Mean Slippage Research Articles

Isolating One-Cell Interactions

Robust regression can be used to identify one-cell interactions in multiway factorial designs. One-cell interactions appear as mean slippage outliers to a low-order model, and robust regression gives these cells low mean weight. I use mean cell weight as a diagnostic criterion for one-cell interactions and provide approximate critical values for mean cell weights. Several examples illustrate the method.

The power of some nonparametric test statistics for the location and mean slippage problems

Abstract Many nonparametric test statistics for the location problem or mean slippage problem are based on extreme order statistics. A generalized class of statistics related to those of Rosenbaum (1954) and Mosteller (1948) are considered in this paper. Analytic formulae for the large sample power of these test statistics are derived for Lehmann alternatives and for pure-shift alternatives for various common population distributions. Under Lehmann alternatives, the large sample power is independent of the population distributions and the limiting power is less than one, which implies that these test statistics are asymptotically poor. The large sample power under pure-shift alternatives depends greatly on the population distributions. For example, it tends asymptotically to one for uniform or normal distributions but converges to the significance level for lognormal or Cauchy distributions. A simulation study indicates that the large sample results are highly predictive of the small and moderate sample size behavior. Care must therefore be exercised in the use of such tests for long-tailed distributions.

Joint slippage in the Hoffmann external fixator: No effect of loading rate in bench experiments

For tibial fractures, half-frames, such as the Hoffmann fixation device, sometimes fail when subjected to weight-bearing loads. Because the joints of the Hoffmann system are known to slip, which could lead to frame failure, three interfaces of the standard Hoffmann joint were tested at different clamp torques and different rates of load application. No difference in mean slippage values was noted for any interface at similar clamp torques. Joint slippage and any subsequent frame failure are thus not related to rate of load application, but to the magnitude of the load alone.

On detection of outliers in symmetric normal models

Extensions of recent results for detection of mean slippage type outliers from i.i.d. multivariate normal and elliptically symmetric distributions are made to symmetric case, that is, when the observations are equicorrelated. The main tool used is Wijsman's (1967) representation theorem. The results obtained can be viewed as a robustness property of the use of Mardia's multivariate kurtosis as a locally optimal test statistic to detect outliers against equicorrelated distributions.

A Note on Restricted Maximum Likelihood Estimation with an Alternative Outlier Model

SUMMARY For single outliers in normal theory fixed effects models a mean slippage model is commonly used. An alternative is to model the outlier as arising from an unknown observation with inflated variance. Maximum likelihood estimates for the position of the outlier under the two models need not agree. This paper considers maximizing a restricted part of the likelihood to estimate the variance parameters and characterizes these estimates in terms of standard least squares parameters. It is shown that the residual variance and outlier position are the same under both models.

DETECTION AND TESTING OF DIFFEFENT TYPES OF OUTLIER IN LINEAR STRAUCTURAL RELATIONASHIPS

SummaryThe linear structural model provides one way of modelling a linear relationship between two random variables. It is well known that problems of unidentifiability arise for unreplicated observations and normal error structure. As in all data sets, outliers can arise and methods are needed for detecting and testing them. An outlier‐generating model of mean–slippage type can be used to characterise four different forms of outlier manifestation. It is interesting to find that the unidentifiability problem provides no obstacle for detecting or testing the outliers for three of the four forms. Detection principles, and specific discordancy tests, are derived and illustrated by application to some data on physical measurements of Pacific squid.

Detection of Multivariate Outliers in Elliptically Symmetric Distributions

An extension of Ferguson's (Fourth Berkeley Symposium on Probability and Mathematical Statistics, 1961, Volume 1) univariate normal results and Schwager and Margolin's (1982) multivariate normal results for detection of outliers is made to the multivariate elliptically symmetric case with mean slippage. The main result can be viewed as a robustness property of the use of Mardia's multivariate kurtosis statistic as a locally optimum test statistic to detect outliers against nonnormal multivariate distributions.

Detection of Multivariate Normal Outliers

The general outlier problem for a multivariate normal random sample with mean slippage is defined and is shown to be invariant under a natural group of transformations. A family of maximal invariants is obtained, and the common distribution of its members is derived. The critical region for the locally best invariant test of the null hypothesis, that there are no outliers, versus the alternative hypothesis, that some outliers are present, is found. Under very general conditions, this test is equivalent to rejecting the null hypothesis whenever Mardia's multivariate sample kurtosis is sufficiently large.

A Note on an Alternative Outlier Model

Summary This paper examines modelling a single outlier in the normal theory fixed effects linear model as arising from an unknown observation with inflated variance. The maximum likelihood estimates are characterized in terms of standard least squares statistics. The estimated position of the outlier does not necessarily agree with the estimated position under the usual mean slippage outlier model, and an example where they differ is presented. A sufficient and common condition for agreement is given.