Fixed Width Confidence Interval ofP(X&lt;Y) in Partial Sequential Sampling Scheme

Bandyopadhyay, Uttam; Das, Radhakanta; Biswas, Atanu

doi:10.1081/sqa-120022084

Cited by 5 publications

(3 citation statements)

References 11 publications

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“…As our limit result encompasses all H-differentiable functionals, this leads to new confidence sets for many estimators, the Nelson-Aalen estimator being one of them. In this connection we remark that Bandyopadhyay et al (2003) find fixedvalue confidence intervals for the H-differentiable functional ( 16)…”

Section: Sequential Confidence Setsmentioning

confidence: 82%

The Copula Information Criterion and Its Implications for the Maximum Pseudo-Likelihood Estimator

Grønneberg¹

2010

Dependence Modeling

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Chapter 1. Introduction to the Thesis 1. From the ancients to 1640 2. The first limit theorem and the variable N ε 2.1. Improvements on the Bernoulli bound 2.2. Uniformity and the Vapnik-Chervonenkis inequalities 2.3. CLT-based approximations for the tail of N ε 2.4. Full circle: Calculating the quantiles of the limiting distribution 2.5. A new type of sequential confidence bands for the Nelson-Aalen estimator 3. Gorgias' revenge: Model selection and pragmatism 3.1. Two-stage model selection procedures 3.2. The way ahead: Non-asymptotic model-selection 3.3. A connection between the AIC and N ε 4. Non-standard alternative models: Regression with jumps Chapter 2. Paper 1: On the errors committed by sequences of estimator functionals Chapter 3. Paper 2: The Copula Information Criterion and its implications for the Maximum Pseudo Likelihood Estimator Chapter 4. Paper 3: The Copula Information Criteria Chapter 5. Paper 4: Estimation and Inference for Jump Regression Models 1 That is, the time between around 1750 to 1830, not the classical period of the ancients.

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Section: Sequential Confidence Setsmentioning

confidence: 82%

The Copula Information Criterion and Its Implications for the Maximum Pseudo-Likelihood Estimator

Grønneberg¹

2010

Dependence Modeling

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“…Govindarajulu (1974) has considered the sequential procedure for the problem of obtaining the confidence interval for the parameter R in three cases, the first of which assumes that (X, Y) follow the bivariate normal distribution and the next two apply the nonparametric approaches. Bandyopadhyay et al (2003) considered a nonparametric fixed-width confidence interval estimation for the parameter R by adopting a partial sequential sampling scheme. Recently, Mukhopadhyay and Zhuang (2016) have considered a fixed-accuracy interval for the reliability parameter under a bivariate exponential model, namely, the Fisher's Nile example.…”

Section: Introductionmentioning

confidence: 99%

Sequential-Based Approach for Estimating the Stress-Strength Reliability Parameter for Exponential Distribution

Khalifeh

Mahmoudi

Dolati

2020

JIRSS

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In this paper, two-stage and purely sequential estimation procedures are considered to construct fixed-width confidence intervals for the reliability parameter under the stress-strength model when the stress and strength are independent exponential random variables with different scale parameters. The exact distribution of the stopping rule under the purely sequential procedure is approximated using the law of large numbers and Monte Carlo integration. For the two-stage sequential procedure, explicit formulas for the distribution of the total sample size, the expected value and mean squared error of the maximum likelihood estimator of the reliability parameter under the stress-strength model are provided. Moreover, it is shown that both proposed sequential procedures are finite, and in exceptional cases, the exact distribution of stopping times is degenerate distribution at the initial sample size. The performances of the proposed methodologies are investigated with the help of simulations. Finally using real data, the procedures are clearly illustrated.

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Section: Sequential Confidence Setsmentioning

confidence: 99%

On the errors committed by sequences of estimator functionals

Grønneberg

Hjort

2011

Math. Meth. Stat.

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Abstract. Consider a sequence of estimatorsθ n which converges almost surely to θ 0 as the sample size n tends to infinity. Under weak smoothness conditions, we identify the asymptotic limit of the last timeθ n is further than ε away from θ 0 when ε → 0 + . These limits lead to the construction of sequentially fixed width confidence regions for which we find analytic approximations. The smoothness conditions we impose is thatθ n is to be close to a Hadamard-differentiable functional of the empirical distribution, an assumption valid for a large class of widely used statistical estimators. Similar results were derived in Hjort and Fenstad (1992, Annals of Statistics) for the case of Euclidean parameter spaces; part of the present contribution is to lift these results to situations involving parameter functionals. The apparatus we develop is also used to derive appropriate limit distributions of other quantities related to the far tail of an almost surely convergent sequence of estimators, like the number of times the estimator is more than ε away from its target. We illustrate our results by giving a new sequential simultaneous confidence set for the cumulative hazard function based on the Nelson-Aalen estimator and investigate a problem in stochastic programming related to computational complexity.

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Fixed Width Confidence Interval ofP(X<Y) in Partial Sequential Sampling Scheme

Cited by 5 publications

References 11 publications

The Copula Information Criterion and Its Implications for the Maximum Pseudo-Likelihood Estimator

The Copula Information Criterion and Its Implications for the Maximum Pseudo-Likelihood Estimator

Sequential-Based Approach for Estimating the Stress-Strength Reliability Parameter for Exponential Distribution

On the errors committed by sequences of estimator functionals

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