Testing optimality of experimental designs for a regression model with random variables |
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Authors: | Rameshwar Gupta Donald Richards |
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Institution: | Department of Mathematics, University of New Brunswick, St. John, New Brunswick, Canada;Department of Statistics, University of North Carolina, Chapel Hill, NC 27514, USA |
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Abstract: | Tsukanov (Theor. Probab. Appl. 26 (1981) 173–177) considers the regression model , , where is a vector of measured values, contains the control variables, contains the observed values, and and are being estimated. Assuming that , where is non-random, and the rows of are i.i.d. , we extend Tsukanov's results by (i) computing E(detHp), where Hp is the covariance matrix of p?, the l.s.e. of p, (ii) considering ‘optimality in the mean’ for the largest root criterion, (iii) discussing these equations when the matrix R has a left-spherical distribution. |
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Keywords: | Primary 62K05 Secondary 62H10 Optimality criteria Left-spherical Multivariate normal Zonal polynomial Hypergeometric function |
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