Multiple crossing sequential fixed-size confidence region methodologies for a multivariate normal mean vector

Mukhopadhyay, Nitis; Poruthotage, Sankha Muthu

doi:10.1016/j.stamet.2014.03.003

Statistical Methodology

2014

DOI: 10.1016/j.stamet.2014.03.003

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Multiple crossing sequential fixed-size confidence region methodologies for a multivariate normal mean vector

Nitis Mukhopadhyay

Sankha Muthu Poruthotage

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2014

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Cited by 2 publications

References 16 publications

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Discussion on “Sequential Estimation for Time Series Models” by T. N. Sriram and Ross Iaci

Solanky

2014

Sequential Analysis

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Professors T. N. Sriram and Ross Iaci have considered the problem of sequential estimation of the autoregressive parameter in an AR(1) model and construction of sequential confidence region for a parameter vector in a TAR(1) model. Using extensive simulations, the authors have attempted to resolve the theoretical conjuncture that a fully sequential stopping time can have a negative regret. Their work opens up new directions for further research and establishes the need for second-order expansions for the regret. In this discussion, I briefly address some issues related to the simulation studies for an AR(1) model.

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Discussion on “Sequential Estimation for Time Series Models” by T. N. Sriram and Ross Iaci

Solanky

2014

Sequential Analysis

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Multiple Crossing Sequential Fixed-Size Confidence Regions for Regression Parameters Under Normality

Poruthotage

Mukhopadhyay

2014

Sri Lankan J App Stats

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The purely sequential sampling procedure proposed by Mukhopadhyay and Abid (1986) is customarily used to construct a fixed-size confidence region for regression parameters. This methodology has asymptotic efficiency and asymptotic consistency properties, but it does not have the exact consistency property. We propose that sequential sampling be continued allowing the sample size to cross a corresponding boundary multiple times. The asymptotic efficiency and asymptotic consistency properties are ascertained for multiple crossing stopping rules (Theorem 2.1). A truncation technique as well as a fine-tuning adjustment are developed. The simulated data are generated by realistic models arising from a study that investigates the association between prostate-specific antigen (PSA) and a number of appropriate prognostic clinical covariates. We highlight via large-scale simulations the remarkable gain in nearly achieving the target coverage without significant over-sampling.

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Multiple crossing sequential fixed-size confidence region methodologies for a multivariate normal mean vector

Cited by 2 publications

References 16 publications

Discussion on “Sequential Estimation for Time Series Models” by T. N. Sriram and Ross Iaci

Discussion on “Sequential Estimation for Time Series Models” by T. N. Sriram and Ross Iaci

Multiple Crossing Sequential Fixed-Size Confidence Regions for Regression Parameters Under Normality

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