.beta <- function(x,z,y,p,nknots,m=2,lambda,sigma_error=diag(1,length(y)),Dm){
n <- length(y)
df1 <- nknots+p
Psi <- bs(z,df=df1,degree = p)
Psi <- as.matrix(Psi[1:n,1:df1])
x1 <- diag(x)
if(lambda!=0){
solve(t(Psi) %*% x1 %*% solve(sigma_error) %*% x1 %*% Psi +
(1/lambda)*(nknots^(2*m-1))*t(Dm)%*%(Dm)) %*%t(Psi) %*% x1 %*% solve(sigma_error) %*% y
}else
solve(t(Psi) %*% x1 %*% solve(sigma_error) %*% x1 %*% Psi) %*%
t(Psi) %*% x1 %*% solve(sigma_error) %*% y
}
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