Miscellanea. The directed modified profile likelihood in models with many nuisance parameters

Sartori, Nicola; Bellio, Ruggero; Salvan, Alessandra; Pace, Luigi

doi:10.1093/biomet/86.3.735

Cited by 23 publications

(15 citation statements)

References 8 publications

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“…A more challenging example, considered by Sartori et al (1999), involves a high-dimensional nuisance parameter. We observe Y i j (i = 1, .…”

Section: ·2 Multisample Normal Modelmentioning

confidence: 99%

Distribution of likelihood-basedp-values under a local alternative hypothesis

Lee¹,

Young

2016

Biometrika

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SUMMARYWe consider inference on a scalar parameter of interest in the presence of a nuisance parameter, using a likelihood-based statistic which is asymptotically normally distributed under the null hypothesis. Higher-order expansions are used to compare the repeated sampling distribution, under a general contiguous alternative hypothesis, of p-values calculated from the asymptotic normal approximation to the null sampling distribution of the statistic with the distribution of p-values calculated by bootstrap approximations. The results of comparisons in terms of power of different testing procedures under an alternative hypothesis are closely related to differences under the null hypothesis, specifically the extent to which testing procedures are conservative or liberal under the null. Empirical examples are given which demonstrate that higher-order asymptotic effects may be seen clearly in small-sample contexts.

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“…A more challenging example, considered by Sartori et al (1999), involves a high-dimensional nuisance parameter. We observe Y i j (i = 1, .…”

Section: ·2 Multisample Normal Modelmentioning

confidence: 99%

Distribution of likelihood-basedp-values under a local alternative hypothesis

Lee¹,

Young

2016

Biometrika

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“…See e.g. simulation results in DiCiccio and Martin (1993), DiCiccio and Stern (1994), Sartori et al (1999), Bellio and Sartori (2006). Therefore, broader perspectives for theoretical justification of adjustments of profile loglikelihood are called for.…”

Section: Modifications Of Profile Likelihoodmentioning

confidence: 99%

Adjustments of profile likelihood through predictive densities

2010

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“…However, the standard normal approximation for the modiÿed signed proÿle likelihood ratio has only ÿrst-order accuracy (Sartori et al, reference [9], p. 737), thus we will not explore it further in the paper.…”

Section: Likelihood-based Confidence Intervalsmentioning

confidence: 99%

Likelihood‐based confidence intervals for a log‐normal mean

Jiang²

2003

Statistics in Medicine

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To construct a confidence interval for the mean of a log-normal distribution in small samples, we propose likelihood-based approaches - the signed log-likelihood ratio and modified signed log-likelihood ratio methods. Extensive Monte Carlo simulation results show the advantages of the modified signed log-likelihood ratio method over the signed log-likelihood ratio method and other methods. In particular, the modified signed log-likelihood ratio method produces a confidence interval with a nearly exact coverage probability and highly accurate and symmetric error probabilities even for extremely small sample sizes. We then apply the methods to two sets of real-life data.

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Miscellanea. The directed modified profile likelihood in models with many nuisance parameters

Cited by 23 publications

References 8 publications

Distribution of likelihood-basedp-values under a local alternative hypothesis

Distribution of likelihood-basedp-values under a local alternative hypothesis

Adjustments of profile likelihood through predictive densities

Likelihood‐based confidence intervals for a log‐normal mean

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