Asymptotic normality of MRPP statistics from invariance principles of u-statistics

O'Reilly, Federico J.; Mielke, Paul W.

doi:10.1080/03610928008827907

Cited by 41 publications

(14 citation statements)

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“…28,29 While the manner in which the concentration of lead and the other metals occurred, and the environmental and public health problems related to these findings need further investigation, there is no reasonable doubt that lead and the other metals studied are excessively concentrated in the inner-city of Baltimore relative to surrounding areas. Given the extraordinary probability value (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23) for lead concentration in the center of Baltimore, and the fact that Baltimore is fundamentally similar to other large urban centers, we expect the distribution pattern of soil lead of all large cities to be similar to Baltimore. Thus, the inner-city is a location where, in the course of everyday activities, children face a higher possibility of being exposed to lead than children living in other urban locations.…”

Section: Discussionmentioning

confidence: 99%

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Lead concentrations in inner-city soils as a factor in the child lead problem.

Mielke¹,

Anderson²,

Berry³

et al. 1983

Am J Public Health

253

145

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Abstract. Soil samples were randomly collected from 422 vegetable gardens in a study area centered in downtown Baltimore, Maryland, and having a radius of 48.28 km (30 miles). The levels of lead, four other metals (cadmium, copper, nickel, and zinc), and pH were measured for each location. The application of multi-response permutation procedures, which are compatible with mapping techniques, reveals that lead (as well as cadmium, copper, nickel, and

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Section: Discussionmentioning

confidence: 99%

“…The probability values that the concentration of metals occurred by chance alone vary from about 10-' to [10][11][12][13][14][15][16][17][18][19][20][21][22][23] tic'°0" is approximated by the standard normal distribution. 13 …”

mentioning

confidence: 99%

Lead concentrations in inner-city soils as a factor in the child lead problem.

Mielke¹,

Anderson²,

Berry³

et al. 1983

Am J Public Health

253

145

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“…, aN are independent identically distributed random variables with distribution function F and satisfying some mild regularity conditions. Then O'Reilly &Mielke (1980) have shown that…”

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confidence: 99%

Approximations to Some Test Statistics for Permutation Tests in a Completely Randomized Design1

Robinson

1983

Australian Journal of Statistics

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Summary Under a randomization model for a completely randomized design permutation tests are considered based on the usual F statistic and on a multi‐response permutation procedure statistic. For the first statistic the first two moments are obtained so a comparision with the distribution under the normal theory model can be made. The second statistic is shown to converge in distribution to an infinite weighted sum of chi‐squared variates, the weights being the limits of the eigenvalues of a matrix depending on the distance measure used and the order statistics of the observations.

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“…Examples include two‐sample t tests, various F tests, ordinary least‐squares regression, and nonparametric tests such as the WMW rank sum test, the Kruskal–Wallis one‐way analysis of variance by ranks, and the Friedman two‐way analysis of variance by ranks. A Euclidean distance function based on absolute distances between data points was incorporated into new permutation tests for matched pairs designs by Mielke and Berry,140 Berry and Mielke,175,176 Brockwell and Mielke,177 Mielke and Berry,178 and Mielke et al179; completely randomized designs by Mielke et al,148 Berry et al,180,181 Berry and Mielke,182–184 O’Reilly and Mielke,185 Brockwell et al,186 Mielke,187,188 Mielke et al,189 and Mielke and Berry190; randomized block designs by Mielke,149 Tucker et al,152 Brockwell and Mielke,177 Mielke and Berry,178 Berry and Mielke,191 and Mielke and Iyer192; contingency table analyses by Berry and Mielke,114,122,134,167,193,194 Mielke,195 Mielke and Berry,131 and Zelterman et al136; goodness‐of‐fit tests by Mielke and Berry163 and Berry and Mielke196; multiple regression by Mielke and Berry197,198 and Berry and Mielke;184,191,199–201 and measures of agreement and consensus by Berry and Mielke 168,193,194,202,203…”

Section: A Chronology Of Permutation Methodsmentioning

confidence: 99%

Permutation methods

Berry

Johnston

Mielke

2011

WIREs Computational Stats

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Permutation tests are a paradox of old and new. Permutation tests pre-date most traditional parametric statistics, but only recently have become part of the mainstream discussion regarding statistical testing. Permutation tests follow a permutation or 'conditional on errors' model whereby a test statistic is computed on the observed data, then (1) the data are permuted over all possible arrangements of the data-an exact permutation test; (2) the data are used to calculate the exact moments of the permutation distribution-a moment approximation permutation test; or (3) the data are permuted over a subset of all possible arrangements of the data-a resampling approximation permutation test. The earliest permutation tests date from the 1920s, but it was not until the advent of modern day computing that permutation tests became a practical alternative to parametric statistical tests. In recent years, permutation analogs of existing statistical tests have been developed. These permutation tests provide noteworthy advantages over their parametric counterparts for small samples and populations, or when distributional assumptions cannot be met. Unique permutation tests have also been developed that allow for the use of Euclidean distance rather than the squared Euclidean distance that is typically employed in parametric tests. This overview provides a chronology of the development of permutation tests accompanied by a discussion of the advances in computing that made permutation tests feasible. Attention is paid to the important differences between 'population models' and 'permutation models', and between tests based on Euclidean and squared Euclidean distances.

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Asymptotic normality of MRPP statistics from invariance principles of u-statistics

Cited by 41 publications

References 4 publications

Lead concentrations in inner-city soils as a factor in the child lead problem.

Lead concentrations in inner-city soils as a factor in the child lead problem.

Approximations to Some Test Statistics for Permutation Tests in a Completely Randomized Design1

Permutation methods

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