放回抽样下HT估计量的性质及应用

放回抽样下传统的估计方法是采用Hansen-Hurwitz估计。而放回抽样下HH估计量并不是一致最小方差无偏估计,本文提出了另一种估计方法,即采用Horvitz-Thompson估计,并论证了放回抽样下HT估计量的三条定理,及与HH估计量的比较。然后以放回简单随机抽样和PPS抽样为例,通过理论公式、计算机模拟以及具体案例,进行更具体的分析。说明在一定条件下,HT估计量相对更优。在实际应用中,本文也提出了通过比较方差估计作为选取估计量的准则。     

随机效应空间滞后单指数面板模型

对随机效应空间滞后单指数面板模型,本文构建了该模型的截面极大似然估计方法,从理论证明和数值模拟两方面分别考察了其估计量的大样本性质和小样本表现。研究结果表明:(1)在大样本条件下,估计量均具有一致性,并且参数估计量具有渐近正态性。(2)在小样本条件下,各估计量依然具有良好的表现,其精度随着样本容量的增加而提高;空间权重矩阵结构的复杂性对空间相关系数的估计量影响较大,但对其他估计量的影响较小。     

混合类型辅助变量下模型校准抽样估计研究

在超总体模型中,一般用于构建模型的辅助变量多为连续型变量,对混合类型辅助变量的模型研究较少.为了同时利用与研究变量相关的连续型和离散型辅助变量的信息,本文提出在模型校准的框架下,利用非参数核回归方法,得到混合类型辅助变量下的模型校准估计量.研究证明,该估计量是渐进设计无偏、设计一致和渐进正态的,并给出了估计量的方差和方差的估计量.数值模拟的结果显示,本文在总体回归函数为线性和非线性的情况下,估计效果均有所提高.此外,通过CLHLS数据的验证也表明该估计量的效果优于仅利用连续型辅助变量的估计量.     

随机效应广义空间滞后半参数变系数面板模型的估计

通过构建同时包含因变量和误差项空间滞后的随机效应半参数变系数面板模型,拓展了现有模型的灵活性和适应性。采用截面极大似然估计方法得出了参数和非参数的估计,理论证明发现：在一定的正则条件下,所有估计量具有一致性和渐近正态性。数值模拟显示：估计量具有良好的小样本性质,估计精度随着样本容量的增加而增加;空间权重矩阵的选择对估计量的表现没有产生显著差异,但是在Case权重矩阵下,当样本量相同时,空间相关系数的估计偏差随着空间权重结构复杂度的增加而扩大。     

双因素效应的动态二值logit模型的参数估计及应用

文章考虑了带有个体效应和时间效应的双因素面板数据动态二值logit模型，在周期T固定的条件下，提出了一种新的方法估计模型参数。从理论层面指出了该估计量满足一致性和渐近正态性；数值模拟研究了估计量的小样本性质，模拟结果表明，该估计方法在有限样本下具有良好的统计性质。最后，将该方法应用于洗涤剂的购买数据进行实证分析。     

随机效应变系数空间自回归面板模型的估计

具有良好可读性和稳健性的变系数模型在各学科领域应用广泛.本文构建了一种新的随机效应变系数空间自回归面板模型,运用截面极大似然估计方法,导出了模型的估计量,证明其具备一致性和渐近正态性,蒙特卡洛模拟研究显示估计量的小样本表现效果良好.     

线性回归模型在因变量缺失下的约束估计

文章主要研究了线性回归模型在因变量缺失下的约束估计,基于完整数据方法和单点插补方法,我们给出了模型系数的两种约束估计,并研究了估计量的渐近正态性.最后,我们通过数值模拟验证了所提方法的有效性.     

