An empirical goodness-of-fit test for multivariate distributions
نویسنده
چکیده
An empirical test is presented by which one may determine whether a specified multivariate probability model is suitable to describe the underlying distribution of a set of observations. This test is based on the premise that, given any probability distribution, the Mahalanobis distances corresponding to data generated from that distribution will likewise follow a distinct distribution that can be estimated well by means of a large sample. We demonstrate the effectiveness of the test for detecting departures from the multivariate normal and from the multivariate beta distributions. In the latter case, we apply the test to real mulivariate data to confirm that it is consistent with a multivariate beta model.
منابع مشابه
On the Canonical-Based Goodness-of-fit Tests for Multivariate Skew-Normality
It is well-known that the skew-normal distribution can provide an alternative model to the normal distribution for analyzing asymmetric data. The aim of this paper is to propose two goodness-of-fit tests for assessing whether a sample comes from a multivariate skew-normal (MSN) distribution. We address the problem of multivariate skew-normality goodness-of-fit based on the empirical Laplace tra...
متن کاملEmpirical Hankel transforms and its applications to goodness-of-fit tests
We introduce a special Hankel transform for probability distributions on the nonnegative half-line and discuss some of its properties. Due to the uniqueness of the transform we suggest an integral type test statistic based on the empirical Hankel transform to treat simple and composite hypotheses goodness-of-fit problems. The special case of exponential distributions is studied in detail. © 200...
متن کاملA New Goodness-of-Fit Test for a Distribution by the Empirical Characteristic Function
Extended Abstract. Suppose n i.i.d. observations, X1, …, Xn, are available from the unknown distribution F(.), goodness-of-fit tests refer to tests such as H0 : F(x) = F0(x) against H1 : F(x) $neq$ F0(x). Some nonparametric tests such as the Kolmogorov--Smirnov test, the Cramer-Von Mises test, the Anderson-Darling test and the Watson test have been suggested by comparing empirical ...
متن کاملTests of Fit for Normal Variance Inverse Gaussian Distributions
Goodness–of–fit tests for the family of symmetric normal variance inverse Gaussian distributions are constructed. The tests are based on a weighted integral incorporating the empirical characteristic function of suitably standardized data. An EM– type algorithm is employed for the estimation of the parameters involved in the test statistic. Monte Carlo results show that the new procedure is com...
متن کاملEmpirical characteristic function-based tests for multivariate stable distributions
We consider goodness–of–fit testing for multivariate stable distributions. The proposed test statistics exploit a characterizing property of the characteristic function of these distributions and are consistent under some conditions. The asymptotic distribution is derived under the null hypothesis as well as under local alternatives. Conditions for an asymptotic null distribution free of parame...
متن کامل