LaTeX errors when creating PDF version.
This typically indicates Rd problems.
LaTeX errors found:
! Undefined control sequence.
<argument> \mathbf {X} \in \mathbb 
                                   {R}^p
l.108 Let \eqn{\mathbf{X} \in \mathbb{R}^p}{}
                                              and \eqn{\mathbf{Y} \in \mathb...
! Undefined control sequence.
<argument> \mathbf {Y} \in \mathbb 
                                   {R}^p
l.108 ...} and \eqn{\mathbf{Y} \in \mathbb{R}^p}{}
                                                  
! Undefined control sequence.
<argument> ...\mathbf {X}_{n_1})^\top \in \mathbb 
                                                  {R}^{n_1\times p}
l.118 ...{n_1})^\top\in\mathbb{R}^{n_1\times p}}{}
                                                  
! Undefined control sequence.
<argument> ...\mathbf {Y}_{n_2})^\top \in \mathbb 
                                                  {R}^{n_2\times p}
l.119 ...{n_2})^\top\in\mathbb{R}^{n_2\times p}}{}
                                                  .
! Undefined control sequence.
<argument> p\text 
                  {-value} = 1-F_{Cauchy}(T_{Cauchy}),
l.336 ...xt{-value} = 1-F_{Cauchy}(T_{Cauchy}),}{}
                                                  
! Undefined control sequence.
<argument> p\text 
                  {-value}=1-\Phi (T_{PE}),
l.397 \deqn{p\text{-value}=1-\Phi(T_{PE}),}{}
                                             
! Undefined control sequence.
<argument> p\text 
                  {-value} = 1-F_{\chi _4^2}(T_{Fisher}),
l.461 ...{-value} = 1-F_{\chi_4^2}(T_{Fisher}),}{}
                                                  
! Undefined control sequence.
<argument> \mathbf {X} \in \mathbb 
                                   {R}^p
l.506 Let \eqn{\mathbf{X} \in \mathbb{R}^p}{}
                                              and \eqn{\mathbf{Y} \in \mathb...
! Undefined control sequence.
<argument> \mathbf {Y} \in \mathbb 
                                   {R}^p
l.506 ...} and \eqn{\mathbf{Y} \in \mathbb{R}^p}{}
                                                  
! Undefined control sequence.
<argument> ...\mathbf {X}_{n_1})^\top \in \mathbb 
                                                  {R}^{n_1\times p}
l.516 ...{n_1})^\top\in\mathbb{R}^{n_1\times p}}{}
                                                  
! Undefined control sequence.
<argument> ...\mathbf {Y}_{n_2})^\top \in \mathbb 
                                                  {R}^{n_2\times p}
l.517 ...{n_2})^\top\in\mathbb{R}^{n_2\times p}}{}
                                                  .
! Undefined control sequence.
<argument> ...{M_{CQ}}=\frac {2}{n_1(n_1-1)}\text 
                                                  {tr}(\mathbf {\Sigma }_1^2...
l.663 ...r}(\mathbf{\Sigma}_1\mathbf{\Sigma}_2)}{}
                                                  ,
! Undefined control sequence.
<argument> ... }_1^2)+ \frac {2}{n_2(n_2-1)}\text 
                                                  {tr}(\mathbf {\Sigma }_2^2...
l.663 ...r}(\mathbf{\Sigma}_1\mathbf{\Sigma}_2)}{}
                                                  ,
! Undefined control sequence.
<argument> ...igma }_2^2)+ \frac {4}{n_1n_2}\text 
                                                  {tr}(\mathbf {\Sigma }_1\m...
l.663 ...r}(\mathbf{\Sigma}_1\mathbf{\Sigma}_2)}{}
                                                  ,
! Undefined control sequence.
<argument> ...frac {2}{n_1(n_1-1)}\widehat {\text 
                                                  {tr}(\mathbf {\Sigma }_1^2...
l.667 ...(\mathbf{\Sigma}_1\mathbf{\Sigma}_2)}.}{}
                                                  
! Undefined control sequence.
<argument> ...frac {2}{n_2(n_2-1)}\widehat {\text 
                                                  {tr}(\mathbf {\Sigma }_2^2...
l.667 ...(\mathbf{\Sigma}_1\mathbf{\Sigma}_2)}.}{}
                                                  
! Undefined control sequence.
<argument> ...}+ \frac {4}{n_1n_2}\widehat {\text 
                                                  {tr}(\mathbf {\Sigma }_1\m...
l.667 ...(\mathbf{\Sigma}_1\mathbf{\Sigma}_2)}.}{}
                                                  
! Undefined control sequence.
<argument> \widehat {\text 
                           {tr}(\mathbf {\Sigma }_1^2)}
l.668 ...idehat{\text{tr}(\mathbf{\Sigma}_1^2)}}{}
                                                  ,
! Undefined control sequence.
<argument> \widehat {\text 
                           {tr}(\mathbf {\Sigma }_2^2)}
l.669 ...idehat{\text{tr}(\mathbf{\Sigma}_2^2)}}{}
                                                  , and
! Undefined control sequence.
<argument> \widehat {\text 
                           {tr}(\mathbf {\Sigma }_1\mathbf {\Sigma }_2)}
l.670 ...}(\mathbf{\Sigma}_1\mathbf{\Sigma}_2)}}{}
                                                  
