In article <[EMAIL PROTECTED]>,
Konrad Den Ende <[EMAIL PROTECTED]> wrote:
>The function
>L = \sum_{i=1}^b \sum_{j=1}^k (y_ij - \beta_i - \mu_j)^2
>is given. The task is to differentiate it with respect to all b times k
>parameters (which isn't very difficult) and use it to calculate the
>estimates for all the \beta_i's and \mu_j's.>Any suggestions on how to do that? I've tried different approaches but the >\beta somehow always gets canceled out and nothing fun comes out of my >calculations... I only see apparently b plus k parameters, but there isn one less. Adding a constant to all the \beta's and subtracting it from all the \mu's leaves the problem unchanged. In fact, this is the classical two-way "analysis of variance" problem, which uses \beta_i + \mu_j + mean, where mean is the overall mean, and the \beta's and \mu's are each required to sum to zero. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
