Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests Under Nonstandard Conditions

Self, Steven G.; Liang, Kung‐Yee

doi:10.2307/2289471

Cited by 967 publications

(931 citation statements)

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“…As M0 represents the case where the variance is constrained to the boundary of the parameter space, the distribution of 4.6 times the LOD score for M1 is a 50 : 50 mixture of a w 2 distribution on one degree of freedom and a point mass at zero. The LOD score for M2 has a more complicated distribution that is a mixture of w 2 random variables, 80 but conservatively, one can use the w 2 with the higher degrees of freedom. To distinguish the type of LOD score reported, we use the term VC-LOD to indicate results from VC analysis, and LOD or LOD max to indicate LOD scores or maximum LOD scores from parametric analysis (see below).…”

Section: Statistical Analysesmentioning

confidence: 99%

A genome scan in multigenerational families with dyslexia: Identification of a novel locus on chromosome 2q that contributes to phonological decoding efficiency

et al. 2005

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Dyslexia is a common and complex developmental disorder manifested by unexpected difficulty in learning to read. Multiple different measures are used for diagnosis, and may reflect different biological pathways related to the disorder. Impaired phonological decoding (translation of written words without meaning cues into spoken words) is thought to be a core deficit. We present a genome scan of two continuous measures of phonological decoding ability: phonemic decoding efficiency (PDE) and word attack (WA). PDE measures both accuracy and speed of phonological decoding, whereas WA measures accuracy alone. Multipoint variance component linkage analyses (VC) and Markov chain Monte-Carlo (MCMC) multipoint joint linkage and segregation analyses were performed on 108 families. A strong signal was observed on chromosome 2 for PDE using both VC (LOD ¼ 2.65) and MCMC methods (intensity ratio (IR) ¼ 32.1). The IR is an estimate of the ratio of the posterior to prior probability of linkage in MCMC analysis. The chromosome 2 signal was not seen for WA. More detailed mapping with additional markers provided statistically significant evidence for linkage of PDE to chromosome 2, with VC-LOD ¼ 3.0 and IR ¼ 59.6 at D2S1399. Parametric analyses of PDE, using a model obtained by complex segregation analysis, provided a multipoint maximum LOD ¼ 2.89. The consistency of results from three analytic approaches provides strong evidence for a locus on chromosome 2 that influences speed but not accuracy of phonological decoding. Molecular Psychiatry (2005) 10, 699-711.

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Section: Statistical Analysesmentioning

confidence: 99%

A genome scan in multigenerational families with dyslexia: Identification of a novel locus on chromosome 2q that contributes to phonological decoding efficiency

et al. 2005

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“…Although a QTL on OAR3 appears to be a common (1) (Self and Liang, 1987 finding across studies, not all have been in the same segment and some large-scale studies (e.g. Crawford et al, 2006) have failed to find any evidence on chromosome 3.…”

Section: Discussionmentioning

confidence: 99%

“…The test statistic was 22[lnL (QTL) 2 lnL (no QTL) ] where L () is the likelihood of each model. Critical values for the LRT were taken from 1 2 x 2 (1) (Self and Liang, 1987) since the null hypothesis represents a boundary value for the variance component.…”

Section: Statistical Analyses For Qtl Verificationmentioning

confidence: 99%

Confirmation of two quantitative trait loci regions for nematode resistance in commercial British terminal sire breeds

Matika

Pong‐Wong

Woolliams

et al. 2011

Animal

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Sheep internal parasites (nematodes) remain a major health challenge and are costly for pasture-based production systems. Most current breeding programmes for nematode resistance are based on indicator traits such as faecal egg counts (FEC), which are costly and laborious to collect. Hence, genetic markers for resistance would be advantageous. However, although some quantitative trait loci (QTL) have been identified, these QTL are often not consistent across breeds and few breeding strategies for nematode resistance in sheep are currently using molecular information. In this study, QTL for nematode resistance on ovine chromosomes (OAR) 3 and 14, previously identified in the Blackface breed, were explored using commercial Suffolk (n 5 336) and Texel lambs (n 5 879) sampled from terminal sire breeder flocks in the United Kingdom. FEC were used as the indicator trait for nematode resistance, and these were counted separately for Nematodirus and Strongyles genera. Microsatellite markers were used to map the QTL and the data were analysed using interval mapping regression techniques and variance component analysis. QTL for Nematodirus and Strongyles FEC were found to be segregating on OAR3 at 5% chromosome region-wide significance threshold in both Suffolk and Texel sheep, and Nematodirus FEC QTL were segregating on OAR14 in both breeds. In addition, QTL for growth traits were also found to be segregating at 5% chromosome region-wide on OAR3 and OAR14. The confirmation that FEC QTL segregate in the same position in three widely used breeds widens their potential applicability to purebred Blackface, Suffolk and Texel sheep, with benefits likely to be observed in their commercial crossbred progeny.

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“…The second step was REML analyses using these matrices as covariance matrices for the QTL effect. The test for a significant variance due to the QTL was performed using a likelihood ratio test (LR) with a 5% significance threshold of 2.71 [23].…”

Section: Interval Mappingmentioning

confidence: 99%

Precision of methods for�calculating identity-by-descent matrices using multiple markers

et al. 2002

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-A rapid, deterministic method (DET) based on a recursive algorithm and a stochastic method based on Markov Chain Monte Carlo (MCMC) for calculating identity-by-descent (IBD) matrices conditional on multiple markers were compared using stochastic simulation. Precision was measured by the mean squared error (MSE) of the relationship coefficients in predicting the true IBD relationships, relative to MSE obtained from using pedigree only. Comparisons were made when varying marker density, allele numbers, allele frequencies, and the size of full-sib families. The precision of DET was 75-99% relative to MCMC, but was not simply related to the informativeness of individual loci. For situations mimicking microsatellite markers or dense SNP, the precision of DET was ≥ 95% relative to MCMC. Relative precision declined for the SNP, but not microsatellites as marker density decreased. Full-sib family size did not affect the precision. The methods were tested in interval mapping and marker assisted selection, and the performance was very largely determined by the MSE. A multi-locus information index considering the type, number, and position of markers was developed to assess precision. It showed a marked empirical relationship with the observed precision for DET and MCMC and explained the complex relationship between relative precision and the informativeness of individual loci. IBD / genetic relationship / multiple markers / complex pedigree / information

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Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests Under Nonstandard Conditions

Cited by 967 publications

References 0 publications

A genome scan in multigenerational families with dyslexia: Identification of a novel locus on chromosome 2q that contributes to phonological decoding efficiency

A genome scan in multigenerational families with dyslexia: Identification of a novel locus on chromosome 2q that contributes to phonological decoding efficiency

Confirmation of two quantitative trait loci regions for nematode resistance in commercial British terminal sire breeds

Precision of methods for�calculating identity-by-descent matrices using multiple markers

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