CHARACTERISTIC FUNCTIONS AND THEIR EMPIRICAL COUNTERPARTS - GEOMETRICAL INTERPRETATIONS AND APPLICATIONS TO STATISTICAL-INFERENCE

被引：15

作者：

EPPS, TW

机构：

来源：

AMERICAN STATISTICIAN | 1993年 / 47卷 / 01期

关键词：

EMPIRICAL CHARACTERISTIC FUNCTION; FOURIER TRANSFORM; WRAPPED-AROUND DISTRIBUTION;

D O I：

10.2307/2684780

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 value of a characteristic function of a random variable X at some real number t is the center of mass of the distribution of tX wrapped around the unit circle in the complex plane. This geometrical representation is used to illustrate how various properties of frequency functions and characteristic functions correspond and to illuminate the role of empirical characteristic functions in statistical inference.

引用

页码：33 / 38

页数：6

共 22 条

[1] [Anonymous], 1989, NUMERICAL RECIPES FO
[2] [Anonymous], 1986, J TEST EVAL, DOI [DOI 10.1080/00949658608810963, 10.1080/00949658608810963]
[3] RECENT AND CLASSICAL TESTS FOR NORMALITY - A COMPARATIVE-STUDY
BARINGHAUS, L
DANSCHKE, R
HENZE, N
[J]. COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 1989, 18 (01) : 363 - 379
[4] Baringhaus L., 1988, METRIKA, V35, P339, DOI [10.1007/BF02613322, DOI 10.1007/BF02613322]
[5] ESTIMATION OF MIXING PROPORTIONS VIA DISTANCE BETWEEN CHARACTERISTIC FUNCTIONS
BRYANT, JL
PAULSON, AS
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 1983, 12 (09) : 1009 - 1029
[6] LIMIT BEHAVIOR OF THE EMPIRICAL CHARACTERISTIC FUNCTION
CSORGO, S
[J]. ANNALS OF PROBABILITY, 1981, 9 (01) : 130 - 144
[7] CSORGO S, 1984, ASYMPTOTIC STATISTIC, V2
[8] A TEST FOR NORMALITY BASED ON THE EMPIRICAL CHARACTERISTIC FUNCTION
EPPS, TW
PULLEY, LB
[J]. BIOMETRIKA, 1983, 70 (03) : 723 - 726
[9] EPPS TW, 1986, J ROY STAT SOC B MET, V48, P206
[10] TESTING THAT A GAUSSIAN PROCESS IS STATIONARY
EPPS, TW
[J]. ANNALS OF STATISTICS, 1988, 16 (04) : 1667 - 1683

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