The Sampling Distribution of the Third Moment Coefficient--An Experiment

Pepper, Joseph

doi:10.2307/2333796

Cited by 4 publications

(4 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The construction of a significance test for the comparison of two skewness estimates requires knowledge about the sampling distribution of the skewness. Early work by Pepper () indicates that the distribution of a skewness estimate may be approximated by a normal distribution (see also Shenton & Bowman, ). D'Agostino () suggested a transformation of the skewness estimate to approach normality more closely.…”

Section: Statistical Inference On γε and γBold-italicε′mentioning

confidence: 99%

Significance tests to determine the direction of effects in linear regression models

Wiedermann

Hagmann

Eye

2014

Brit J Math & Statis

View full text Add to dashboard Cite

Previous studies have discussed asymmetric interpretations of the Pearson correlation coefficient and have shown that higher moments can be used to decide on the direction of dependence in the bivariate linear regression setting. The current study extends this approach by illustrating that the third moment of regression residuals may also be used to derive conclusions concerning the direction of effects. Assuming non-normally distributed variables, it is shown that the distribution of residuals of the correctly specified regression model (e.g., Y is regressed on X) is more symmetric than the distribution of residuals of the competing model (i.e., X is regressed on Y). Based on this result, 4 one-sample tests are discussed which can be used to decide which variable is more likely to be the response and which one is more likely to be the explanatory variable. A fifth significance test is proposed based on the differences of skewness estimates, which leads to a more direct test of a hypothesis that is compatible with direction of dependence. A Monte Carlo simulation study was performed to examine the behaviour of the procedures under various degrees of associations, sample sizes, and distributional properties of the underlying population. An empirical example is given which illustrates the application of the tests in practice.

show abstract

Section: Statistical Inference On γε and γBold-italicε′mentioning

confidence: 99%

Significance tests to determine the direction of effects in linear regression models

Wiedermann

Hagmann

Eye

2014

Brit J Math & Statis

View full text Add to dashboard Cite

show abstract

“…(e) Time series-Working (1934), Quenouille (1949), Cochrane and Orcutt (1949), and in one issue of Sankhya, Das (1951), Matthai and Kannan (1951), Rao and Som (1951), Rao (1951), and Sastry (1951a), (1951b). (f) Others-Sun (1928) on final digits in a reading, Kondo (1929) on mean square contingency, Mahalanobis (1930) on the moments of D2, McKay (1931) on the coefficient of variation, Tokishige (1931Tokishige ( ), (1933 on the median and quartiles, Pepper (1932) on the third moment, E. S. Pearson (1935) on testing for normality, Thompson (1937) on an estimator used by Wilks, Tang (1938) on estimation in plant breeding, Kendall, et al, (1938) Adler and Fricker (1952) on air traffic, Dixon (1950) on extreme values and, Dixon (1952) non-parametric tests.…”

Section: (4)mentioning

confidence: 99%

A History of Distribution Sampling Prior to the Era of the Computer and its Relevance to Simulation

Teichroew¹

1965

Journal of the American Statistical Association

View full text Add to dashboard Cite

“…Here b (X-X)3/n 1=l 3 i {Y2(X -X)2/n}l' where X is the sample mean and n the sample size. This required the first eight moments, all of which were known exactly (Fisher, 1930;Pepper, 1932). t distributions, where the required moments were either approximate (Pearson, 1931(Pearson, , 1936 or exact (Williams, 1935).…”

Section: Introductionmentioning

confidence: 99%

Approaches to the Null Distribution of √b 1

D’Agostino¹,

Tietjen²

1973

Biometrika

View full text Add to dashboard Cite

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. This content downloaded from 128.235.251.160 on Mon, SUMMARY A comparative study of approximations to the null distribution of VbL is given for small sample sizes, i.e. n < 35. The approximations studied are the approximations by the normal distribution, the Johnson Su distributions, the t or Pearson Type VII distributions, the Cornish-Fisher expansions using moments up to the eighth, with and without Geary's adjustment, and, finally, Monte-Carlo simulations. For the usual levels of significance all the approximations, except the normal approximation, appear satisfactory for n > 8. Because the Su and t distributions allow approximations to the probability integrals, they can be used to combine the results of independently drawn samples.

show abstract

The Sampling Distribution of the Third Moment Coefficient--An Experiment

Cited by 4 publications

References 0 publications

Significance tests to determine the direction of effects in linear regression models

Significance tests to determine the direction of effects in linear regression models

A History of Distribution Sampling Prior to the Era of the Computer and its Relevance to Simulation

Approaches to the Null Distribution of √b 1

Contact Info

Product

Resources

About