Exponential Family Nonlinear Models, Statistical Diagnostics And Its Experimental Design

This paper first builds the geometric framework for the mean shift model, then gives two kinds of the curvature arrays and gets the second order expression of the MLE of the parameter, and then carries out the expression of the diagnostic statistic with the curvature array, and also carries out the second-order diagnostic statistic for the models with linear restriction. Second we calculate the volume of the confidence region of the parameters βwith a confidence level 1 - α , in order to make the calculating easier, it is necessary to map the confidence region into tangent space, and the confidence region, which, after having been mapped, will present itself as an ellipsoid. We use the Taylor series expansion method to get the second-order approximate expression of the confidence region of the parameters, and then according to the principle of minimizing the volume of the confidence region, this paper carries out experimental design for the regression model, and then fixes the point range in the domain of definition of design variable for the model function so as to select the designing point, which can minimize the volume of the confidence region.