! Undefined control sequence.
<argument> p\text 
                  {-value} = 1-F_{Cauchy}(M_{Cauchy}),
l.736 ...xt{-value} = 1-F_{Cauchy}(M_{Cauchy}),}{}
                                                  
! Undefined control sequence.
<argument> p\text 
                  {-value}= 1-\Phi (M_{PE}),
l.801 \deqn{p\text{-value}= 1-\Phi(M_{PE}),}{}
                                              
! Undefined control sequence.
<argument> p\text 
                  {-value} = 1-F_{\chi _4^2}(M_{Fisher}),
l.865 ...{-value} = 1-F_{\chi_4^2}(M_{Fisher}),}{}
                                                  
! Undefined control sequence.
<argument> \mathbf {X} \in \mathbb 
                                   {R}^p
l.914 Let \eqn{\mathbf{X} \in \mathbb{R}^p}{}
                                              and \eqn{\mathbf{Y} \in \mathb...
! Undefined control sequence.
<argument> \mathbf {Y} \in \mathbb 
                                   {R}^p
l.914 ...} and \eqn{\mathbf{Y} \in \mathbb{R}^p}{}
                                                  
! Undefined control sequence.
<argument> ... }_1 = \boldsymbol {\mu }_2 \ \text 
                                                  { and } \ \mathbf {\Sigma ...
l.921 \ \mathbf{\Sigma}_1 = \mathbf{\Sigma}_2. }{}
                                                  
! Undefined control sequence.
<argument> ...\mathbf {X}_{n_1})^\top \in \mathbb 
                                                  {R}^{n_1\times p}
l.925 ...{n_1})^\top\in\mathbb{R}^{n_1\times p}}{}
                                                  
! Undefined control sequence.
<argument> ...\mathbf {Y}_{n_2})^\top \in \mathbb 
                                                  {R}^{n_2\times p}
l.926 ...{n_2})^\top\in\mathbb{R}^{n_2\times p}}{}
                                                  .
! Undefined control sequence.
<argument> ... }_1 = \boldsymbol {\mu }_2 \ \text 
                                                  { and } \ \mathbf {\Sigma ...
l.1031 \ \mathbf{\Sigma}_1 = \mathbf{\Sigma}_2}{}
                                                 ,
! Undefined control sequence.
<argument> p\text 
                  {-value} = 1-F_{Cauchy}(C_{n_1,n_2}),
l.1036 ...{-value} = 1-F_{Cauchy}(C_{n_1,n_2}),}{}
                                                  
! Undefined control sequence.
<argument> ... }_1 = \boldsymbol {\mu }_2 \ \text 
                                                  { and } \ \mathbf {\Sigma ...
l.1102 \ \mathbf{\Sigma}_1 = \mathbf{\Sigma}_2}{}
                                                 ,
! Undefined control sequence.
<argument> p\text 
                  {-value} = 1-F_{\chi _2^2}(S_{n_1,n_2}),
l.1107 ...value} = 1-F_{\chi_2^2}(S_{n_1,n_2}),}{}
                                                  
! Undefined control sequence.
<argument> ... }_1 = \boldsymbol {\mu }_2 \ \text 
                                                  { and } \ \mathbf {\Sigma ...
l.1166 \ \mathbf{\Sigma}_1 = \mathbf{\Sigma}_2}{}
                                                 ,
! Undefined control sequence.
<argument> p\text 
                  {-value} = 1-F_{\chi _4^2}(J_{n_1,n_2}),
l.1171 ...value} = 1-F_{\chi_4^2}(J_{n_1,n_2}),}{}
                                                  
! Undefined control sequence.
<argument> ... }_1 = \boldsymbol {\mu }_2 \ \text 
                                                  { and } \ \mathbf {\Sigma ...
l.1236 \ \mathbf{\Sigma}_1 = \mathbf{\Sigma}_2}{}
                                                 ,
! Undefined control sequence.
<argument> p\text 
                  {-value} = 1-F_{Cauchy}(C_{PE}),
l.1241 ...\text{-value} = 1-F_{Cauchy}(C_{PE}),}{}
                                                  
! Undefined control sequence.
<argument> ... }_1 = \boldsymbol {\mu }_2 \ \text 
                                                  { and } \ \mathbf {\Sigma ...
l.1304 \ \mathbf{\Sigma}_1 = \mathbf{\Sigma}_2}{}
                                                 ,
! Undefined control sequence.
<argument> p\text 
                  {-value} = 1-F_{\chi _2^2}(S_{PE}),
l.1309 ...ext{-value} = 1-F_{\chi_2^2}(S_{PE}),}{}
                                                  
! Undefined control sequence.
<argument> ... }_1 = \boldsymbol {\mu }_2 \ \text 
                                                  { and } \ \mathbf {\Sigma ...
l.1373 \ \mathbf{\Sigma}_1 = \mathbf{\Sigma}_2}{}
                                                 ,
! Undefined control sequence.
<argument> p\text 
                  {-value} = 1-F_{\chi _4^2}(J_{PE}),
l.1378 ...ext{-value} = 1-F_{\chi_4^2}(J_{PE}),}{}