D-optimal Design for Polynomial Regression: Choice of Degree and Robustness (150,00 руб.)

G. Antille, A. Weinberg Allen D-optimal Design for Polynomial Regression: Choice of Degree and Robustness In this paper we show that for the D-optimal design, departures from the design are much less important than a departure from the model. <...> As a consequence, we propose, based on D-optimality, a rule for choosing the regression degree. <...> Wealso study different types of departures from the model to define a new class ofD-optimal designs, which is robust and more efficient than the uniform one. 1. <...> Introduction O ne of the main problems in the polynomial regression concerns a choice of the regression degree. <...> In the literature on optimal design it is usually assumed that a statistical model is known. <...> In practice, however, the exact degree of the polynomial is not known with certainty. <...> Moreover, the design support may not correspond to the optimal one given by an analytical solution. <...> ria. For ma 1 55 E11 m ‚ Российскошвейцарский семинар по эконометрике и статистике f x x T x f <...> d . In that case the covariance matrix of the generalized least squares estimates of ˜ is NME , and the variance of the prediction at a given point x is 21 fx M f x .|( )|ME1 T () ( ) () E , a specific convex (or concave) function of the  is the total number of observa <...> lity. TheD-optimality corresponds tom0, the criteria based on the determinant of the information m <...> trix. The purpose of this paper is, for a certain class of efficiency functions and D-optimality, to study the influence of departures from the optimal design on the values of the cri <...> eria. Our numerical results show that the influence on the value of D-efficiency is more important when perturbations are applied to boundary points than to o <...> hers. As a consequence of a numerical study of the behavior of the standardized determinant of the information matrix with respect to the degree of the polynomial regression for classical efficiency functions, we propose the following rule for choosing the regression d <...> gree. For homoscedastic cases and for Jacobi’s type efficiency functions the regression degree should be ‘the smallest reason <...> ble’. For Laguerre efficiency functions the regression degree should be the ‘the largest reason <...> ble’. For the Hermite function there is no general <...> rule. We also point out that departures from the design are much less important than a departure from the <...> odel. Finally we <...>