rm(list=ls()) library(MASS) m=c(1,1,1,1,1) sigma=diag(m) alpha=20 gamma=c(1,-0.5,0.7,2.5,-0.8) f=function(n,J,K,l,t){ zz=matrix(NA,n,5); for(i in 1:n){ zz[i,]=mvrnorm(1, rep(0, 5), sigma)} u1=matrix(NA,J,n); for(i in 1:n){ for(j in 1:J){ u1[,i]=rnorm(J,0,(10/(j-0.5)*pi)^2)}} u2=matrix(NA,J,n); for(r in 1:n){ for(j in 1:J){ u2[,r]=rnorm(J,0,(10/(j-0.5)*pi)^2)}} u=c(); ss=matrix(NA,n,K); xt=array(NA,dim=c(J,K,n)) h=runif(K,0,1) x=c();x1=c(); X=function(K,J){ for(i in 1:n){ for(k in 1:K){ for(j in 1:J){ xt[j,k,i]=sqrt(2)*(u1[,i])[j]*sin((j-0.5)*pi*h[k])}}} for(l in 1:n){ u=c(u,apply(xt[,,l],2,sum))} ss=matrix(u,n,K) ss} XX=X(K,J) b=c(); beta=function(K){ for(k in 1:K){ b[k]=sqrt(2)*sin(pi*h[k]/2)+2*sqrt(2)*sin(3*pi*h[k]/2)} b} bb=beta(K) xb=matrix(NA,n,K); XB=function(K,J,n){ for(i in 1:n){ for(k in 1:K){ xb[i,k]=(XX[i,k])*(bb[k])}} xb} riman=c(); for(i in 1:n){ riman[i]=sum(XB(K,J,n)[i,])/K} e=rnorm(n) y=c(); Y=function(n){ for(i in 1:n){ y[i]=alpha+t(zz[i,])%*%as.matrix(gamma)+riman[i]+e[i]} y} x3=c(); Sigma=function(n,J){ s=matrix(NA,n,n) for(r in 1:n){ for(i in 1:n){ for(j in 1:J){ x3[j]=((u1[,i])[j])*((u2[,r])[j])*((-2*cos(j-0.5)*pi/(j-0.5)*pi)+(2*sin(j-0.5)*pi/((j-0.5)*pi)^2) -((4/3)*(1/((j-0.5)*pi)^2))*((cos(j-0.5)*pi)-1))} s[i,r]=sum(x3)}} s} x1=c();t1=c(); T1=function(n,J){ for(i in 1:n){ for(j in 1:J){ x1[j]=(u1[,i])[j]*sqrt(2)*(1/(j-0.5)*pi)*(1-cos((j-0.5)*pi))} t1[i]=sum(x1)} t1} x2=c();y1=c();t2=c(); T2=function(n,J){ for(i in 1:n){ for(j in 1:J){ x2[j]=-(u1[,i])[j]*sqrt(2)*(1/(j-0.5)*pi)*cos((j-0.5)*pi) y1[j]=(u1[,i])[j]*sqrt(2)*(1/((j-0.5)*pi))^2*sin((j-0.5)*pi)} t2[i]=(sum(x2)+sum(y1))} t2} T=matrix(NA,n,8) for(i in 1:n){ T[i,1]=1 T[i,2]=as.matrix(T1(n,J))[i,1] T[i,3]=as.matrix(T2(n,J))[i,1] T[i,4:8]=zz[i,] } lambda=c(10^-10,10^-9,10^-8,10^-7,10^-6,10^-5,10^-4,10^-3,10^-2,10^-1,1,10,10^2,10^3) M=function(n,l){ a=rep(1,n) diag(a) m=Sigma(n,J)+n*lambda[l]*diag(a) m} d1=solve(t(T)%*%solve(M(n,l))%*%T)%*%t(T)%*%solve(M(n,l))%*%as.matrix(Y(n)) c1=solve(M(n,l))%*%(1-T%*%solve(t(T)%*%solve(M(n,l))%*%T)%*%t(T)%*%solve(M(n,l)))%*%as.matrix(Y(n)) d=t(d1) c=t(c1) x4=c();y2=c();x5=c();xk=c(); XK=function(t){ for(i in 1:n){ for(j in 1:J){ x4[j]=-(u1[,i])[j]*sqrt(2)*(1/(j-0.5)*pi)*cos((j-0.5)*pi) y2[j]=(u1[,i])[j]*sqrt(2)*(1/((j-0.5)*pi))^2*sin((j-0.5)*pi) x5[j]=(u1[,i])[j]*sqrt(2)*(1/(j-0.5)*pi)*(1-cos((j-0.5)*pi))} xk[i]=(t-1/2)*(sum(x4)+sum(y2))+(1/3-t/2)*sum(x5)} xk} betahat=function(t){ beta=d[2]+d[3]*t+sum(c*XK(t)) beta} beta=function(t){ sqrt(2)*sin(pi*t/2)+2*sqrt(2)*sin(3*pi*t/2)} c=c();theta=c();tt=c();yl=c(); YL=function(n){ for(i in 1:n){ theta[i]=exp(5.4+0.6*zz[i,1]-0.3*zz[i,2]) c[i]=rexp(1,1/theta[i]) tt[i]=min(Y(n)[i],c[i]) yl[i]=(theta[i])*(exp((1/theta[i])*tt[i])-1) } yl} d2=solve(t(T)%*%solve(M(n,l))%*%T)%*%t(T)%*%solve(M(n,l))%*%as.matrix(YL(n)) c2=solve(M(n,l))%*%(1-T%*%solve(t(T)%*%solve(M(n,l))%*%T)%*%t(T)%*%solve(M(n,l)))%*%as.matrix(YL(n)) dest=t(d2) cest=t(c2) betahat=function(t){ beta=dest[2]+dest[3]*t+sum(cest*XK(t)) beta} c(betahat(t),dest[1],dest[4:8],beta(t)) } #########################100 biasbeta=mean(replicate(1000,f(100,100,100000,14,0.2)[1]))-f(100,100,100000,14,0.2)[2] varbeta=var(replicate(1000,f(100,100,100000,14,0.2)[1])) msebeta1=varbeta+biasbeta^2 biasalpha=mean(replicate(1000,f(100,100,100000,14,0.2)[2]))-alpha