半参数回归模型估计的平均相合性

在误差序列为Lqmixingale情形下，给出了半参数回归模型中β和g(t)估计，研究了估计量的q阶平均相合性在较一般的条件下，得到了理想的结果     

Strong near-epoch dependence

We introduce a new class of dependent sequences of random variables, which is a subclass of near-epoch dependent sequences, but can also be approximated by mixing sequences. For this kind of sequences of random variables, we call them strong near-epoch dependent sequences, ap-order,p > 2, (maximum) moment inequality is established under weaker dependence sizes.     

The strong law of large numbers for weighted averages under dependence assumptions

Strong laws of large numbers (SLLN) for weighted averages are proved under various dependence assumptions when the variables are not necessarily independent or identically distributed. The results considerably extend the existing results. Weighted versions of the Marcinkiewicz-Zygmund SLLN are also formulated and proved under a similar set up. It seems that such results are not known even for independent and identically distributed random variables.     

Hájek-Rényi-type inequality and strong law of large numbers for some dependent sequences

In this paper, we get the Hjek-Rényi-type inequalities for a pairwise NQD sequence, an Lr (r > 1) mixingale and a linear process, which have the concrete coefficients. In addition, we obtain the strong law of large numbers, strong growth rate and the integrability of supremum for the above sequences, which generalize and improve Corollary 2 for Lr (r > 1) mixingale of Hansen.