Edgeworth expansion of the Studentized product-limit estimator for truncated and censored data

Based on random left truncated and right censored data we investigate the one-term Edgeworth expansion for the Studentized product-limit estimator, and show that the Edgeworth expansion is close to the exact distribution of the Studentized product-limit estimator with a remainder of On(su-1/2).     

The almost sure behavior of the oscillation modulus for PL-process and cumulative hazard process under random censorship

The local behavior of oscillation modulus of the product-limit (PL) process and the cumulative hazard process is investigated when the data are subjected to random censoring. Laws of the iterated logarithm of local oscillation modulus for the PL-process and the cumulative hazard process are established. Some of these results are applied to obtain the almost sure best rates of convergence for various types of density estimators as well as the Bahadur-Kiefer type process. Project supported in part by the National Natural Science Foundation of China (Grant No. 19701037).     

Congruences modulo powers of 5 for two restricted bipartitions

Let \(B_{5}(n)\) denote the number of 5-regular bipartitions of n. We establish some Ramanujan-type congruences like \(B_{5}(4n+3) \equiv 0\) (mod 5) and many infinite families of congruences for \(B_{5}(n)\) modulo higher powers of 5 such as

$$\begin{aligned} B_{5}\left( 5^{2k-1}n+\frac{2\cdot 5^{2k-1}-1}{3}\right) \equiv 0 \pmod {5^k}. \end{aligned}$$

We also apply the same method to obtain some similar results for another type of bipartition function. Meanwhile, we give a new interesting interlinked q-series identity related with Rogers–Ramanujan continued fraction, which answers a question of M. Hirschhorn.

     

Edgeworth expansion for the survival function estimator in the Koziol-Green model

In the Koziol-Green or proportional hazards random censorship model, the asymptotic accuracy of the estimated one-term Edgeworth expansion and the smoothed bootstrap approximation for the Studentized Abdushukurov-Cheng-Lin estimator is investigated. It is shown that both the Edgeworth expansion estimate and the bootstrap approximation are asymptotically closer to the exact distribution of the Studentized Abdushukurov-Cheng-Lin estimator than the normal approximation.     

机载千兆网络数据记录器设计与实现

为了满足对新一代网络化机载测试系统输出的海量高速网络化测试数据记录的需要,设计并实现了一种基于COMe主控模块和工业级通用固态硬盘的机载千兆网络数据记录器。该记录器使用集成有英特尔处理器、板载DDR3内存和FLASH存储器的COMe主控模块,可进行IRIGB-AC时间码授时的底板和作为数据存贮介质的固态硬盘构成硬件系统平台,并采用Linux嵌入式操作系统和优化的数据存贮算法程序,完成了一路千兆机载测试网络数据流的接收、打包和记录。试验室和飞机上大量实验结果表明该记录器工作性能稳定,无误码和丢包现象,可以大量应用在使用环境复杂的飞机网络化机载测试系统中。     

Arithmetic properties of 7-regular partitions

Let \(b_{\ell }(n)\) denote the number of \(\ell \)-regular partitions of n. By employing the modular equation of seventh order, we establish the following congruence for \(b_{7}(n)\) modulo powers of 7: for \(n\ge 0\) and \(j\ge 1\),

$$\begin{aligned} b_{7}\left( 7^{2j-1}n+\frac{3\cdot 7^{2j}-1}{4}\right) \equiv 0 \pmod {7^j}. \end{aligned}$$

We also find some infinite families of congruences modulo 2 and 7 satisfied by \(b_{7}(n)\).

     

BAHADUR REPRESENTATION OF THEKERNEL QUANTILE ESTIMATOR UNDER TRUNCATED AND CENSORED DATA

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