Confidence intervals and point estimators for a normal mean under purely sequential strategies involving Gini’s mean difference and mean absolute deviation

Mukhopadhyay, Nitis; Jun, Hu

doi:10.1080/07474946.2017.1319684

Cited by 14 publications

(10 citation statements)

References 31 publications

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“…(C4) follows from (C5) to (C6) as shown in Lemma 3.2. (C7) can be verified in the spirit of the proof of Lemma 3.3 in Mukhopadhyay and Hu (2017). A direct proof of (5.12) will follow from our main result, Theorem 4.1, since W n substituted by M n will satisfy all the stated conditions (C1)-(C7).…”

Section: Illustration 3:  ≡ mentioning

confidence: 70%

“…It is clear that our brief justifications of Theorems 3.1 and 3.2 under general conditions mildly overlap with the lines of proofs of Theorems 3.2 and 4.2 from Mukhopadhyay and Hu (2017). However, we keep these justifications for identifying which sufficient conditions from (C1) to (C7) are specifically used in validating the respective steps.…”

Section: Remark 33mentioning

confidence: 85%

“…From a practical point of view, one should lean in favor of using W n 's from either  2 or  3 . More pertinent details with regard to robustness issues are found in Mukhopadhyay and Hu (2017).…”

Section: Illustration 3:  ≡ mentioning

confidence: 99%

“…In the spirit of Mukhopadhyay and Hu (2017), we implemented the purely sequential MRPE methodologies based on various stopping rules given by (5.3), (5.7), and (5.11) respectively under the normal case. To be more specific, we generated pseudorandom samples from a N(5, 4) population.…”

Section: Simulationsmentioning

confidence: 99%

“…The objective of this paper is to revisit in depth the purely sequential minimum risk point estimation methodologies involving GMD or MAD established in Mukhopadhyay and Hu (2017). Having proposed a new purely sequential methodology based on nonparametric estimators with some certain conditions satisfied, we develop asymptotic second-order results which are considerably stronger than those reported.…”

Section: Introduction and A Brief Reviewmentioning

confidence: 97%

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Second-order asymptotics in a class of purely sequential minimum risk point estimation (MRPE) methodologies

Jun

Mukhopadhyay

2018

Jpn J Stat Data Sci

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Under the squared error loss plus linear cost of sampling, we revisit the minimum risk point estimation (MRPE) problem for an unknown normal mean when the variance 2 also remains unknown. We begin by defining a new class of purely sequential MRPE methodologies based on a general estimator W n for satisfying a set of conditions in proposing the requisite stopping boundary. Under such appropriate set of sufficient conditions on W n and a properly constructed associated stopping variable, we show that (i) the normalized stopping time converges in law to a normal distribution (Theorem 3.3), and (ii) the square of such a normalized stopping time is uniformly integrable (Theorem 3.4). These results subsequently lead to an asymptotic second-order expansion of the associated regret function in general (Theorem 4.1). After such general considerations, we include a number of substantial illustrations where we respectively substitute appropriate multiples of Gini's mean difference and the mean absolute deviation in the place of the general estimator W n . These illustrations show a number of desirable asymptotic first-order and secondorder properties under the resulting purely sequential MRPE strategies. We end this discourse by highlighting selected summaries obtained via simulations.

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Section: Illustration 3:  ≡ mentioning

confidence: 70%

Section: Remark 33mentioning

confidence: 85%

Section: Illustration 3:  ≡ mentioning

confidence: 99%

Section: Simulationsmentioning

confidence: 99%

Section: Introduction and A Brief Reviewmentioning

confidence: 97%

See 3 more Smart Citations