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! Undefined control sequence.
<recently read> \pmb 
                     
l.205 ...} is that \eqn{\pmb{\mu} = \pmb{\mu}_0}{}
                                                   and the constraint impose...
! Undefined control sequence.
<argument> \pmb {\mu } = \pmb 
                              {\mu }_0
l.205 ...} is that \eqn{\pmb{\mu} = \pmb{\mu}_0}{}
                                                   and the constraint impose...
! Undefined control sequence.
<argument> ...i=1}^{n}\left \lbrace \left [1+\pmb 
                                                  {\lambda }^T\left ({\bf x}...
l.208 }{}
         
! Undefined control sequence.
<argument> ...b {\lambda }^T\left ({\bf x}_i-\pmb 
                                                  {\mu }_0 \right )\right ]^...
l.208 }{}
         
! Undefined control sequence.
<argument> ...)\right ]^{-1}\left ({\bf x}_i-\pmb 
                                                  {\mu }_0\right )\right \rb...
l.208 }{}
         
! Undefined control sequence.
<recently read> \pmb 
                     
l.209 where the \eqn{\pmb{\lambda}}{}
                                      is the Lagrangian parameter introduced...
! Undefined control sequence.
<recently read> \pmb 
                     
l.209 ...with respect to the \eqn{\pmb{\lambda}}{}
                                                  . The probabilities have t...
! Undefined control sequence.
<argument>  p_i=\frac {1}{n}\left [1+\pmb 
                                          {\lambda }^T \left ({\bf x}_i-\pmb...
l.212 }{}
         
! Undefined control sequence.
<argument> ... {\lambda }^T \left ({\bf x}_i-\pmb 
                                                  {\mu }_0 \right )\right ]^...
l.212 }{}
         
! Undefined control sequence.
<recently read> \pmb 
                     
l.292 ...is that \eqn{\pmb{\mu}_1 = \pmb{\mu}_2}{}
                                                   and the two constraints i...
! Undefined control sequence.
<argument> \pmb {\mu }_1 = \pmb 
                                {\mu }_2
l.292 ...is that \eqn{\pmb{\mu}_1 = \pmb{\mu}_2}{}
                                                   and the two constraints i...
! Undefined control sequence.
<argument> ...1}^{n_j}\left \lbrace \left [1+\pmb 
                                                  {\lambda }_j^T\left ({\bf ...
l.295 }{}
         
! Undefined control sequence.
<argument> ...ambda }_j^T\left ({\bf x}_{ji}-\pmb 
                                                  {\mu } \right )\right ]^{-...
l.295 }{}
         
! Undefined control sequence.
<argument> ...ight ]^{-1}\left ({\bf x}_{ij}-\pmb 
                                                  {\mu }\right )\right \rbra...
l.295 }{}
         
! Undefined control sequence.
<recently read> \pmb 
                     
l.296 ...j=1,2}{} and the \eqn{\pmb{\lambda}_js}{}
                                                   are Lagrangian parameters...
! Undefined control sequence.
<recently read> \pmb 
                     
l.296 ...h respect to the \eqn{\pmb{\lambda}_js}{}
                                                  . The probabilities of the...
! Undefined control sequence.
<argument>  p_{ji}=\frac {1}{n_j} \left [1+\pmb 
                                                {\lambda }_j^T \left ({\bf x...
l.298 ... x}_{ji}-\pmb{\mu} \right)\right]^{-1}}{}
                                                  . The log-likelihood ratio...
! Undefined control sequence.
<argument> ...mbda }_j^T \left ({\bf x}_{ji}-\pmb 
                                                  {\mu } \right )\right ]^{-1}
l.298 ... x}_{ji}-\pmb{\mu} \right)\right]^{-1}}{}
                                                  . The log-likelihood ratio...
! Undefined control sequence.
<recently read> \pmb 
                     
l.395 ... some population mean \eqn{\pmb{\mu}_0}{}
                                                  , under the \eqn{H_0}{}. U...
! Undefined control sequence.
<argument> \sum _{i=1}^np_i{\bf x}_i=\pmb 
                                          {\mu }_0
l.399 ...n{\sum_{i=1}^np_i{\bf x}_i=\pmb{\mu}_0}{}
                                                  . The probabilities take t...
! Undefined control sequence.
<argument> e^{\pmb 
                   {\lambda }^T{\bf x}_i}
l.402 }{}
         
