假設 為獨立且相同(independent and identically distributed,簡記 i.i.d.)的隨機數列.其共同分布函數為 ,且 .
數列 有一個未知樣本 分位(Sample quantile) 滿足 , .
為異於 的樣本 分位,滿足
.
為了要估計 ,在本文中會先介紹Bahadur(1966)曾做過的一個結果,在符合規則要件 下,可表示出下式.

當 為真時, 漸近中位分布(asymptotically nomally distriduted)至 .
然而,假定有一數列 使得
且
當 ,則 ,並改善上述要求的規則要件為
,我們希望同樣能得到 相同的結果.

none

[1] Billingsley, P. (1968). Convergence of Probability Measure.Johnson Wiley and Sons.
[2] Fu, J. C. (1982) . Large sample point estimation : A large deviation theory approach. Ann. Statist. 10, 762-771 .
[3] Bahadur,R . R. (1966) . A note on quantiles in large samples. Ann. Math. Statist.
[4] Hoeffding, W. (1948) . A class of statistics with asymptotically normal distribution. Ann. Math.Statist. 19 ,193-325.
[5] Sen, P. K. (1968) . Asymptotic normality of sample , quantiles for m-dependent processes. Ann. Math.Statist. 39 ,1724-1730.
[6] Uspensky, J . V . (1937) . Introduction to Mathematical Probability.
Mcgraw-Hill, New York.
[7] Ghosh. J .K. (1971). The Annals of Mathmatical Statistics .Vol.42 .No .6. 1957-1961
[8] Gnedenko B.V. , Korolev V.Yu. (1996) . Random Summation :Limit Theorems and Applications. CRC Press, New York-London-Tokyo