缺失数据下的逆概率多重加权分位回归估计及其应用

数据缺失问题普遍存在于应用研究中。在随机缺失机制假定下,本文从模型推断角度出发,针对线性缺失分位回归模型,提出一种新的有效估计方法——逆概率多重加权（IPMW）估计。该方法是在逆概率加权（IPW）估计的基础上,结合倾向得分匹配及模型平均思想,经过多次估计,加权确定最终参数估计结果。该方法适用于响应变量是独立同分布或独立非同分布的情形,并适用于绝大多数缺失场景。经过理论推导及模拟研究发现,IPMW估计量在继承IPW估计量的优势上具有更稳健的性质。最后,将该方法应用于含有缺失数据的微观调查数据中,研究了经济较发达的准一线城市中等收入群体消费水平的影响因素,对比两种估计方法的估计结果及置信带,发现逆概率多重加权估计量的标准偏差更小,估计结果更稳健。     

样本选择模型的一个简单半参数估计量

本文发展了一个针对样本选择模型的两阶段半参数估计量,其首先在第一阶段基于对数欧几里得分布差异测度估计离散选择概率,进而在第二阶段利用非参数sieve方法估计一个包含参数和非参数部分的部分线性模型以得到模型参数的估计。相对于文献中已有的半参数估计量,该估计量的计算更加简便,且计算负担相对较小。我们说明了该半参数估计量的一致性和渐近正态性,同时给出了其渐近方差的计算公式。蒙特卡洛模拟结果符合我们的理论结论。     

非线性GARCH族的模型平均估计方法

本文考虑了非线性GARCH族的模型平均估计方法。在备选模型集合包含拥有不同模型结构的非线性GARCH族的情况下,本文构建了非线性GARCH族的模型平均估计量,并给出相应的权重选择准则。在一定正则条件下,本文证明上述模型平均估计量具有渐近最优性,即渐近实现真实最优的KL偏离度。蒙特卡洛模拟结果表明,在大部分情形下,本文提出的模型平均估计量取得了更小的相对KL偏离值。作为非线性GARCH族的模型平均估计方法的应用,本文对2016年6月1日至2017年6月1日上证指数的日波动率进行估计,与现有模型选择与模型平均方法相比较,本文模型平均估计方法具有更高的精度。     

Local Box–Cox transformation on time-varying parametric models for smoothing estimation of conditional CDF with longitudinal data

Nonparametric estimation and inferences of conditional distribution functions with longitudinal data have important applications in biomedical studies, such as epidemiological studies and longitudinal clinical trials. Estimation approaches without any structural assumptions may lead to inadequate and numerically unstable estimators in practice. We propose in this paper a nonparametric approach based on time-varying parametric models for estimating the conditional distribution functions with a longitudinal sample. Our model assumes that the conditional distribution of the outcome variable at each given time point can be approximated by a parametric model after local Box–Cox transformation. Our estimation is based on a two-step smoothing method, in which we first obtain the raw estimators of the conditional distribution functions at a set of disjoint time points, and then compute the final estimators at any time by smoothing the raw estimators. Applications of our two-step estimation method have been demonstrated through a large epidemiological study of childhood growth and blood pressure. Finite sample properties of our procedures are investigated through a simulation study. Application and simulation results show that smoothing estimation from time-variant parametric models outperforms the existing kernel smoothing estimator by producing narrower pointwise bootstrap confidence band and smaller root mean squared error.     

带线性约束的多元线性回归模型参数估计

本文首先构造线性约束条件下的多元线性回归模型的样本似然函数,利用Lagrange法证明其合理性。其次,从似然函数的角度讨论线性约束条件对模型参数的影响,对由传统理论得出的参数估计作出贝叶斯与经验贝叶斯的改进。做贝叶斯改进时,将矩阵正态-Wishart分布作为模型参数和精度阵的联合共轭先验分布,结合构造的似然函数得出参数的后验分布,计算出参数的贝叶斯估计;做经验贝叶斯改进时,将样本分组,从方差的角度讨论由子样得出的参数估计对总样本的参数估计的影响,计算出经验贝叶斯估计。最后,利用Matlab软件生成的随机矩阵做模拟。结果表明,这两种改进后的参数估计均较由传统理论得出的参数估计更精确,拟合结果的误差比更小,可信度更高,在大数据的情况下,这种计算方法的速度更快。     

t-Type corrected-loss estimation for error-in-variable model

In this article, we consider a linear model in which the covariates are measured with errors. We propose a t-type corrected-loss estimation of the covariate effect, when the measurement error follows the Laplace distribution. The proposed estimator is asymptotically normal. In practical studies, some outliers that diminish the robustness of the estimation occur. Simulation studies show that the estimators are resistant to vertical outliers and an application of 6-minute walk test is presented to show that the proposed method performs well.     

