TY - JOUR

T1 - Letter to the Editor

T2 - Hyndman, R.J. & Wand, M.P. (1997) Nonparametric autocovariance function estimation

AU - Neudecker, Heinz

AU - Liu, Shuangzhe

PY - 2000

Y1 - 2000

N2 - Hyndman & Wand (1997 Theorem 1 and Appendix) established expressions for the conditional bias and, under normality, for the variance of γˆj , an estimator of the conditional autocovariance function γj at lag j. Although they were aware of the relevance of the Hadamard matrix product, they did not fully explore its richness. In Lemma 1 they considered the variance of Ay BsAy, where the random vector y obeyed a normal law with mean m and variance V , and matrices A and Bs were square and constant. They used a procedure based on generalized cumulants. They also considered the case of an unspecified distribution. They showed that each element of D(Ay BsAy) depended on a typical term involving fourth-order moments, for which it was ‘not easy to express this term in matrix notation’. It is, however, possible to get D(Ay BsAy) for normal and unspecified distributions by using algebraic procedures based upon the Hadamard and Kronecker matrix products

AB - Hyndman & Wand (1997 Theorem 1 and Appendix) established expressions for the conditional bias and, under normality, for the variance of γˆj , an estimator of the conditional autocovariance function γj at lag j. Although they were aware of the relevance of the Hadamard matrix product, they did not fully explore its richness. In Lemma 1 they considered the variance of Ay BsAy, where the random vector y obeyed a normal law with mean m and variance V , and matrices A and Bs were square and constant. They used a procedure based on generalized cumulants. They also considered the case of an unspecified distribution. They showed that each element of D(Ay BsAy) depended on a typical term involving fourth-order moments, for which it was ‘not easy to express this term in matrix notation’. It is, however, possible to get D(Ay BsAy) for normal and unspecified distributions by using algebraic procedures based upon the Hadamard and Kronecker matrix products

U2 - 10.1111/1467-842X.00144

DO - 10.1111/1467-842X.00144

M3 - Letter

SN - 1467-842X

VL - 42

SP - 497

EP - 498

JO - Australian & New Zealand Journal of Statistics

JF - Australian & New Zealand Journal of Statistics

IS - 4

ER -