On the Principal Component Liu-type Estimator in Linear Regression

In this article, we present a principal component Liu-type estimator (LTE) by combining the principal component regression (PCR) and LTE to deal with the multicollinearity problem. The superiority of the new estimator over the PCR estimator, the ordinary least squares estimator (OLSE) and the LTE are studied under the mean squared error matrix. The selection of the tuning parameter in the proposed estimator is also discussed. Finally, a numerical example is given to explain our theoretical results.     

Confidence intervals for extreme Pareto-type quantiles

In this paper, we revisit the construction of confidence intervals for extreme quantiles of Pareto-type distributions. A novel asymptotic pivotal quantity is proposed for these quantile estimators, which leads to new asymptotic confidence intervals that exhibit more accurate coverage probability. This pivotal quantity also allows for the construction of a saddle-point approximation, from which a second set of new confidence intervals follows. The small-sample properties and utility of these confidence intervals are studied using simulations and a case study from insurance.     

Regression models with ordered multiple categorical predictors

Ordered multiple categorical (MC) variable has been widely considered and studied as response variable, and few studies have carefully considered it as a predictor in linear regression. When doing this, the existence of some pseudo-categories may result in overfitting, and to detect those pseudo-categories by hypothesis test of all dummy variables might have low specificity. In this paper, we propose a transformation method of dummy variables for such ordered MC predictors, after which a model selection method combined with BIC will be elaborated. Theoretical consistency of our model selection method is established under some common assumptions. Both simulation studies and real data analysis of a medical survey indicate that our method provides good performance and is applicable to a wide range of biomedical research.     

合作社提高了种植户的增收能力吗？——来自陕西省600户苹果种植户的经验证据

依据组织参与程度将种植户分为非社员、普通社员和标准化社员三类,利用600份苹果种植户调研数据,采用偏最小二乘回归法分别从整体和群组视角分析了苹果生产经营行为对种植户增收能力的影响。结果表明：种植户的生产经营行为会对其增收能力产生影响,这种影响在三种类型种植户间存在显著差异;果园管理、农资采购、技术获取、品质管理和销售管理行为选择是影响种植户增收的关键因素;果园管理对非社员增收能力有显著负向影响,对其他两类种植户的影响不显著;技术获取对三种类型的种植户增收能力均有显著正向影响;农资采购、品质管理、销售管理对普通社员和标准化社员增收能力有显著正向影响,对非社员的影响不显著。因此,政府在政策的制定中,应充分考虑到异质农户的现状和实际需求。     

End‐of‐Sample Instability Tests

This paper considers tests for structural instability of short duration, such as at the end of the sample. The key feature of the testing problem is that the number, m, of observations in the period of potential change is relatively small—possibly as small as one. The well‐known F test of Chow (1960) for this problem only applies in a linear regression model with normally distributed iid errors and strictly exogenous regressors, even when the total number of observations, n+m, is large. We generalize the F test to cover regression models with much more general error processes, regressors that are not strictly exogenous, and estimation by instrumental variables as well as least squares. In addition, we extend the F test to nonlinear models estimated by generalized method of moments and maximum likelihood. Asymptotic critical values that are valid as n→∞ with m fixed are provided using a subsampling‐like method. The results apply quite generally to processes that are strictly stationary and ergodic under the null hypothesis of no structural instability.     

Model selection using information criteria under a new estimation method: least squares ratio

In this study, we evaluate several forms of both Akaike-type and Information Complexity (ICOMP)-type information criteria, in the context of selecting an optimal subset least squares ratio (LSR) regression model. Our simulation studies are designed to mimic many characteristics present in real data – heavy tails, multicollinearity, redundant variables, and completely unnecessary variables. Our findings are that LSR in conjunction with one of the ICOMP criteria is very good at selecting the true model. Finally, we apply these methods to the familiar body fat data set.     

基于ARCH-Expectile方法的VaR和ES尾部风险测量

甄别和确定风险因素的贡献是资产或资产组合风险管理的重要研究内容。近十年,下端风险越来越受到关注,在险价值（Value at Risk,VaR）和预期不足（Expected Shortfall,ES）是资产组合风险管理中两个常用的风险度量工具。Kuan等^[1]在一类条件自回归模型（CARE）下提出了基于expectile的VaR度量-EVaR。本文扩展了Kuan等^[2]的CARE模型到带有异方差的数据,引入ARCH效应提出了一个线性ARCH-Expectile模型,旨在确定资产或资产组合的风险来源以及评估各风险因素的贡献大小,并应用expectile间接评估VaR和ES风险大小。同时给出了参数的两步估计算法,并建立了参数估计的大样本理论。最后,将本文所提出的方法应用于民生银行股票损益的风险分析,从公司基本面、市场流动性和宏观层面三个方面选取影响股票损益的风险因素,分析结果表明,各风险因素随股票极端损失大小的水平不同,其风险因素的来源及其大小和方向也是随之变化的。     

The relative efficiency of the restricted estimators in linear regression models

This paper deals with the problem of multicollinearity in a multiple linear regression model with linear equality restrictions. The restricted two parameter estimator which was proposed in case of multicollinearity satisfies the restrictions. The performance of the restricted two parameter estimator over the restricted least squares (RLS) estimator and the ordinary least squares (OLS) estimator is examined under the mean square error (MSE) matrix criterion when the restrictions are correct and not correct. The necessary and sufficient conditions for the restricted ridge regression, restricted Liu and restricted shrunken estimators, which are the special cases of the restricted two parameter estimator, to have a smaller MSE matrix than the RLS and the OLS estimators are derived when the restrictions hold true and do not hold true. Theoretical results are illustrated with numerical examples based on Webster, Gunst and Mason data and Gorman and Toman data. We conduct a final demonstration of the performance of the estimators by running a Monte Carlo simulation which shows that when the variance of the error term and the correlation between the explanatory variables are large, the restricted two parameter estimator performs better than the RLS estimator and the OLS estimator under the configurations examined.     

Forecasting with serially correlated regression models

In this article we investigate the asymptotic and finite-sample properties of predictors of regression models with autocorrelated errors. We prove new theorems associated with the predictive efficiency of generalized least squares (GLS) and incorrectly structured GLS predictors. We also establish the form associated with their predictive mean squared errors as well as the magnitude of these errors relative to each other and to those generated from the ordinary least squares (OLS) predictor. A large simulation study is used to evaluate the finite-sample performance of forecasts generated from models using different corrections for the serial correlation.