摘要
本文主要在探討絕對正則隨機變數序列的隨機修剪L統計量的漸近性，當修剪係系數收斂至a和b時(O<a<b<l)，對它們的分配函數限制並不多；然而當a=0及b=1 時，則限制的條件須更加嚴格，這也就是為什麼我們要做隨機修剪的主要原因。同時，由於大部分的時間序列模式都是絕對正則的隨機變數序列，這也是研究本文的主要動機之一。
本文是想嘗試著把G. R. Shorack (1989)的論文隨機修剪L統計量，推廣，把該文中立相獨立的隨機變數序列換成絕對正則的隨機變數序列。在這同時，我們必需將一些經驗累積分配函數的不等式推廣，推廣過程中將重覆使用Yoshihara (1978) 的機率不等式。 / ABSTRACT
We will prove central limit theorem for randomly trimmed L-statistics with absolutely regular random variables. When the fractions trimmed converge to a and l-b, (with 0<a<b<l) there are little restrictions on the df's of the r.v.'s, - but the limiting r.v. has several contributing terms, making the studentization complicated unless the trimming fractions converge fast enough.
For a=0 and b=l, the restriction on the rate of convergence of the trimming fractions is more severe, however this is a most reasonable way to trim.
| Identifer | oai:union.ndltd.org:CHENGCHI/B2002005101 |
| Creators | 陳宗雄 |
| Publisher | 國立政治大學 |
| Source Sets | National Chengchi University Libraries |
| Detected Language | English |
| Type | text |
| Rights | Copyright © nccu library on behalf of the copyright holders |
Page generated in 0.0024 seconds