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

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 eq...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2014-11, Vol.154, p.26-38
Main Authors: Chang, Fu-Chuen, Tsai, Jhong-Shin
Format: Article
Language:English
Subjects:
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
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Summary: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 density design; (iii) J1/2,1/2 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.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2014.04.006