A limit theorem of D-optimal designs for weighted polynomial regression

作者：Chang, Fu Chuen^*; Tsai, Jhong Shin

来源：Journal of Statistical Planning and Inference, 2014, 154: 26-38.

DOI：10.1016/j.jspi.2014.04.006

• Arcsin distribution
• Arcsin support design
• D-criterion
• D-efficiency
• D-equivalence theorem
• D-optimal design
• Euler-Maclaurin summation formula
• Hankel matrix
• Jacobi polynomial
• Legendre polynomial
• Uniform support design

Consider the D-optimal designs for the dth-degree polynomial regression model with a continuous weight function on a compact interval. As the degree of the model goes to infinity, we derive the asymptotic value of the logarithm of the determinant of the D-optimal design. If the weight function is equal to 1, we derive the formulae of the values of the D-criterion for five classes of designs including (i) uniform density design; (ii) arcsin; (iii) J(1/2,1/2) density design density design; (iv) arcsin support design and (v) uniform support design. The comparison of D-efficiencies among these designs is investigated; besides, the asymptotic expansions and limits of their D-efficiencies are also given. It shows that the D-efficiency of the arcsin support design is the highest among the first four designs.

• 出版日期2014-11
• 单位中山大学