Some New Aspects of Statistical Inference for Multistage Dose-Response Models with Applications

Sinha, Bimal K.; Kopylev, Leonid; Fox, John

doi:10.18187/pjsor.v8i3.519

Cited by 4 publications

(11 citation statements)

References 19 publications

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“…They also explicitly derived the LRT for several particular situations but were not completely correct for some of these. Sinha et al [12] and Kopylev and Sinha [13] solved some of the cases in [2] and derived asymptotic distribution of the LRT for some other important special cases. All these results are summarized below.…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

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Constrained Parameters in Applications: Review of Issues and Approaches

Kopylev

2012

ISRN Biomathematics

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This review article provides an introduction to statistical issues that arise when some statistical model parameters are constrained. This often happens in applications, in particular in testing for variance components (e.g., genomics) and construction of one-sided confidence intervals (e.g., environmental risk analysis). Heuristic explanations are provided, and a number of general and recent statistical results that appeared in statistical literature are summarized for use in applications. Simulation results are shown for illustration of consequences of ignoring parameters on the boundary. Special attention is paid to likelihood ratio tests, but other approaches to confidence interval construction, such as Wald, bootstrap, and Bayesian are also briefly discussed. This paper presents examples from the risk assessment field and genomics, but all conclusions apply to whenever one-sided testing is conducted. Recommendations are provided for dealing with parameters on the boundary for a range of situations.

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Section: Maximum Likelihood Estimationmentioning

confidence: 99%

“…(i) When one or several parameters of interest not on the boundary and some nuisance parameters are on the boundary, the asymptotic distribution of the LRT remains χ 2 with corresponding degrees of freedom [12].…”

Section: Likelihood Ratio Tests a Pioneering Theoretical Articlementioning

confidence: 99%

Constrained Parameters in Applications: Review of Issues and Approaches

Kopylev

2012

ISRN Biomathematics

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“…39 and 40 of Sinha et al (2007) that the min θ 1 =0,θ 2 ≥0,θ 3 ≥0 Q 0 (θ |Z) will consist of four terms depending on the signs of the four residual random variables:…”

Section: Two Nuisance Parameters On the Boundarymentioning

confidence: 99%

“…2.20, upon direct simplification, the minimum value of Q 0 (Z) under H 0 is (quoted from the Eq. 40 of Sinha et al 2007)…”

Section: Two Nuisance Parameters On the Boundarymentioning

confidence: 99%

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On the asymptotic distribution of likelihood ratio test when parameters lie on the boundary

Kopylev

Sinha

2011

Sankhya B

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The paper discusses statistical inference dealing with the asymptotic theory of likelihood ratio tests when some parameters may lie on boundary of the parameter space. We derive a closed form solution for the case when one parameter of interest and one nuisance parameter lie on the boundary. The asymptotic distribution is not always a mixture of several chi-square distributions. For the cases when one parameter of interest and two nuisance parameters or two parameters of interest and one nuisance parameter are on the boundary, we provide an explicit solution which can be easily computed by simulation. These results can be used in many applications, e.g. testing for random effects in genetics. Contrary to the claim of some authors in the applied literature that use of chi-square distribution with degrees of freedom as in case of interior parameters will be too conservative when some parameters are on the boundary, we show that when nuisance parameters are on the boundary, that approach may often be anti-conservative.Keywords Likelihood ratio test · Nuisance parameters on the boundary · One-sided tests · Parameters of interest on the boundary · Quadratic forms

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Improved inference for a boundary parameter

et al. 2023

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The limiting distributions of statistics used to test hypotheses about parameters on the boundary of their domains may provide very poor approximations to the finite‐sample behaviour of these statistics, even for very large samples. We review theoretical work on this problem, describe hard and soft boundaries and iceberg estimators, and give examples highlighting how the limiting results greatly underestimate the probability that the parameter lies on its boundary even in very large samples. We propose and evaluate some simple remedies for this difficulty based on normal approximation for the profile score function, and then outline how higher order approximations yield excellent results in a range of hard and soft boundary examples. We use the approach to develop an accurate test for the need for a spline component in a linear mixed model.

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Some New Aspects of Statistical Inference for Multistage Dose-Response Models with Applications

Abstract: Applications of the results to dose-response multistage models serve as illustrations. The paper considers various scenarios, and is expected to be of interest to practitioners of risk analysis.

Cited by 4 publications

References 19 publications

Constrained Parameters in Applications: Review of Issues and Approaches

Constrained Parameters in Applications: Review of Issues and Approaches

On the asymptotic distribution of likelihood ratio test when parameters lie on the boundary

Improved inference for a boundary parameter

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