I want to estimate the unknown parameter of normal distribution by MLE of my data set of weight of new born babies of Nepal Demographic Health Survey. I want to construct confidence interval of parameter.
If the H is the Hessian of the log likelihood evaluated at the maximum, then the diagonal elements of (-H)-1 are the estimated variances. Their square-roots are the standard errors (SE), and the approximate 95% (Wald-) confidence intervals are given by the MLE ± 2*SE. If the variance of the response is not known, the SE are scaled so that the ratios of the MLEs and the scaled SEs are t-distributed. You would then get the confidence interval from the quantiles of the t-distribution.