1d:T7de,# Error rate of the Bayes rule for a g-class Gaussian mixture model ```r erate(dat, p, g, pi = NULL, mu = NULL, sigma = NULL, paralist = NULL, clust) ``` ## Arguments - `dat`: An $n\times p$ matrix where each row represents an individual observation - `p`: Dimension of observation vecor. - `g`: Number of multivariate normal classes. - `pi`: A g-dimensional vector for the initial values of the mixing proportions. - `mu`: A $p \times g$ matrix for the initial values of the location parameters. - `sigma`: A $p\times p$ covariance matrix,or a list of g covariance matrices with dimension $p\times p \times g$. It is assumed to fit the model with a common covariance matrix if `sigma` is a $p\times p$ covariance matrix; otherwise it is assumed to fit the model with unequal covariance matrices. - `paralist`: A list containing the required parameters $(\pi, \mu, \Sigma)$. - `clust`: An n-dimensional vector of class partition. ## Returns - **errval**: a value of error rate ## Details The error rate of the Bayes rule for a g-class Gaussian mixture model is given by $$ err(y;\theta)=1-\sum_{i=1}^g\pi_i Pr\{R(y;\theta)=i\mid Z \in C_i\}. $$ Here, we write $$ Pr\{R(y;\theta) \in C_i\mid Z\in C_i\}=\frac{\sum_{j=1}^nI_{C_i}(z_j)Q[z_j,R(y;\theta) ]}{\sum_{j=1}^nI_{C_i}(z_j)}, $$ where $Q[u,v]=1$ if $u=v$ and $Q[u,v]=0$ otherwise, and $I_{C_i}(z_j)$ is an indicator function for the $i$th class. ## Examples ```r n<-150 pi<-c(0.25,0.25,0.25,0.25) sigma<-array(0,dim=c(3,3,4)) sigma[,,1]<-diag(1,3) sigma[,,2]<-diag(2,3) sigma[,,3]<-diag(3,3) sigma[,,4]<-diag(4,3) mu<-matrix(c(0.2,0.3,0.4,0.2,0.7,0.6,0.1,0.7,1.6,0.2,1.7,0.6),3,4) dat<-rmix(n=n,pi=pi,mu=mu,sigma=sigma) xi<-c(-0.5,1) m<-rlabel(dat=dat$Y,pi=pi,mu=mu,sigma=sigma,xi=xi) zm<-dat$clust zm[m==1]<-NA inits<-initialvalue(g=4,zm=zm,dat=dat$Y) fit_pc<-gmmsslm(dat=dat$Y,zm=zm,pi=inits$pi,mu=inits$mu,sigma=inits$sigma,xi=xi,type='full') parlist<-paraextract(fit_pc) erate(dat=dat$Y,p=3,g=4,paralist=parlist,clust=dat$clust) ```

erate function