缺失数据下部分线性变系数EV模型在生鲜产品销售量预测中的应用

Application of Partial Linear Variable Coefficient EV Model in Fresh Product Sales Forecast under Missing Data

摘要: 本文主要研究了在响应变量随机缺失同时非参数分量带测量误差的条件下，部分线性变系数模型的统计推断。利用局部线性光滑、profile最小二乘及偏差纠正方法，构造了模型中参数分量和非参数分量的估计；另外，为了避免使用近似正态方法构造参数置信域时估计渐近协方差，我们又利用经验似然方法研究了参数置信域的构造问题，进而给出了参数分量的置信区间，模拟研究表明经验似然方法相比正态近似方法具有更好的有限样本性质。最后使用超市生鲜产品销售量数据集进行了实例分析，得到了更好的结果。

Abstract: In this paper, we mainly consider the statistical inference for partially linear varying coefficient errors in variables models in the nonparametric part and the responses are missing at random. Based on local linear smoothing techniques, profile least-squares and bias-corrected methods, we obtained estimators successfully about both parametric and nonparametric components. Besides, to avoid to estimate the asymptotic covariance in establishing confidence region of the parametric component with the normal-approximation method, we define an empirical likelihood based sta-tistic. Then, the confidence regions of the parametric component with asymptotically correct cov-erage probabilities can be constructed by the result. The simulation results show that the empirical likelihood method has better finite sample properties compared with the normal approximation method. Finally, the method is applied to a real data analysis of the supermarket fresh sales volume data and gives better estimation.