54 research outputs found

    Robust estimators of ar-models : a comparison

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    Many regression-estimation techniques have been extended to cover the case of dependent observations. The majority of such techniques are developed from the classical least squares, M and GM approaches and their properties have been investigated both on theoretical and empirical grounds. However, the behavior of some alternative methods- with satisfactory performance in the regression case- has not received equal attention in the context of time series. A simulation study of four robust estimators for autoregressive models containing innovation or additive outliers is presented. The robustness and efficiency properties of the methods are exhibited, some finite-sample results are discussed in combination with theoretical properties and the relative merits of the estimators are viewed in connection with the outlier-generating scheme.peer-reviewe

    Goodness--of--Fit Tests Based on the Min--Characteristic Function

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    We propose tests of fit for classes of distributions that include the Weibull, the Pareto and the Fr\'echet, distributions. The new tests employ the novel tool of the min--characteristic function and are based on an L2--type weighted distance between this function and its empirical counterpart applied on suitably standardized data. If data--standardization is performed using the MLE of the distributional parameters then the method reduces to testing for the standard member of the family, with parameter values known and set equal to one. We investigate asymptotic properties of the tests, while a Monte Carlo study is presented that includes the new procedure as well as competitors for the purpose of specification testing with three extreme value distributions. The new tests are also applied on a few real--data sets

    Invariant tests for symmetry about an unspecified point based on the empirical characteristic function

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    Abstract. This paper considers a flexible class of omnibus affine invariant tests for the hypothesis that a multivariate distribution is symmetric about an unspecified point. The test statistics are weighted integrals involving the imaginary part of the empirical characteristic function of suitably standardized given data, and they have an alternative representation in terms of an L 2 -distance of nonparametric kernel density estimators. Moreover, there is a connection with two measures of multivariate skewness. The tests are performed via a permutational procedure that conditions on the data. Keywords. Test for symmetry, affine invariance, Mardia's measure of multivariate skewness, skewness in the sense of Móri, Rohatgi and Székely, empirical characteristic function, permutational limit theorem

    Goodness-of-Fit Tests for Symmetric Stable Distributions -- Empirical Characteristic Function Approach

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    We consider goodness-of-fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard symmetric stable distribution with the characteristic exponent α\alpha estimated from the data. We treat α\alpha as an unknown parameter, but for theoretical simplicity we also consider the case that α\alpha is fixed. For estimation of parameters and the standardization of data we use maximum likelihood estimator (MLE) and an equivariant integrated squared error estimator (EISE) which minimizes the weighted integral. We derive the asymptotic covariance function of the characteristic function process with parameters estimated by MLE and EISE. For the case of MLE, the eigenvalues of the covariance function are numerically evaluated and asymptotic distribution of the test statistic is obtained using complex integration. Simulation studies show that the asymptotic distribution of the test statistics is very accurate. We also present a formula of the asymptotic covariance function of the characteristic function process with parameters estimated by an efficient estimator for general distributions
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