m相依序列的样本分位数核估计的中偏差和大偏差

The Moderate Deviation and Large Deviation for the Smooth Estimate on the m-dependent Sequences

分位数是统计学中的一个重要概念,它在可靠性统计分析以及经济、金融、生物信息、医学等领域都有非常广泛的应用.相依随机序列削弱了独立性的限制,得到了众多关注和研究.因此,本文基于m相依序列,研究了样本分位数核估计的大样本性质.首先,利用m相依序列的极限理论,通过计算Cramer函数,证明了样本分位数核估计的中偏差原理.其次,通过验证Cramer条件成立,得到了样本分位数核估计的大偏差原理.研究结果简化并推广了独立同分布样本情形下的证明方法及结果,为讨论其他类型相依序列的中偏差及大偏差性质提供了重要依据.

The quantile is an important concept in statistics. It has been widely used in many fields such as reliability statistical analysis, economics, finance, bioinformatics and medicine.The study of the dependent random sequences has received a lot of attention since it weakens the limitation of independence. Therefore, based on the m-dependent sequences, this paper studies the large sample properties of the sample quantile kernel estimation. Firstly, using the limit theorem of m-dependent sequences, the Cramer function is calculated, and the moderate deviation principle of sample quantile kernel estimation is proved. Secondly, by verifying the Cramer condition, large deviation results of the sample quantile kernel estimation are obtained.The proof methods and results of the independent and identically distributed samples are simplified and generalized. Also the results provide an important basis for discussing the moderate deviation and large deviation of other types of dependent sequences.