and model selection for multivariate normal mixtures using parallel computing with graphics processing units

In applications of multivariate finite mixture models, estimating the number of unknown components is often difficult. We propose a bootstrap information criterion, whereby we calculate the expected log-likelihood at maximum a posteriori estimates for model selection. Accurate estimation using the bootstrap requires a large number of bootstrap replicates. We accelerate this computation by employing parallel processing with graphics processing units (GPUs) on the Compute Unified Device Architecture (CUDA) platform. We conducted a runtime comparison of CUDA algorithms between implementation on the GPU and that on a CPU. The results showed significant performance gains in the proposed CUDA algorithms over multithread CPUs.     

Measuring Nonlinear Granger Causality in Mean

We propose model-free measures for Granger causality in mean between random variables. Unlike the existing measures, ours are able to detect and quantify nonlinear causal effects. The new measures are based on nonparametric regressions and defined as logarithmic functions of restricted and unrestricted mean square forecast errors. They are easily and consistently estimated by replacing the unknown mean square forecast errors by their nonparametric kernel estimates. We derive the asymptotic normality of nonparametric estimator of causality measures, which we use to build tests for their statistical significance. We establish the validity of smoothed local bootstrap that one can use in finite sample settings to perform statistical tests. Monte Carlo simulations reveal that the proposed test has good finite sample size and power properties for a variety of data-generating processes and different sample sizes. Finally, the empirical importance of measuring nonlinear causality in mean is also illustrated. We quantify the degree of nonlinear predictability of equity risk premium using variance risk premium. Our empirical results show that the variance risk premium is a very good predictor of risk premium at horizons less than 6 months. We also find that there is a high degree of predictability at the 1-month horizon, that can be attributed to a nonlinear causal effect. Supplementary materials for this article are available online.     

Bootstrap tests for time varying cointegration

This article proposes wild and the independent and identically distibuted (i.i.d.) parametric bootstrap implementations of the time-varying cointegration test of Bierens and Martins (2010 Bierens, H. J., Martins, L. F. (2010). Time varying cointegration. Econometric Theory 26:1453–1490.[Crossref], [Web of Science ®] , [Google Scholar]). The bootstrap statistics and the original likelihood ratio test share the same first-order asymptotic null distribution. Monte Carlo results suggest that the bootstrap approximation to the finite-sample distribution is very accurate, in particular for the wild bootstrap case. The tests are applied to study the purchasing power parity hypothesis for twelve Organisation for Economic Cooperation and Development (OECD) countries and we only find evidence of a constant long-term equilibrium for the U.S.–U.K. relationship.     

Bootstrap Determination of the Co‐Integration Rank in Vector Autoregressive Models

This paper discusses a consistent bootstrap implementation of the likelihood ratio (LR) co‐integration rank test and associated sequential rank determination procedure of Johansen (1996). The bootstrap samples are constructed using the restricted parameter estimates of the underlying vector autoregressive (VAR) model that obtain under the reduced rank null hypothesis. A full asymptotic theory is provided that shows that, unlike the bootstrap procedure in Swensen (2006) where a combination of unrestricted and restricted estimates from the VAR model is used, the resulting bootstrap data are I(1) and satisfy the null co‐integration rank, regardless of the true rank. This ensures that the bootstrap LR test is asymptotically correctly sized and that the probability that the bootstrap sequential procedure selects a rank smaller than the true rank converges to zero. Monte Carlo evidence suggests that our bootstrap procedures work very well in practice.     

Quantile Regression Methods for Longitudinal Data with Drop-outs: Application to CD4 Cell Counts of Patients Infected with the Human Immunodeficiency Virus

Patients infected with the human immunodeficiency virus (HIV) generally experience a decline in their CD4 cell count (a count of certain white blood cells). We describe the use of quantile regression methods to analyse longitudinal data on CD4 cell counts from 1300 patients who participated in clinical trials that compared two therapeutic treatments: zidovudine and didanosine. It is of scientific interest to determine any treatment differences in the CD4 cell counts over a short treatment period. However, the analysis of the CD4 data is complicated by drop-outs: patients with lower CD4 cell counts at the base-line appear more likely to drop out at later measurement occasions. Motivated by this example, we describe the use of `weighted' estimating equations in quantile regression models for longitudinal data with drop-outs. In particular, the conventional estimating equations for the quantile regression parameters are weighted inversely proportionally to the probability of drop-out. This approach requires the process generating the missing data to be estimable but makes no assumptions about the distribution of the responses other than those imposed by the quantile regression model. This method yields consistent estimates of the quantile regression parameters provided that the model for drop-out has been correctly specified. The methodology proposed is applied to the CD4 cell count data and the results are compared with those obtained from an `unweighted' analysis. These results demonstrate how an analysis that fails to account for drop-outs can mislead.     

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.