动态面板空间随机前沿模型的参数估计及应用

生产效率一般会受到空间相关性和时间滞后效应的影响,不易准确测算。本文考虑时空双重滞后特征,提出一种动态面板数据空间随机前沿模型,针对模型的内生性问题,借鉴已有的估计方法,本文提出一种广义矩估计方法（Generalized Method of Moments,GMM）,并证明了参数估计的一致性。在应用分析中,利用本文所提出的理论模型实证分析了我国战略性新兴产业发展的效率,该理论模型能够客观、科学地测算技术效率,实证结论验证了理论模型的应用效果。     

General purpose multiply robust data integration procedures for handling nonprobability samples

In recent years, there has been an increased interest in combining probability and nonprobability samples. Nonprobability sample are cheaper and quicker to conduct but the resulting estimators are vulnerable to bias as the participation probabilities are unknown. To adjust for the potential bias, estimation procedures based on parametric or nonparametric models have been discussed in the literature. However, the validity of the resulting estimators relies heavily on the validity of the underlying models. Also, nonparametric approaches may suffer from the curse of dimensionality and poor efficiency. We propose a data integration approach by combining multiple outcome regression models and propensity score models. The proposed approach can be used for estimating general parameters including totals, means, distribution functions, and percentiles. The resulting estimators are multiply robust in the sense that they remain consistent if all but one model are misspecified. The asymptotic properties of point and variance estimators are established. The results from a simulation study show the benefits of the proposed method in terms of bias and efficiency. Finally, we apply the proposed method using data from the Korea National Health and Nutrition Examination Survey and data from the National Health Insurance Sharing Services.     

Estimation of semiparametric regression model with longitudinal data

In a longitudinal study, an individual is followed up over a period of time. Repeated measurements on the response and some time-dependent covariates are taken at a series of sampling times. The sampling times are often irregular and depend on covariates. In this paper, we propose a sampling adjusted procedure for the estimation of the proportional mean model without having to specify a sampling model. Unlike existing procedures, the proposed method is robust to model misspecification of the sampling times. Large sample properties are investigated for the estimators of both regression coefficients and the baseline function. We show that the proposed estimation procedure is more efficient than the existing procedures. Large sample confidence intervals for the baseline function are also constructed by perturbing the estimation equations. A simulation study is conducted to examine the finite sample properties of the proposed estimators and to compare with some of the existing procedures. The method is illustrated with a data set from a recurrent bladder cancer study.     

Quantile regression for competing risks analysis under case-cohort design

The case-cohort design brings cost reduction in large cohort studies. In this paper, we consider a nonlinear quantile regression model for censored competing risks under the case-cohort design. Two different estimation equations are constructed with or without the covariates information of other risks included, respectively. The large sample properties of the estimators are obtained. The asymptotic covariances are estimated by using a fast resampling method, which is useful to consider further inferences. The finite sample performance of the proposed estimators is assessed by simulation studies. Also a real example is used to demonstrate the application of the proposed methods.     

Robust Mean Estimation Under a Possibly Incorrect Log-Normality Assumption

Nonparametric and parametric estimators are combined to minimize the mean squared error among their linear combinations. The combined estimator is consistent and for large sample sizes has a smaller mean squared error than the nonparametric estimator when the parametric assumption is violated. If the parametric assumption holds, the combined estimator has a smaller MSE than the parametric estimator. Our simulation examples focus on mean estimation when data may follow a lognormal distribution, or can be a mixture with an exponential or a uniform distribution. Motivating examples illustrate possible application areas.