Model selection under order restriction

Lincheng, Zhao; Peng, Limin

doi:10.1016/s0167-7152(01)00200-0

Cited by 6 publications

(3 citation statements)

References 4 publications

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“…However, the widely used AIC and BIC are designed for models with a fixed number of parameters, whereas the inequality constraints do not really specify any parameters explicitly. Some information criteria for order-restricted inference have been proposed recently [ 32 , 33 ], but they only apply to simple order constraints (3). We have recently proposed a new order-restricted information criterion (ORIC) function for general inequality profiles, which we show to always select the correct profile when the sample size is large enough (unpublished manuscript).…”

Section: Resultsmentioning

confidence: 99%

Information criterion-based clustering with order-restricted candidate profiles in short time-course microarray experiments

et al. 2009

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Background: Time-course microarray experiments produce vector gene expression profiles across a series of time points. Clustering genes based on these profiles is important in discovering functional related and co-regulated genes. Early developed clustering algorithms do not take advantage of the ordering in a time-course study, explicit use of which should allow more sensitive detection of genes that display a consistent pattern over time. Peddada et al.[1] proposed a clustering algorithm that can incorporate the temporal ordering using order-restricted statistical inference. This algorithm is, however, very time-consuming and hence inapplicable to most microarray experiments that contain a large number of genes. Its computational burden also imposes difficulty to assess the clustering reliability, which is a very important measure when clustering noisy microarray data.

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Section: Resultsmentioning

confidence: 99%

Information criterion-based clustering with order-restricted candidate profiles in short time-course microarray experiments

et al. 2009

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“…Several model or variable selection methods have been proposed involving isotonic or ordering restrictions, where the relationships are assumed to be monotone and variables can be chosen or not. Anraku (1999) proposed an information criterion specific to the order-restricted models, and Zhao and Peng (2002) used this for an isotonic dose-response problem, to determine at which levels the probability of a success increases. Peddada et al (2003) proposed a method for selecting and clustering genes in gene expression data, based on traditional order-restricted models.…”

Section: Shape and Model Selectionmentioning

confidence: 99%

A Framework for Estimation and Inference in Generalized Additive Models with Shape and Order Restrictions

Meyer¹

2018

Statist. Sci.

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Methodology for the partial linear generalized additive model is presented, where components for continuous predictors may be modeled with shape-constrained regression splines, and components for ordinal predictors may have partial orderings. The estimated mean function is obtained through a projection (or iteratively re-weighted projections) onto a polyhedral convex cone; this is key for formally derived inference procedures. Point-wise confidence bands and hypothesis tests for the individual components, as well as a model selection method, are proposed. These methods are available in the R package cgam.

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“…The use of the AIC statistic in isotonic models backs to Anraku (1999), yet posterior modifications have been introduced (see Zhao andPeng, 2002, andLiu et al 2009). In this paper, the idea of Kato (2009) and Rueda (2013) proposing a penalty term equal to 2D K (v) in a regression context has been applied.…”

Section: The Aic Criterion and The Degrees Of Freedommentioning

confidence: 99%

Checking unimodality using isotonic regression: an application to breast cancer mortality rates

Rueda

Ugarte

Militino

2015

Stoch Environ Res Risk Assess

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In some diseases it is well-known that a unimodal mortality pattern exists. A clear example in developed countries is breast cancer, where mortality increased sharply until the nineties and then decreased. This clear unimodal pattern is not necessarily applicable to all regions within a country. In this paper, we develop statistical tools to check if the unimodality pattern persists within regions using order restricted inference. Break points as well as confidence intervals are also provided. In addition, a new test for checking monotonicity against unimodality is derived allowing to discriminate between a simple increasing pattern and an up-then-down response pattern. A comparison with the widely used joinpoint regression technique under unimodality is provided. We show that the joinpoint technique could fail when the underlying function is not piecewise linear. Results will be illustrated using age-specific breast cancer mortality data from Spain in the period 1975-2005.

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Model selection under order restriction

Cited by 6 publications

References 4 publications

Information criterion-based clustering with order-restricted candidate profiles in short time-course microarray experiments

Information criterion-based clustering with order-restricted candidate profiles in short time-course microarray experiments

A Framework for Estimation and Inference in Generalized Additive Models with Shape and Order Restrictions

Checking unimodality using isotonic regression: an application to breast cancer mortality rates

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