! Undefined control sequence.
<argument> \sum _{j=1}^ne^{\pmb 
                                {\lambda }^T{\bf x}_j}
l.402 }{}
         
! Undefined control sequence.
<argument> \sum _{i=1}^ne^{\pmb 
                                {\lambda }^T{\bf x}_i}\left ({\bf x}_i-\pmb ...
l.406 }{}
         
! Undefined control sequence.
<argument> ... }^T{\bf x}_i}\left ({\bf x}_i-\pmb 
                                                  {\mu }_0\right )
l.406 }{}
         
! Undefined control sequence.
<argument> \sum _{j=1}^ne^{\pmb 
                                {\lambda }^T{\bf x}_j}
l.406 }{}
         
! Undefined control sequence.
<argument> \sum _{i=1}^n{\bf x}_ie^{\pmb 
                                         {\lambda }^T{\bf x}_i}
l.406 }{}
         
! Undefined control sequence.
<argument> \sum _{j=1}^ne^{\pmb 
                                {\lambda }^T{\bf x}_j}
l.406 }{}
         
! Undefined control sequence.
<argument> ...^{\pmb {\lambda }^T{\bf x}_j}}-\pmb 
                                                  {\mu }_0={\bf 0}. 
l.406 }{}
         
! Undefined control sequence.
<recently read> \pmb 
                     
l.407 ...merical search over \eqn{\pmb{\lambda}}{}
                                                   is required. Under \eqn{H...
! Undefined control sequence.
<recently read> \pmb 
                     
l.501 ...to some population mean \eqn{\pmb{\mu}}{}
                                                  , under the \eqn{H_0}{}. U...
! Undefined control sequence.
<argument> \sum _{i=1}^np_i{\bf x}_i=\pmb 
                                          {\mu }
l.505 ...eqn{\sum_{i=1}^np_i{\bf x}_i=\pmb{\mu}}{}
                                                  . The probabilities take t...
! Undefined control sequence.
<argument> e^{\pmb 
                   {\lambda }^T{\bf x}_i}
l.508 }{}
         
! Undefined control sequence.
<argument> \sum _{j=1}^ne^{\pmb 
                                {\lambda }^T{\bf x}_j}
l.508 }{}
         
! Undefined control sequence.
<argument> \sum _{i=1}^ne^{\pmb 
                                {\lambda }^T{\bf x}_i}\left ({\bf x}_i-\pmb ...
l.512 }{}
         
! Undefined control sequence.
<argument> ... }^T{\bf x}_i}\left ({\bf x}_i-\pmb 
                                                  {\mu }\right )
l.512 }{}
         
! Undefined control sequence.
<argument> \sum _{j=1}^ne^{\pmb 
                                {\lambda }^T{\bf x}_j}
l.512 }{}
         
! Undefined control sequence.
<argument> \sum _{i=1}^n{\bf x}_ie^{\pmb 
                                         {\lambda }^T{\bf x}_i}
l.512 }{}
         
! Undefined control sequence.
<argument> \sum _{j=1}^ne^{\pmb 
                                {\lambda }^T{\bf x}_j}
l.512 }{}
         
! Undefined control sequence.
<argument> ...^{\pmb {\lambda }^T{\bf x}_j}}-\pmb 
                                                  {\mu }=0. 
l.512 }{}
         
! Undefined control sequence.
<recently read> \pmb 
                     
l.513 ...merical search over \eqn{\pmb{\lambda}}{}
                                                   is required.
! Undefined control sequence.
<argument> ...cc} \left (\sum _{j=1}^{n_1}e^{\pmb 
                                                  {\lambda }_1^T{\bf x}_j}\r...
l.524 }{}
         
! Undefined control sequence.
<argument> ... (\sum _{i=1}^{n_1}{\bf x}_ie^{\pmb 
                                                  {\lambda }_1^T {\bf x}_i}\...
l.524 }{}
         
! Undefined control sequence.
<argument> ...mbda }_1^T {\bf x}_i}\right ) -\pmb 
                                                  {\mu } & = & {\bf 0} \\ \l...
l.524 }{}
         
! Undefined control sequence.
<argument> ... \\ \left (\sum _{j=1}^{n_2}e^{\pmb 
                                                  {\lambda }_2^T{\bf y}_j}\r...
l.524 }{}
         
! Undefined control sequence.
<argument> ... (\sum _{i=1}^{n_2}{\bf y}_ie^{\pmb 
                                                  {\lambda }_2^T {\bf y}_i}\...
l.524 }{}
         
