The exponentiated Burr Type XII (EBXII) distribution has wide applications in reliability and economic studies. In this article, the estimation of the probability density function and the cumulative distribution function of EBXII distribution is considered. We examine the maximum likelihood...

This paper provides a test of convexity of a regression function. This test is based on the least squares splines. The test statistic is shown to be asymptotically of size equal to the nominal level, while diverging to infinity if the convexity is misspecified. Therefore, the test is consistent...

This paper proposes a nonparametric test of the non-convexity of a smooth regression function based on least squares or hybrid splines. By a simple formulation of the convexity hypothesis in the class of all polynomial cubic splines, we build a test which has an asymptotic size equal to the...

This paper provides a test of convexity of a regression function. This test is based on the least squares splines. The test statistic is shown to be asymptotically of size equal to the nominal level, while diverging to infinity if the convexity is misspecified. Therefore, the test is consistent...

This paper proposes a nonparametric test of the non-convexity of a smooth regression function based on least squares or hybrid splines. By a simple formulation of the convexity hypothesis in the class of all polynomial cubic splines, we build a test which has an asymptotic size equal to the...