# Bootstrap Method Estimate the value of parameters several times by bootstrap method where the parameters are estimated by EM algorithm. In this way, we can observe the distribution of parameter. ```r EMbootstrap(X, Y, Z, samplesize, boots_samplesize, boots_expriments, classsize = 2, learning_rate = 0.1, regular_parameter_eta = 0.001, max_iteration = 10000, max_iteration_eta = 10000, compact_flag = FALSE, C0 = 5, C1 = 2, C2 = 9) ``` ## Arguments - `X`: the co-variables of the mean of each subgroup - `Y`: the respond variable - `Z`: the co-variables determining subgroup - `samplesize`: the size of this sample. - `boots_samplesize`: the size of chosen sample in one step of bootstrap - `boots_expriments`: the steps of bootstrap - `classsize`: the number of subgroup types in your model assumption - `learning_rate`: learning rate of updating eta - `regular_parameter_eta`: regular value of updating eta by gradient descending method. - `max_iteration`: maximum steps of iteration to avoid unlimited looping. - `max_iteration_eta`: maximal steps of eta iteration to avoid unlimited looping. - `compact_flag`: if the value of eta is limited in a compact set, set it TRUE - `C0`: the maximum of intercept of eta. - `C1`: the minimum of the norm of slope of eta - `C2`: the maximum of the norm of slope of eta ## Details Actually, the method can be extended to other parameter estimation where the standard error of parameter can't be calculated in a simple way. ## Returns - **alpha**: alpha estimated by bootstrap method. - **eta**: eta estimated by bootstrap method. - **sigma**: sigma estimated by bootstrap method. ## Author(s) Linsui Deng ## Examples ```r #parameter initialization etasize <- 2 classsize <- 2 alphasize <- 3 samplesize <- 1000 etatest <- matrix(c(1,1, 0,0),etasize,classsize) alphatest <- matrix(c(1,0,2, 4,3,5),alphasize,classsize) sigmatest <- 0.5 #test of EMbootstrap X <- matrix(c(matrix(1,samplesize), rnorm(samplesize*(etasize-1))+1),samplesize,etasize) Z <- matrix(c(matrix(1,samplesize),rbinom(prob=1/2,size=1,n=samplesize), rnorm(samplesize*(alphasize-2))+1),samplesize,alphasize) Wtest <- Wgenerate(alpha=alphatest,eta=etatest,sigma=sigmatest,X=X,Z=Z) boots_samplesize <- 100 boots_expriments <- 30 samplesize <- dim(Wtest$X)[1] EMbootstrap_theta <- EMbootstrap(Wtest$X,Wtest$Y,Wtest$Z,samplesize, boots_samplesize,boots_expriments, classsize=2,compact_flag=TRUE,C0=5,C1=0.2,C2=5) index <- which(EMbootstrap_theta$sigma<0.8) EMsimulation_result_sort <- EM_result_sort(EMbootstrap_theta$alpha[index,,], EMbootstrap_theta$eta[index,,]) EM_parameter <- EM_parameter_sd(EMsimulation_result_sort$alpha, EMsimulation_result_sort$eta, EMbootstrap_theta$sigma[index]) ```

EMbootstrap function