! Undefined control sequence.
<argument> ...mbda }_2^T {\bf y}_i}\right ) -\pmb 
                                                  {\mu } & = & {\bf 0} \\ n_...
l.524 }{}
         
! Undefined control sequence.
<argument> ...pmb {\mu } & = & {\bf 0} \\ n_1\pmb 
                                                  {\lambda }_1+n_2\pmb {\lam...
l.524 }{}
         
! Undefined control sequence.
<argument> ... 0} \\ n_1\pmb {\lambda }_1+n_2\pmb 
                                                  {\lambda }_2 & = & {\bf 0}...
l.524 }{}
         
! Undefined control sequence.
<recently read> \pmb 
                     
l.525 ...combination of the \eqn{\pmb{\lambda}s}{}
                                                   is set to zero. We can eq...
! Undefined control sequence.
<argument>  \left (\sum _{j=1}^{n_1}e^{\pmb 
                                            {\lambda }_1^T{\bf x}_j}\right )...
l.531 }{}
         
! Undefined control sequence.
<argument> ... (\sum _{i=1}^{n_1}{\bf x}_ie^{\pmb 
                                                  {\lambda }_1^T {\bf x}_i}\...
l.531 }{}
         
! Undefined control sequence.
<argument> ... )= \left (\sum _{j=1}^{n_2}e^{\pmb 
                                                  {\lambda }_2^T{\bf y}_j}\r...
l.531 }{}
         
! Undefined control sequence.
<argument> ... (\sum _{i=1}^{n_2}{\bf y}_ie^{\pmb 
                                                  {\lambda }_2^T {\bf y}_i}\...
l.531 }{}
         
! Undefined control sequence.
<recently read> \pmb 
                     
l.532 ...bda}_2=-\frac{n_1}{n_2}\pmb{\lambda}_1}{}
                                                   and thus rewrite the firs...
! Undefined control sequence.
<argument> ... {\lambda }_2=-\frac {n_1}{n_2}\pmb 
                                                  {\lambda }_1
l.532 ...bda}_2=-\frac{n_1}{n_2}\pmb{\lambda}_1}{}
                                                   and thus rewrite the firs...
! Undefined control sequence.
<argument>  \left (\sum _{j=1}^{n_1}e^{\pmb 
                                            {\lambda }^T{\bf x}_j}\right )^{...
l.538 }{}
         
! Undefined control sequence.
<argument> ... (\sum _{i=1}^{n_1}{\bf x}_ie^{\pmb 
                                                  {\lambda }^T {\bf x}_i}\ri...
l.538 }{}
         
! Undefined control sequence.
<argument> ...{j=1}^{n_2}e^{-\frac {n_1}{n_2}\pmb 
                                                  {\lambda }^T{\bf y}_j}\rig...
l.538 }{}
         
! Undefined control sequence.
<argument> ...2}{\bf y}_ie^{-\frac {n_1}{n_2}\pmb 
                                                  {\lambda }^T {\bf y}_i}\ri...
l.538 }{}
         
! Undefined control sequence.
<recently read> \pmb 
                     
l.540 ...y searching for the \eqn{\pmb{\lambda}}{}
                                                   which makes the last equa...
! Undefined control sequence.
<argument> H_0:\pmb 
                    {\mu }=\pmb {\mu }_0
l.646 ... vector \eqn{H_0:\pmb{\mu}=\pmb{\mu}_0}{}
                                                  . We assume that \eqn{\pmb...
! Undefined control sequence.
<argument> H_0:\pmb {\mu }=\pmb 
                                {\mu }_0
l.646 ... vector \eqn{H_0:\pmb{\mu}=\pmb{\mu}_0}{}
                                                  . We assume that \eqn{\pmb...
! Undefined control sequence.
<recently read> \pmb 
                     
l.646 ...0}{}. We assume that \eqn{\pmb{\Sigma}}{}
                                                   is unknown. The first app...
! Undefined control sequence.
<argument> ...right )p}\left (\bar {{\bf X}}-\pmb 
                                                  {\mu }\right )^T{\bf S}^{-...
l.649 }{}
         
! Undefined control sequence.
<argument> ...f S}^{-1}\left (\bar {{\bf X}}-\pmb 
                                                  {\mu } \right ). 
l.649 }{}
         
