A General Theory of Three-Stage Estimation Strategy with Second-Order Asymptotics and Its Applications

Nitis Mukhopadhyay () and Soumik Banerjee ()
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Nitis Mukhopadhyay: University of Connecticut-Storrs
Soumik Banerjee: University of Connecticut-Storrs

Sankhya A: The Indian Journal of Statistics, 2023, vol. 85, issue 1, No 15, 440 pages

Abstract: Abstract We begin with a generic expression of an optimal fixed-sample-size n∗ which has an expression λg(𝜃) with λ > 0 and g(𝜃) > 0 where 𝜃 is an unknown parameter. A consistent estimator of 𝜃 is a sample mean of independent and identically distributed (i.i.d.) random variables. Under fairly relaxed set of conditions on g(.), we have developed a general theory of three-stage sampling strategy detailing requisite mathematical techniques for proving both asymptotic (as λ → ∞ $\lambda \rightarrow \infty $ ) first-order and second-order analyses. We believe that this theory is broad and rich especially since the technicalities developed are not tailored to fit a specific inference problem of choice. We have validated this sentiment with the help of illustrations which cannot be handled satisfactorily by improvising upon some of the existing methodologies. For example, (i) Illustration 1 proposes a three-stage strategy under Linex loss in a recently developed inference problem; (ii) Illustration 2 handles estimation of 𝜃 in a Uniform(0,𝜃) distribution which obviously stays outside an exponential family; and (iii) Illustration 3 incorporates expressions of g(.) functions which no existing paper’s analyses could treat.

Keywords: Estimation; First-order; Linex; Risk; Regret; Second-order; Unified theory.; 62L12; 62L05; 62L10 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13171-021-00253-4

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