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1
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
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Approximate bias for first-order autoregressive model with uniform innovations. Small sample case

100%
Nouali K., Fellag H.
Discussiones Mathematicae Probability and Statistics
|
2002
|
tom 22
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nr 1-2
15-26
EN
The first-order autoregressive model with uniform innovations is considered. The approximate bias of the maximum likelihood estimator (MLE) of the parameter is obtained. Also, a formula for the approximate bias is given when a single outlier occurs at a specified time with a known amplitude. Simulation procedures confirm that our formulas are suitable. A small sample case is considered only.
3
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Testing on the first-order autoregressive model with contaminated exponential white noise finite sample case

100%
Fellag H.
Discussiones Mathematicae Probability and Statistics
|
2001
|
tom 21
|
nr 1
11-20
EN
The testing problem on the first-order autoregressive parameter in finite sample case is considered. The innovations are distributed according to the exponential distribution. The aim of this paper is to study how much the size of this test changes when, at some time k, an innovation outlier contaminant occurs. We show that the test is rather sensitive to these changes.
4
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Unit root test in the presence of a single additive outlier small sample case

88%
Fellag H.
Discussiones Mathematicae Probability and Statistics
|
2001
|
tom 21
|
nr 2
89-97
EN
The one sided unit root test of a first-order autoregressive model in the presence of an additive outlier is considered. In this paper, we present a formula to compute the size and the power of the test when an AO (additive outlier) occurs at a time k. A small sample case is considered only.
5
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Unit root test in the presence of a single additive outlier small sample case

88%
Fellag H., Abdouche S.
Discussiones Mathematicae Probability and Statistics
|
2002
|
tom 22
|
nr 1-2
5-13
EN
The one sided unit root test of a first-order autoregressive model in the presence of an additive outlier is considered. In this paper, we present a formula to compute the size and the power of the test when an AO (additive outlier) occurs at a time k. A small sample case is considered only.
6

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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