! Undefined control sequence.
<argument> ...ft (n-1\right )}\left \lbrace \text 
                                                  {tr}\left ({\bf S}_n^2\rig...
l.828 ...f S}_n\right)\right]^2 \right\rbrace }}{}
                                                  .
! Undefined control sequence.
<argument> ...2\right )- \frac {1}{n}\left [\text 
                                                  {tr}\left ({\bf S}_n\right...
l.828 ...f S}_n\right)\right]^2 \right\rbrace }}{}
                                                  .
! Undefined control sequence.
<argument> ...}_1-\bar {{\bf X}}_2\right ) -\text 
                                                  {tr}\left ({\bf S}_n\right )
l.833 }{}
         
! Undefined control sequence.
<argument> \left (\text 
                        {tr} \tilde {{\bf S}}^{-1}\tilde {{\bf S}_i}\right )^2
l.918 ...de{{\bf S}_i}\right)^2}{n_i-1} \right]}{}
                                                  .
! Undefined control sequence.
<argument>  \hat {\pmb 
                       {\mu }}_c = \left (n_1{\bf S}_1^{-1}+n_2{\bf S}_2^{-1...
l.925 }{}
         
! Undefined control sequence.
<argument> \frac {1}{n_1}\left \lbrace \text 
                                             {tr}\left [ \left ( {\bf S}_1\t...
l.934 }{}
         
! Undefined control sequence.
<argument> ...{{\bf S}} \right )^2\right ]+ \text 
                                                  {tr}\left [ \left ( {\bf S...
l.934 }{}
         
! Undefined control sequence.
<argument> ...+ \frac {1}{n_2}\left \lbrace \text 
                                                  {tr}\left [ \left ( {\bf S...
l.934 }{}
         
! Undefined control sequence.
<argument> ... {{\bf S}}\right )^2\right ]+ \text 
                                                  {tr}\left [ \left ( {\bf S...
l.934 }{}
         
! Undefined control sequence.
<argument> H_0:\pmb 
                    {\Sigma }=\pmb {\Sigma }_0
l.1026 ... \eqn{H_0:\pmb{\Sigma}=\pmb{\Sigma}_0}{}
                                                  , with \eqn{\pmb{\mu}}{} u...
! Undefined control sequence.
<argument> H_0:\pmb {\Sigma }=\pmb 
                                   {\Sigma }_0
l.1026 ... \eqn{H_0:\pmb{\Sigma}=\pmb{\Sigma}_0}{}
                                                  , with \eqn{\pmb{\mu}}{} u...
! Undefined control sequence.
<recently read> \pmb 
                     
l.1026 ...pmb{\Sigma}_0}{}, with \eqn{\pmb{\mu}}{}
                                                   unknown. The algorithm fo...
! Undefined control sequence.
<argument>  -2\log {\lambda }=n \text 
                                      {tr}\left \lbrace \pmb {\Sigma }_0^{-1...
l.1030 }{}
          
! Undefined control sequence.
<argument> ...da }=n \text {tr}\left \lbrace \pmb 
                                                  {\Sigma }_0^{-1}{\bf S}\ri...
l.1030 }{}
          
! Undefined control sequence.
<argument> ...}\right \rbrace -n\log {\left |\pmb 
                                                  {\Sigma }_0^{-1}{\bf S} \r...
l.1030 }{}
          
! Undefined control sequence.
<recently read> \pmb 
                     
l.1031 ... the sample size, \eqn{\pmb{\Sigma}_0}{}
                                                   is the specified covarian...
! Undefined control sequence.
<recently read> \pmb 
                     
