A New Framework of Multistage Estimation
arXiv:0809.1241 · doi:10.1103/PhysRevE.79.026307
Abstract
In this paper, we have established a unified framework of multistage parameter estimation. We demonstrate that a wide variety of statistical problems such as fixed-sample-size interval estimation, point estimation with error control, bounded-width confidence intervals, interval estimation following hypothesis testing, construction of confidence sequences, can be cast into the general framework of constructing sequential random intervals with prescribed coverage probabilities. We have developed exact methods for the construction of such sequential random intervals in the context of multistage sampling. In particular, we have established inclusion principle and coverage tuning techniques to control and adjust the coverage probabilities of sequential random intervals. We have obtained concrete sampling schemes which are unprecedentedly efficient in terms of sampling effort as compared to existing procedures.
254 pages, no figure; added more references; main results appeared in Proceedings of SPIE, Orlando, Florida, USA, April 2010 and 2011
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- Drop Splashing on a Dry Smooth Surface
- Coalescence in low-viscosity liquids
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Cited by in corpus (20)
- Coalescence of bubbles and drops in an outer fluid
- Viscous to Inertial Crossover in Liquid Drop Coalescence
- The inexorable resistance of inertia determines the initial regime of drop coalescence
- Coalescence of Liquid Drops: Different Models Versus Experiment
- Approach and Coalescence of Liquid Drops in Air
- Coalescence of Pickering emulsion droplets induced by an electric field
- Perturbed breakup of gas bubbles in water: Memory, gas flow, and coalescence
- Confidence Interval for the Mean of a Bounded Random Variable and Its Applications in Point Estimation
- A New Framework of Multistage Hypothesis Tests
- A Likelihood Ratio Approach for Probabilistic Inequalities
- New Probabilistic Inequalities from Monotone Likelihood Ratio Property
- Estimating the Parameters of Binomial and Poisson Distributions via Multistage Sampling
- Multistage Estimation of Bounded-Variable Means
- Sequential Tests of Statistical Hypotheses with Confidence Limits
- A Geometric Approach for Bounding Average Stopping Time
- Sequential Estimation Methods from Inclusion Principle
- Exact Methods for Multistage Estimation of a Binomial Proportion
- Multistage Hypothesis Tests for the Mean of a Normal Distribution
- On Estimation of Finite Population Proportion
- Asymptotically Optimal Sequential Estimation of the Mean Based on Inclusion Principle