Almost Sure Confidence Intervals and One‐Sided Estimation in Non‐Regular Cases with Applications

Abstract

Abstract: An estimator T n of the unknown parameter θ ε 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. AMS (2000) Subject Classification: Primary 60F15, Secondary 62G32.