# CategoryStatistical Inference

## Maximum Likelihood Estimation

Let X1, . . . Xn be IID with PDF f(x; θ). The likelihood function is defined byThe log-likelihood function

## Parametric Inference and Method of moments

Till now, we have covered the estimation of statistical functionals i.e. functions of CDF – Fx. They are Non-parametric Inference.

## Bootstrap Confidence Interval

Normal Interval The normal confidence interval is defined asTn ± zα/2sêbootwhere sêboot is the bootstrap estimate of standard error. Pivotal

## Bootstrap

Bootstrap is a non-parametric method for estimating accuracy defined in terms of standard error, bias, variance, confidence interval, etc. Suppose

## Empirical Distribution Function and Estimation of Statistical Functionals

When starting with the inference problem, the most basic is the non-parametric estimation of CDF and functions of CDF. Let

## Confidence set

For a parameter θ, a 1-α confidence interval is Cn = (a, b)where a = A(X1,. . , Xn) and