varalpha=var(replicate(1000,f(100,100,100000,14,0.2)[2])) msealpha1=varalpha+biasalpha^2 biasgamma1=mean(replicate(1000,f(100,100,100000,14,0.2)[4]))-gamma[1] vargamma1=var(replicate(1000,f(100,100,100000,14,0.2)[4])) msegamma11=vargamma1+(biasgamma1)^2 biasgamma2=mean(replicate(1000,f(100,100,100000,14,0.2)[5]))-gamma[2] vargamma2=var(replicate(1000,f(100,100,100000,14,0.2)[5])) msegamma21=vargamma2+(biasgamma2)^2 biasgamma3=mean(replicate(1000,f(100,100,100000,14,0.2)[6]))-gamma[3] vargamma3=var(replicate(1000,f(100,100,100000,14,0.2)[6])) msegamma31=vargamma3+(biasgamma3)^2 biasgamma4=mean(replicate(1000,f(100,100,100000,14,0.2)[7]))-gamma[4] vargamma4=var(replicate(1000,f(100,100,100000,14,0.2)[7])) msegamma41=vargamma4+(biasgamma4)^2 biasgamma5=mean(replicate(1000,f(100,100,100000,14,0.2)[8]))-gamma[5] vargamma5=var(replicate(1000,f(100,100,100000,14,0.2)[8])) msegamma51=vargamma5+(biasgamma5)^2 ################################200 biasbeta=mean(replicate(1000,f(200,100,100000,14,0.2)[1]))-f(200,100,100000,14,0.2)[2] varbeta=var(replicate(1000,f(200,100,100000,14,0.2)[1])) msebeta2=varbeta+biasbeta^2 biasalpha=mean(replicate(1000,f(200,100,100000,14,0.2)[2]))-alpha varalpha=var(replicate(1000,f(200,100,100000,14,0.2)[2])) msealpha2=varalpha+biasalpha^2 biasgamma1=mean(replicate(1000,f(200,100,100000,14,0.2)[4]))-gamma[1] vargamma1=var(replicate(1000,f(200,100,100000,14,0.2)[4])) msegamma12=vargamma1+(biasgamma1)^2 biasgamma2=mean(replicate(1000,f(200,100,100000,14,0.2)[5]))-gamma[2] vargamma2=var(replicate(1000,f(200,100,100000,14,0.2)[5])) msegamma22=vargamma2+(biasgamma2)^2 biasgamma3=mean(replicate(1000,f(200,100,100000,14,0.2)[6]))-gamma[3] vargamma3=var(replicate(1000,f(200,100,100000,14,0.2)[6])) msegamma32=vargamma3+(biasgamma3)^2 biasgamma4=mean(replicate(1000,f(200,100,100000,14,0.2)[7]))-gamma[4] vargamma4=var(replicate(1000,f(200,100,100000,14,0.2)[7])) msegamma42=vargamma4+(biasgamma4)^2 biasgamma5=mean(replicate(1000,f(200,100,100000,14,0.2)[8]))-gamma[5] vargamma5=var(replicate(1000,f(200,100,100000,14,0.2)[8])) msegamma52=vargamma5+(biasgamma5)^2 ###################################400 biasbeta=mean(replicate(1000,f(400,100,100000,14,0.2)[1]))-f(400,100,100000,14,0.2)[2] varbeta=var(replicate(1000,f(400,100,100000,14,0.2)[1])) msebeta4=varbeta+biasbeta^2 biasalpha=mean(replicate(1000,f(400,100,100000,14,0.2)[2]))-alpha varalpha=var(replicate(1000,f(400,100,100000,14,0.2)[2])) msealpha4=varalpha+biasalpha^2 biasgamma1=mean(replicate(1000,f(400,100,100000,14,0.2)[4]))-gamma[1] vargamma1=var(replicate(1000,f(400,100,100000,14,0.2)[4])) msegamma14=vargamma1+(biasgamma1)^2 biasgamma2=mean(replicate(1000,f(400,100,100000,14,0.2)[5]))-gamma[2] vargamma2=var(replicate(1000,f(400,100,100000,14,0.2)[5])) msegamma24=vargamma2+(biasgamma2)^2 biasgamma3=mean(replicate(1000,f(400,100,100000,14,0.2)[6]))-gamma[3] vargamma3=var(replicate(1000,f(400,100,100000,14,0.2)[6])) msegamma34=vargamma3+(biasgamma3)^2 biasgamma4=mean(replicate(1000,f(400,100,100000,14,0.2)[7]))-gamma[4] vargamma4=var(replicate(1000,f(400,100,100000,14,0.2)[7])) msegamma44=vargamma4+(biasgamma4)^2 biasgamma5=mean(replicate(1000,f(400,100,100000,14,0.2)[8]))-gamma[5] vargamma5=var(replicate(1000,f(400,100,100000,14,0.2)[8])) msegamma54=vargamma5+(biasgamma5)^2
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