It is well known that when the random errors are iid. with finite variance, the week and the strong consiStency of LS estimate of multiple regression coefficients are equivalent. This note, by constructing a counter-e...It is well known that when the random errors are iid. with finite variance, the week and the strong consiStency of LS estimate of multiple regression coefficients are equivalent. This note, by constructing a counter-example, shows that this equivalence no longer holds true in case that the random errors possess only the r-th moment with 1≤5 T ＜ 2.展开更多
Let Yi=x'iβo+ei. 1≤i≤n, n≥1 be a linear regression model. Denote by βn the M-estimateof βo, using a convex function ρ. In [1], a basic theorem (Theorem A below) concerning the weakconsistency of βn. is est...Let Yi=x'iβo+ei. 1≤i≤n, n≥1 be a linear regression model. Denote by βn the M-estimateof βo, using a convex function ρ. In [1], a basic theorem (Theorem A below) concerning the weakconsistency of βn. is established. This theorem raises further questions concerning the consistencyof βn. In this note, some of these questions are considered for the special cases of LAD and LSestimates.展开更多
基金the National Natural Science Foundation of China (No.19631040).
文摘It is well known that when the random errors are iid. with finite variance, the week and the strong consiStency of LS estimate of multiple regression coefficients are equivalent. This note, by constructing a counter-example, shows that this equivalence no longer holds true in case that the random errors possess only the r-th moment with 1≤5 T ＜ 2.
文摘Let Yi=x'iβo+ei. 1≤i≤n, n≥1 be a linear regression model. Denote by βn the M-estimateof βo, using a convex function ρ. In [1], a basic theorem (Theorem A below) concerning the weakconsistency of βn. is established. This theorem raises further questions concerning the consistencyof βn. In this note, some of these questions are considered for the special cases of LAD and LSestimates.
