EDA on the asymptotic normality of the standardized sequential stopping times, Part-I: Parametric models

DOI10.1080/07474946.2018.1548847zbMath1421.62114OpenAlexW2919256905MaRDI QIDQ4632467

Nitis Mukhopadhyay, Chen Zhang

Publication date: 29 April 2019

Published in: Sequential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07474946.2018.1548847

zbMATH Keywords

reliabilityasymptoticsstopping timeconfidence intervalpoint estimationKolmogorov-Smirnov testshelf lifetumor studiesnormal populationsecond-order efficiencylinex losscancer researchnegative exponential populationselstandardized stopping variable

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Parametric tolerance and confidence regions (62F25) Applications of statistics to biology and medical sciences; meta analysis (62P10) Approximations to statistical distributions (nonasymptotic) (62E17) Sequential statistical analysis (62L10) Sequential estimation (62L12) Optimal stopping in statistics (62L15)

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Cites Work

• The order of the normal approximation for a Studentized U-statistic
• Asymptotic normality of the stopping time of some sequential procedures
• Second order approximations for sequential point and interval estimation
• A nonlinear renewal theory with applications to sequential analysis. I
• The Berry-Esseen theorem for U-statistics
• A nonlinear renewal theory with applications to sequential analysis II
• Some recent results on the distributions of stopping times of compound Poisson processes with linear boundaries
• Modified Linex two-stage and purely sequential estimation of the variance in a normal distribution with illustrations using horticultural data
• Sample path analysis and distributions of boundary crossing times
• Multistage point estimation methodologies for a negative exponential location under a modified linex loss function: Illustrations with infant mortality and bone marrow data
• On fixed-accuracy and bounded accuracy confidence interval estimation problems in Fisher’s “Nile” example
• Stage‐Wise Adaptive Designs
• Sequential estimation problems for negative exponential populations
• Sequential Methods and Their Applications
• On Exact and Asymptotic Properties of Two-Stage and Sequential Estimation of the Normal Mean Under LINEX Loss
• On the Asymptotic Regret While Estimating the Location of an Exponential Distribution
• Asymptotic results for stopping times based on u-statistics
• On the convergence rate of fixed-width sequential confidence intervals
• Analysis of data from life-test experiments under an exponential model
• Convergence rates of sequential confidence intervals and tests for the mean of a u-statistic
• The exact approximation order in the central-limit-theorem for random summation
• Fixed width confidence intervals for the location parameter of an exponential distribution
• On the Asymptotic Theory of Fixed-Width Sequential Confidence Intervals for the Mean
• On the Asymptotic Efficiency of a Sequential Procedure for Estimating the Mean
• Approximate Fiducial Bounds on Reliability for the Two Parameter Negative Exponential Distribution
• Linear Statistical Inference and its Applications
• A Class of Statistics with Asymptotically Normal Distribution
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