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

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 $\alpha$ estimated from the data. We treat $\alpha$ as an unknown parameter, but for theoretical simplicity we also consider the case that $\alpha$ 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

Finite-sample performance of alternative estimators for autoregressive models in the presence of outliers

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 is presented. The discussion of the results takes into account theoretical findings and reveals some finite-sample properties of the estimators. (C) 1999 Elsevier Science B.V. All rights reserved

Recent and classical tests for exponentiality: a partial review with comparisons

A wide selection of classical and recent tests for exponentiality are discussed and compared. The classical procedures include the statistics of Kolmogorov-Smirnov and Cramer-von Mises, a statistic based on spacings, and a method involving the score function. Among the most recent approaches emphasized are methods based on the empirical Laplace transform and the empirical characteristic function, a method based on entropy as well as tests of the Kolmogorov-Smirnov and Cramer-von Mises type that utilize a characterization of exponentiality via the mean residual life function. We also propose a new goodness-of-fit test utilizing a novel characterization of the exponential distribution through its characteristic function. The finite-sample performance of the tests is investigated in an extensive simulation study

A comparative study of some robust methods for coefficient-estimation in linear regression

Robust regression estimators are known to perform well in the presence of outliers. Although theoretical properties of these estimators have been derived, there is always a need for empirical results to assist their implementation in practical situations. A simulation study of four robust alternatives to the least-squares method is presented within a set of error-distributions which includes many outlier-generating models. The robustness and efficiency features of the methods are exhibited, some finite-sample results are discussed in combination with asymptotic properties, and the relative merits of the estimators are viewed in connection with the tail-length of the underlying error-distribution

A class of goodness-of-fit tests for circular distributions based on trigonometric moments

We propose a class of goodness-of-fit test procedures for arbitrary parametric families of circular distributions with unknown parameters. The tests make use of the specific form of the characteristic function of the family being tested, and are shown to be consistent. We derive the asymptotic null distribution and suggest that the new method be implemented using a bootstrap resampling technique that approximates this distribution consistently. As an illustration, we then specialize this method to testing whether a given data set is from the von Mises distribution, a model that is commonly used and for which considerable theory has been developed. An extensive Monte Carlo study is carried out to compare the new tests with other existing omnibus tests for this model. An application involving five real data sets is provided in order to illustrate the new procedure

A unified approach of testing for discrete and continuous Pareto laws

Zipf distribution, Riemann zeta distribution, Moment-type statistic, Mellin transform,