| 摘要: |
| 针对响应变量随机缺失且解释变量带有测量误差的部分函数型线性回归模型，讨论了模型中未知参数和未知系数函数的估计问题及其渐近性质；先通过一定方法对缺失数据和带有测量误差的数据进行处理，然后将模型转化为一般的函数型线性回归模型，再利用Karhumen Loevez展开和主成分分析法给出模型的经验形式，最后运用经典的多元统计分析极小化目标函数得到相应未知量的最小二乘估计，并在一定的条件下给出了参数估计量的渐近正态性和斜率函数估计量的收敛速度；从而说明给出的估计量是有效估计，完全观测下的函数型数据统计推断方法可以被推广到不完全观测的情形。 |
| 关键词: 函数型数据 测量误差 K-L展开 响应缺失 |
| DOI： |
| 分类号: |
| 基金项目: |
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| Statistical Inference of Partial Function EV Regression Model with Missing Response |
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FANG Lian-di1,2
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1.School of Mathematics and Computer Science, Tongling University,Anhui Tongling 244000, China;2.School of Electrical and Information Engineering,Jiangsu University,Jiangsu Zhenjiang 212013,China
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| Abstract: |
| The purpose of this paper is to study the partial functional linear regression model with a random missing response and measurement errors in explanatory variables.The estimators of unknown parameters and unknown coefficient functions in the model and their asymptotic properties are discussed, respectively. Firstly, the missing data and the data with measurement errors are processed by some data preprocessing method, as well as the model is transformed into a general functional linear regression model. Then the empirical form of the model is given by Karhumen-Loeve expansion (K-L expansion) and principal component analysis. Finally, the least squares estimates of the corresponding unknown variables are obtained by minimizing the objective function with classical multivariate statistical analysis, and the asymptotic normality of the parameter estimators is proved under certain conditions. The convergence rate of the estimator of function and slope function shows that the estimators given are effective estimators, and the statistical inference method of functional data under complete observation is extended to the case of incomplete observation under certain conditions. |
| Key words: functional data measurement error K-L expansion response missing |
