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Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Some inferential questions in regard to analysing two-way Layouts and associated linear model theory and practice

100%
Clarke B., Monaco A.
Discussiones Mathematicae Probability and Statistics
|
2004
|
tom 24
|
nr 2
183-195
EN
In analysing a well known data set from the literature which can be thought of as a two-way layout it transpires that a robust adaptive regression approach for identifying outliers fails to be sensitive enough to detect the possible interchange of two observations. On the other hand if one takes the classical approach of diagnostic checking one may also stop too early and be satisfied with a model that falls short of a more detailed analysis that takes account of heteroscedasticity in the data. An exact F-test for heteroscedasticity in the two way layout is compared with various more general tests proposed by Shukla. In conclusion it is noted that when modelling the particular form of heteroscedasticity countenanced here, the estimated column effects are unchanged from those estimated from the model assuming homogeneous error variance structure. It is only the estimated variances of these column effects that changes.
2
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Adaptive trimmed likelihood estimation in regression

100%
Bednarski T., Clarke B., Schubert D.
Discussiones Mathematicae Probability and Statistics
|
2010
|
tom 30
|
nr 2
203-219
EN
In this paper we derive an asymptotic normality result for an adaptive trimmed likelihood estimator of regression starting from initial high breakdownpoint robust regression estimates. The approach leads to quickly and easily computed robust and efficient estimates for regression. A highlight of the method is that it tends automatically in one algorithm to expose the outliers and give least squares estimates with the outliers removed. The idea is to begin with a rapidly computed consistent robust estimator such as the least median of squares (LMS) or least trimmed squares (LTS) or for example the more recent MM estimators of Yohai. Such estimators are now standard in statistics computing packages, for example as in SPLUS or R. In addition to the asymptotics we provide data analyses supporting the new adaptive approach. This approach appears to work well on a number of data sets and is quicker than the related brute force adaptive regression approach described in Clarke (2000). This current approach builds on the work of Bednarski and Clarke (2002) which considered the asymptotics for the location estimator only.
3

An adaptive method of estimation and outlier detection in regression applicable for small to moderate sample sizes

75%
Clarke B.
Discussiones Mathematicae Probability and Statistics
|
2000
|
tom 20
|
nr 1
25-50
EN
In small to moderate sample sizes it is important to make use of all the data when there are no outliers, for reasons of efficiency. It is equally important to guard against the possibility that there may be single or multiple outliers which can have disastrous effects on normal theory least squares estimation and inference. The purpose of this paper is to describe and illustrate the use of an adaptive regression estimation algorithm which can be used to highlight outliers, either single or multiple of varying number. The outliers can include 'bad' leverage points. Illustration is given of how 'good' leverage points are retained and 'bad' leverage points discarded. The adaptive regression estimator generalizes its high breakdown point adaptive location estimator counterpart and thus is expected to have high efficiency at the normal model. Simulations confirm this. On the other hand, examples demonstrate that the regression algorithm given highlights outliers and 'potential' outliers for closer scrutiny. The algorithm is computer intensive for the reason that it is a global algorithm which is designed to highlight outliers automatically. This also obviates the problem of searching out 'local minima' encountered by some algorithms designed as fast search methods. Instead the objective here is to assess all observations and subsets of observations with the intention of culling all outliers which can range up to as much as approximately half the data. It is assumed that the distributional form of the data less outliers is approximately normal. If this distributional assumption fails, plots can be used to indicate such failure, and, transformations may be ;required before potential outliers are deemed as outliers. A well known set of data illustrates this point.
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