l.1031 ...es of \eqn{\pmb{\Sigma}_0^{-1}{\bf S}}{}
                                                  , so that \eqn{tr\left\lbr...
! Undefined control sequence.
<argument> tr\left \lbrace \pmb 
                                {\Sigma }_0^{-1}{\bf S}\right \rbrace =p\alpha 
l.1031 ...a}_0^{-1}{\bf S}\right\rbrace=p\alpha}{}
                                                   and
! Undefined control sequence.
<argument> \left |\pmb 
                       {\Sigma }_0^{-1}{\bf S} \right |=g^p
l.1032 ...pmb{\Sigma}_0^{-1}{\bf S} \right|=g^p}{}
                                                  , then the test statistic ...
! Undefined control sequence.
<argument> H_0:\pmb 
                    {\Sigma }_1=\ldots =\pmb {\Sigma }_k
l.1094 ...:\pmb{\Sigma}_1=\ldots=\pmb{\Sigma}_k}{}
                                                  . The algorithm is taken f...
! Undefined control sequence.
<argument> H_0:\pmb {\Sigma }_1=\ldots =\pmb 
                                             {\Sigma }_k
l.1094 ...:\pmb{\Sigma}_1=\ldots=\pmb{\Sigma}_k}{}
                                                  . The algorithm is taken f...
! Undefined control sequence.
<argument> \left [\text 
                        {tr}\left ({\bf I}_p-{\bf W}^{-1}{\bf W}_i\right )\r...
l.1166 ...{-1}{\bf W}_i\right)\right]^2}{n_i-1}}{}
                                                   and \eqn{B= \frac{1}{r\le...
! Undefined control sequence.
<argument> \text 
                 {tr}\left [\left ({\bf I}_p-{\bf W}^{-1}{\bf W}_i\right )^2...
l.1166 ...^2}{2\left(n_i-1\right)}\right\rbrace}{}
                                                  .
! Undefined control sequence.
<argument> \left [\text 
                        {tr}\left ({\bf I}_p-{\bf W}^{-1}{\bf W}_i\right )\r...
l.1166 ...^2}{2\left(n_i-1\right)}\right\rbrace}{}
                                                  .
! Undefined control sequence.
<recently read> \pmb 
                     
l.1303 ...e of the common mean, \eqn{\pmb{mu}_c}{}
                                                   (see the function \code{\...
! Undefined control sequence.
<recently read> \pmb 
                     
l.1303 ...or the expression of \eqn{\pmb{\mu}_c}{}
                                                  ), is in general, for \eqn...
! Undefined control sequence.
<argument>  \hat {\pmb 
                       {\mu }}_c = \left (\sum _{i=1}^gn_i{\bf S}_i^{-1}\rig...
l.1306 }{}
          
! Undefined control sequence.
<argument>  J\left (\pmb 
                         {\mu }\right ) = T_1^2\left (\pmb {\mu }\right ) + ...
l.1378 }{}
          
! Undefined control sequence.
<argument> ...b {\mu }\right ) = T_1^2\left (\pmb 
                                                  {\mu }\right ) + T_2^2\lef...
l.1378 }{}
          
! Undefined control sequence.
<argument> ...b {\mu }\right ) + T_2^2\left (\pmb 
                                                  {\mu }\right ), 
l.1378 }{}
          
! Undefined control sequence.
<argument> J\left (\pmb 
                        {\mu }\right )
l.1379 where \eqn{J\left(\pmb{\mu}\right)}{}
                                             is the James test statistic (Ja...
! Undefined control sequence.
<argument> T_1^2\left (\pmb 
                            {\mu }\right )
l.1379 ... and \eqn{T_1^2\left(\pmb{\mu}\right)}{}
                                                   and \eqn{T_1^2\left(\pmb{...
! Undefined control sequence.
<argument> T_1^2\left (\pmb 
                            {\mu }\right )
l.1379 ... and \eqn{T_1^2\left(\pmb{\mu}\right)}{}
                                                   are the two one sample Ho...
! Undefined control sequence.
<recently read> \pmb 
                     
l.1379 ...r common mean vector \eqn{\pmb{\mu}_c}{}
                                                   (see the help file of \co...
! Undefined control sequence.
<recently read> \pmb 
                     
l.1379 ...ession with respect to \eqn{\pmb{\mu}}{}
                                                  . The sum is mimized when ...
! Undefined control sequence.
<recently read> \pmb 
                     
l.1379 ...he sum is mimized when \eqn{\pmb{\mu}}{}
                                                   takes the form of the com...
! Undefined control sequence.
<recently read> \pmb 
                     
l.1379 ...e common mean vector \eqn{\pmb{\mu}_c}{}
                                                  . The same is true for the...
! Undefined control sequence.
<argument> ... & -1 \\ \end {array}} \right )\pmb 
                                                  {\mu }={\bf C}\pmb {\mu }. 
l.1466 }{}
          
! Undefined control sequence.
<argument> ...y}} \right )\pmb {\mu }={\bf C}\pmb 
                                                  {\mu }. 
l.1466 }{}
          
! Undefined control sequence.
<argument> {\bf C}\pmb 
                       {\mu }={\bf 0}
l.1468 ...effect, \eqn{{\bf C}\pmb{\mu}={\bf 0}}{}
                                                  .