A NON-ELEMENTARY PROOF BY DIFFERENTIAL EQUATION FOR THE CENTRAL LIMIT THEOREM

被引：0

作者：

Korkmaz, Adil ^{[1
]}

Onemli, Muharrem Burak ^{[2
]}

机构：

[1] Akdeniz Univ, Fac Econ & Social Sci, TR-07058 Antalya, Turkey

[2] Gediz Univ, Fac Econ & Adm Sci, Dept Econ, Izmir, Turkey

来源：

PAKISTAN JOURNAL OF STATISTICS | 2013年 / 29卷 / 03期

关键词：

Central Limit Theorem; Elementary Proof; Non-Elementary Proof;

D O I：

暂无

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The proofs of the central limit theorem are divided into two categories: elementary and non-elementary. Proofs using the characteristic function are called non-elementary while the other proofs are called elementary. Using differential equation, this paper gives a new non-elementary proof for the central limit theorem. This proof is based on a differential equation and does not use second order Taylor expansion of any characteristic function. It is apparent that given proof may only have a pedagogical importance.

引用

页码：307 / 313

页数：7

共 13 条

[1]

Adams W.J., 1974, LIFE TIMES CENTRAL L

[2]

Boyer C., 1989, HIST MATH, V2nd

[3]

Dudewicz E.J., 1988, MODERN MATH STAT

[4]

Greene W. H., 1997, Econometric Analysis, V3rd

[5]

Kolmogorov A.N., 1992, MATH 19 CENTURY

[6] Central Limit Theorems revisited [J].

Kundu, S ;

Majumdar, S ;

Mukherjee, K .

STATISTICS & PROBABILITY LETTERS, 2000, 47 (03) :265-275

[7]

Le Cam L., 1986, Statist. Sci., V1, P78, DOI DOI 10.1214/SS/1177013818

[8] The central limit theorem for cross-variation related to the standard Brownian sheet and Berry-Esseen bounds [J].

Park, Hyun Suk ;

Jeon, Jong Woo ;

Kim, Yoon Tae .

JOURNAL OF THE KOREAN STATISTICAL SOCIETY, 2011, 40 (02) :239-244

[9]

Silverman, 1985, CALCULUS ANAL GEOMET

[10]

Trotter H., 1959, Archiv der Mathematik, V10, P226, DOI [DOI 10.1007/BF01240790, 10.1007/BF01240790]

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