TY - JOUR

T1 - Optimal designs for estimating individual coefficients in trigonometric regression with no intercept

AU - Shpilev, P

AU - Melas, VB

PY - 2026/10

Y1 - 2026/10

N2 - We study the problem of constructing designs that are optimal for estimating individual coefficients in a trigonometric regression model without an intercept on [-a, a]. We provide a complete solution of the e(k)-optimality problem. On the full circle [-pi, pi], optimal designs coincide with their counterparts for the model with an intercept. For partial circles (a < r), sine-coefficient designs are shown to be inherited from the intercept model. For cosine coefficients, we study the problem of constructing e(k)-optimal designs in a trigonometric regression model without an intercept on [-a, a]. For cosine coefficients, we derive an explicit class of designs that provide highly efficient approximations to the optimal ones for a up to a threshold a(max). A key finding is that the designs are strictly optimal for m = 2, while for m > 2 they remain nearly 100% efficient, with the range of practical validity expanding as the model order m increases.

AB - We study the problem of constructing designs that are optimal for estimating individual coefficients in a trigonometric regression model without an intercept on [-a, a]. We provide a complete solution of the e(k)-optimality problem. On the full circle [-pi, pi], optimal designs coincide with their counterparts for the model with an intercept. For partial circles (a < r), sine-coefficient designs are shown to be inherited from the intercept model. For cosine coefficients, we study the problem of constructing e(k)-optimal designs in a trigonometric regression model without an intercept on [-a, a]. For cosine coefficients, we derive an explicit class of designs that provide highly efficient approximations to the optimal ones for a up to a threshold a(max). A key finding is that the designs are strictly optimal for m = 2, while for m > 2 they remain nearly 100% efficient, with the range of practical validity expanding as the model order m increases.

KW - Fourier regression

KW - Individual coefficient

KW - No intercept

KW - Trigonometric regression

KW - c-optimal design

KW - ek-optimal designs

UR - https://www.mendeley.com/catalogue/38bfa12b-1c80-3d20-b400-542b314c4cfe/

U2 - 10.1016/j.spl.2026.110825

DO - 10.1016/j.spl.2026.110825

M3 - Article

VL - 237

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

M1 - 110825

ER -