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Using the likelihood depth, new consistent and robust tests for the parameters of the Weibull distribution are developed. Uncensored as well as type-I right-censored data are considered. Tests are given for the shape parameter and also the scale parameter of the Weibull distribution, where in each case the situation that the other parameter is known as well the situation that both parameter are unknown...
This paper studies tangential and simplicial data depth for simple orthogonal regression. Given N points in the plane, simple orthogonal regression means that we wish to determine the line through the origin that has smallest distance to the points measured in the direction orthogonal to the line. For both depth notions, it is proved that two lines which are orthogonal to each other, i.e. two lines...
M-estimators and M-kernel estimators with a redescending ψ-function are not in general consistent. This is often handled by means of coupling the estimator to a consistent one. Coupling the estimator to the (inconsistent) starting point improves the jump preserving properties. However, the consistency depends heavily on the shape of the density of the residuals. This paper shows inconsistency under...
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