纵向部分线性变系数EV模型的估计

纵向数据是随着时间变化对个体进行重复观测而得到的一种相关性数据，广泛出现在诸多科学研究领域。在对个体进行观测时，测量误差不可避免，忽略测量误差往往会导致有偏估计。本文利用二次推断函数方法研究关于纵向数据的参数部分和非参数部分协变量均含有测量误差的部分线性变系数测量误差(errors-in-variables, EV)模型的估计问题。利用B样条逼近模型中的未知系数函数，构造关于回归参数和B样条系数的偏差修正的二次推断函数以处理个体内相关性和测量误差，得到回归参数和变系数的偏差修正的二次推断函数估计，然后证明了估计方法和结果的渐近性质。数值模拟和实例数据分析结果显示本文提出的方法具有一定的实用价值。

Estimation for Longitudinal Partial Linear Varying CoefficientEV Models

Longitudinal data is a kind of correlated data for repeated observation of individuals over time, which is widely used in many scientific research fields. When observing individuals, measurement error is inevitable. Ignoring measurement errors may lead to biased estimation. This paper considers the estimation of the partial linear varying coefficient errors-in-variables (EV) models with longitudinal data using the quadratic inference functions method. We approximate the unknown varying coefficient by B-spline approximations, construct bias-corrected quadratic inference functions about the regression parameter and coefficients of splines to deal with the within-subject correlation and measurement error, get the bias-corrected quadratic inference functions estimation of the regression parameter and varying coefficients, then prove the asymptotic properties of the proposed method and result. Numerical simulation and real data analysis results show that the proposed method has some practical value.