Some Further Theory of Search Linear Models
J. N. Srivastava · Proceedings of the Fourth International Symposium on Polarization Phenomena in Nuclear Reactions · 1976
Let y(N × 1) be a vector of observations, A 1(N × v 1) and A 2(N × v 2) known matrices, ξ 1(v 1 × 1) and ξ 2(v 2 × 1) vectors of parameters and σ 2 a constant such that 1 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyraiaacI % caieWacaWF5bGaaiykaiabg2da9iaadgeadaWgaaWcbaGaaGymaaqa % baGccqaH+oaEdaWgaaWcbaGaaGymaaqabaGccqGHRaWkcaWGbbWaaS % baaSqaaiaaikdaaeqaaOGaeqOVdG3aaSbaaSqaaiaaikdaaeqaaaaa % !43D3! $$ E(y) = {A_1}{\xi _1} + {A_2}{\xi _2} $$ 18.27 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvaiaacI % caieWacaWF5bGaaiykaiabg2da9iabeo8aZnaaCaaaleqabaGaaGOm % aaaakiaadMeadaWgaaWcbaGaamOtaaqabaaaaa!3EB7! $$ V(y) = {\sigma ^2}{I_N} $$ Here σ 2 may be known or unknown, ξ 1(v 1 × 1) is unknown. About ξ 2, we have partial information. It is known that there is a positive integer k, such that at most k elements of ξ 2 are non-zero, the rest being negligible. However, it is not known which k elements of ξ 2 are (possibly) non-zero. The problem is to search the non-zero elements of ξ 2, and make inferences about these, and about the elements of ξ 1. Such models, called ‘Search Models’, were introduced in Srivastava [1]. In this paper, some further basic developments are made in this direction.