U-STATISTICS, CONDITIONAL-INDEPENDENCE AND GRAPH-THEORY

被引：0

作者：

MENON, VV ^{[1
]}

RAI, VN ^{[1
]}

机构：

[1] BANARAS HINDU UNIV,INST TECHNOL,DEPT APPL MATH,VARANASI 221005,UTTAR PRADESH,INDIA

来源：

SANKHYA-THE INDIAN JOURNAL OF STATISTICS SERIES A | 1991年 / 53卷

关键词：

U-STATISTICS; INDEPENDENCE; CONDITIONAL INDEPENDENCE; GRAPH THEORY; LABELED FORESTS; COUNTING FORMULA; ENUMERATION;

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：

For a subset of the summands of U-statistics with kernel of size 2, based on n i.i.d: r.v.'s X1, ..., X(n), a concept of conditional independence is defined. Conditionally independent sets are completely characterized through graph theory, by constructing a graph corresponding to the given subset. The number of conditionally independent sets is shown to be related to the number of labelled forests on n vertices, and a counting formula for such forests is derived. A relation to Bell polynomials is pointed out.

引用

页码：51 / 59

页数：9

共 9 条

[1]

Berge C., 1973, GRAPHS HYPERGRAPHS

[2] BERRY-ESSEEN THEOREM FOR U-STATISTICS [J].

CALLAERT, H ;

JANSSEN, P .

ANNALS OF STATISTICS, 1978, 6 (02) :417-421

[3] BERRY-ESSEEN THEOREM FOR U-STATISTICS [J].

CHAN, YK ;

WIERMAN, J .

ANNALS OF PROBABILITY, 1977, 5 (01) :136-139

[4]

Fraser D. A. S., 1957, NONPARAMETRIC METHOD

[5] CONVERGENCE RATES FOR U-STATISTICS AND RELATED STATISTICS [J].

GRAMS, WF ;

SERFLING, RJ .

ANNALS OF STATISTICS, 1973, 1 (01) :153-160

[6]

Harary F., 1973, GRAPHICAL ENUMERATIO

[7]

READ C, 1972, GRAPH THEORY COMPUTI

[8]

Riordan J., 1958, INTRO COMBINATORIAL

[9] SHORT DISTANCES, FLAT TRIANGLES AND POISSON LIMITS [J].

SILVERMAN, B ;

BROWN, T .

JOURNAL OF APPLIED PROBABILITY, 1978, 15 (04) :815-825

← 1 →