Simultaneous confidence bounds on the pair of parameters in multivariate Gauss-Markoff model with singular covariance matrix

Rok, strany: 1996, 127 - 131

The three statisticians primarily responsible for the fundamental ideas of multiple comparisons and simultaneous confidence intervals are: D. Duncan (1947–55), H. Scheffè (1959) and J. Tukey (1949). These problems and tests are very popular and discussed in many books and papers (S. N. Roy and Bose, 1953 [S. N. Roy, R. C. Bose: Simultaneous confidence interval estimation, Ann. Math. Statist. 24 (1953), 513–536], S. N. Roy, 1957 [S. N. Roy: Some Aspects of Multivariate Analysis, John Wiley, New York, 1957], Miller, 1966 [R. G. Miller: Simultaneous Statistical Inference, 2-nd ed., Springer–Verlag, New York, 1981], Morrison, 1967 [Morrison: Multivariate Statistical Methods, McGraw–Hill, New York, 1967], Rao, 1973 [C. R. Rao: Linear Statistical Inference and its Applications, 2nd ed., J. Wiley, New York, 1973] and many others).

Simultaneous confidence bounds on the pair of parameters $(Nβ_D,σ ²)$, $β _D=\overset\rightharpoonup \to{B}$, ($\overset\rightharpoonup\to{B}$, is development of matrix $B$) in a multivariate Gauss–Markoff model with singular covariance matrix

$$ (U,XB,σ²Σ \otimes V), σ²>0 ,  Σ >0 ,  V≥ 0, $$

\tag1

or in equivalent developed model $(Y_D, X_Dβ_D,σ²V_D)$ with singular known covariance matrix $σ²V_D$, $V_D≥ 0$, are obtained (Th. 2.1). Ghurye's (1960), theorem and the Browkowicz–Linnik method (1963) as well as Rao's (1973) unified theory of estimation have been applied. Browkowicz–Linnik's (1963) and Wani and Kabe's results (1968) have been generalized from univariate standard model into the model with singular covariance matrix.

ISO 690:

Oktaba, W. 1996. Simultaneous confidence bounds on the pair of parameters in multivariate Gauss-Markoff model with singular covariance matrix. In Tatra Mountains Mathematical Publications, vol. 7, no.1, pp. 127-131. 1210-3195.

APA:

Oktaba, W. (1996). Simultaneous confidence bounds on the pair of parameters in multivariate Gauss-Markoff model with singular covariance matrix. Tatra Mountains Mathematical Publications, 7(1), 127-131. 1210-3195.