Sequential Methods and Their Applications

Minimum Risk Point Estimation of Gini Index

“…Therefore, the Gini index estimator G Nc is indeed AMRPE. The optimality properties in part (ii) and (iii) are well known in the sequential literature as asymptotic first-order efficiency and asymptotic first-order risk efficiency respectively (see Mukhopadhyay and de Silva, 2009). Theorem 3.1 also holds for the stopping rule defined in (2.6).…”

A sequential hypothesis test based on a generalized Azuma inequality

“…of X in a sequential manner (see e.g. [4]), only stopping when we have sufficient evidence to accept either of the two following alternative hypotheses,…”

“…Another, related bound is the Azuma-Hoeffding inequality, which gives a bound on tail probabilities of martingales with bounded differences. 4 Since our process Z n is a martingale with bounded differences, the Azuma-Hoeffding inequality could be used to establish a fixed sample size test, even if the Chernoff-Hoeffding bound may be tighter. This possibility was already mentioned in [3], and was recently investigated in [7] and [8].…”

An Approach to Robustness Evaluation for Sequential Testing under Functional Distortions in L1-metric

“…The sequential approach to hypothesis testing (Wald 1947) is applied in various practical problems of statistical data analysis (Mukhopadhyay and de Silva 2009). If hypothetical suppositions are fulfilled, sequential tests require less observations at average in comparison with classical analogues based on the fixed number of observations, to provide the fixed small levels of error probabilities.…”