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Nitis Mukhopadhyay - One of the best experts on this subject based on the ideXlab platform.

  • Plug-In Sequential Normal Density Estimation Under Unknown Variance: Mise Loss
    Calcutta Statistical Association Bulletin, 2020
    Co-Authors: Nitis Mukhopadhyay, William Pepe
    Abstract:

    Consider independent observations X1, X2,… having a common normal probability density function f(x;σ2)=(σ2π)−1exp(−x2/2σ2) with −∞ 0). We propose estimating f(x; σ2) with a purely sequential methodology under the mean integrated squared error (MISE) loss function. Our goal is to make the associated risk not to exceed a preassigned positive number c, referred to as the risk-bound. Since no fixed-sample-size methodology would be able to handle this estimation problem, Mukhopadhyay and Pepe (2009) first gave a two-stage sampling method. We show that our purely sequential density estimation methodology satisfies asymptotic (i) first-order efficiency property (Theorem 2.1) and (ii) first-order risk-efficiency property (Theorem 2.2) just like the Mukhopadhyay and Pepe two-stage methodology did. But, the present purely sequential density estimation methodology has better second-order efficiency property (Theorems 2.3 and 3.1) than those associated with the Mukhopadhyay and Pepe two-...

  • Two-stage estimation for a normal mean having a known lower bound of variance with final sample size defined via Gini’s mean difference and mean absolute deviation
    Sequential Analysis, 2018
    Co-Authors: Nitis Mukhopadhyay, Jun Hu
    Abstract:

    Revisiting Stein (1945, 1949) as well as Mukhopadhyay and Duggan (1997), we have proposed new two-stage procedures under both minimum risk point estimation and fixed-width confidence interv...

  • Multistage estimation of the difference of locations of two negative exponential populations under a modified Linex loss function: Real data illustrations from cancer studies and reliability analysis
    Sequential Analysis, 2016
    Co-Authors: Nitis Mukhopadhyay, Sudeep R. Bapat
    Abstract:

    ABSTRACTWe have designed modified two-stage and purely sequential strategies to estimate the difference of location parameters from two independent negative exponential populations having unknown but proportional scale parameters under a modified Linex loss function. This article extends one-sample methodologies of Mukhopadhyay and Bapat (2016, Sequential Analysis). Some preliminary results are established along the lines of Mukhopadhyay and Hamdy (1984, Canadian Journal of Statistics) and Mukhopadhyay and Darmanto (1988, Sequential Analysis). We have resorted to Mukhopadhyay and Duggan (1997, Sankhya, Series A) in developing asymptotic second-order properties for the modified two-stage methodology and to nonlinear renewal theory of Lai and Siegmund (1977, 1979, Annals of Statistics) and Woodroofe (1977, Annals of Statistics) in addressing analogous properties under the purely sequential methodology. Then, we supplement with extensive sets of data analysis via computer simulations validating that both mod...

  • Multistage point estimation methodologies for a negative exponential location under a modified linex loss function: Illustrations with infant mortality and bone marrow data
    Sequential Analysis, 2016
    Co-Authors: Nitis Mukhopadhyay, Sudeep R. Bapat
    Abstract:

    ABSTRACTWe have designed Stein-type (Stein, 1945, Annals of Mathematical Statistics) two-stage, modified two-stage (Mukhopadhyay and Duggan, 1997, Sankhya, Series A), and purely sequential strategies (Chow and Robbins, 1965, Annals of Mathematical Statistics) to estimate an unknown location parameter of a negative exponential distribution having an unknown scale parameter under a newly defined and modified Linex loss function. We aim at controlling the associated risk function per unit cost by bounding it from above with a fixed preassigned positive number, ω, and we emphasize both asymptotic first-order and asymptotic second-order properties for the modified two-stage and purely sequential estimation strategies. In developing asymptotic second-order properties for the modified two-stage methodology, we have heavily relied upon basic ideas rooted in Mukhopadhyay and Duggan (1997). In developing asymptotic second-order properties for the purely sequential methodology, however, we have heavily relied upon n...

  • Stirling’s Formula for Gamma Functions, Bounds for Ratios of Gamma Functions, Beta Functions and Percentiles of a Studentized Sample Mean: A Synthesis with New Results
    Methodology and Computing in Applied Probability, 2015
    Co-Authors: Nitis Mukhopadhyay
    Abstract:

    In the context of Stirling’s formula for gamma functions and bounds for ratios of gamma functions, this work has a threefold purpose: (1) Outline recently published literature; (2) Synthesize techniques and results from Bhattacharjee and Mukhopadhyay (Commun Stat, Theory & Methods 39:1046–1053, 2010) and Mukhopadhyay (Commun Stat, Theory & Methods 40:1283–1297, 2011) which have gone perhaps unnoticed by some recent researchers; and (3) Incorporate new results for beta functions and useful bounds for the percentiles of a Studentized sample mean obtained from a normal distribution. This synthesized review may help in gaining a wider perspective about this area.

Elwyn Graham John - One of the best experts on this subject based on the ideXlab platform.

Alan Davies - One of the best experts on this subject based on the ideXlab platform.

Arun Bandopadhyay - One of the best experts on this subject based on the ideXlab platform.