The introduction of shape parameters into the statistical literature opened new areas of research and allowed statisticians to use models that produced better fits to experimental data. The Weibull and gamma families are prime examples wherein shape parameters produce more reliable statistical models than standard exponential models in lifetime studies. In the presence of many gamma-populations...

Consider a linear regression model with unknown regression parameters 0 and independent errors of unknown distribution. Block the observations into q groups whose independent variables have a common value and measure the homogeneity of the blocks of residuals by a Cramér-von Mises q-sample statistic Tq( ). This statistic is designed so that its expected value as a function of the chosen regress...

In this paper, we introduce a Goodness-of-Fit test for the Multivariate Exponential Power (MEP) distribution, a multivariate extension of the Generalized Gaussian, which has recently gained considerable interest as a model for wavelet coefficients in the context of color image retrieval and spread-spectrum watermarking. We present a size and power study of this test and show Goodness-of-Fit res...

Abstract This paper considers the parameter estimation problem of a first-order threshold autoregressive conditional heteroscedasticity model by using empirical likelihood method. We obtain ratio statistic based on estimating equation least squares and construct confidence region for parameters. Simulation studies indicate that method outperforms normal approximation-based in terms coverage pro...

For any generalized linear model, the Pearson goodness of fit statistic is the score test statistic for testing the current model against the saturated model. The relationship between the Pearson statistic and the residual deviance is therefore the relationship between the score test and the likelihood ratio test statistics, and this clarifies the role of the Pearson statistic in generalized li...

The Rao-Blackwell theorem offers a procedure for converting a crude unbiased estimator of a parameter θ into a "better" one, in fact unique and optimal if the improvement is based on a minimal sufficient statistic that is complete. In contrast, behind every minimal sufficient statistic that is not complete, there is an improvable Rao-Blackwell improvement. This is illustrated via a simple examp...

In this paper, in order to test whether changes have occurred in a nonlinear parametric regression, we propose a nonparametric method based on the empirical likelihood. Firstly, we test the null hypothesis of no-change against the alternative of one change in the regression parameters. The asymptotic behaviour of the empirical likelihood statistic under the null hypothesis and its alternative i...

This paper presents a robust approach for the automatic classification of sonar pictures. The classification task deals with t h e segmentation of the sea-bottom thanks t o the observations given by a high resolution sonar antenna. The originality of our approach consists in describing the seabed features with statistic multiresolution parameters. The obtained statistic parameters form a featur...