Almost Sure Confidence Intervals and One-sided Estimation In Non-regular Cases With Applications

摘要

An estimator T_n of the unknown parameter θ ∈ R is said to converge to θ from above (below), if T_n ≥ θ (T_n ≤ θ) for all sufficiently large sample size n and T_n → θ a.s., as n → ∞. Estimation problems of this kind are considered when θ is a finite end point of the distribution function. Confidence interval for θ with highest coverage probability 1, for all sufficiently large n is obtained. Applications to real data sets including industrial data and sea tide data are made.