Restricted Likelihood Ratio Research Articles

Environmental Quality Preference and Benefit Estimation in Multinomial Probit Models: A Simulation Approach

AbstractSimulated maximum likelihood is used to estimate a random parameter multinomial probit model of destination choice for recreational fishing trips, formulated to accommodate varying tastes and varying perceptions of environmental quality across individuals. The restricted likelihood ratio test strongly rejects the independent probit model, which is similar to the independent logit model in both the parameter and benefit estimates. Furthermore, both the Krinsky‐Robb and bootstrapping procedures suggest that the benefit (standard deviation) of an environmental policy is found to be markedly lower (higher) when heterogeneous preferences are taken into account.

Interval Mapping of Quantitative Trait Loci through Order-Restricted Inference

An order-restricted version of the standard interval mapping procedure is introduced. The usual LOD scores (base 10 logs of likelihood ratios) used in interval mapping are replaced with LOD scores based on restricted likelihood ratio test statistics, which make use of known orderings in the genotype effects at the putative quantitative trait loci (QTL). Simulations demonstrate that individual tests based on the restricted LOD scores can be more powerful than tests based on the standard LOD scores. The new procedure appears to improve QTL detection capability and estimates of both position and genotype effects in certain circumstances. Techniques from orderrestricted inference are combined with the EM algorithm to estimate genotype effects and compute the restricted LOD scores.

Evaluation of a restricted likelihood ratio test for mapping quantitative trait loci with extreme discordant sib pairs.

Risch and Zhang recently proposed to use extreme discordant sib pairs for mapping quantitative trait loci. Here, it is shown that the set of genetically possible distributions of the number of marker alleles in such sib-pairs is described by two inequalities. Thus, a likelihood ratio test analogous to Holmans's possible triangle test for affected sib pairs can be defined. The performance of this test is compared to the mean test considered by Risch and Zhang. For most of the genetic models considered, the mean test is slightly more powerful than the restricted likelihood ratio test. However, for models with a rare recessive gene (or equivalently a common dominant gene), the restricted likelihood ratio test is much more powerful.

Evaluation of a restricted likelihood ratio test for mapping quantitative trait loci with extreme discordant sib pairs

Evaluation of a restricted likelihood ratio test for mapping quantitative trait loci with extreme discordant sib pairs

UI Score Tests for Some Restricted Alternatives in Exponential Families

In an exponential family of distributions, the problem of testing for homogeneity of a set of parameters against some restricted alternatives is considered. Incorporating Roy′s union-intersection (UI) principle, Rao′s efficient score test is extended to such restricted alternatives, and is shown to be asymptotically power-equivalent to the corresponding restricted likelihood ratio tests (for contiguous alternatives). Asymptotic null distributions of such UI score test statistics and their rates of convergence are studied. Multivariase problems for general forms of restricted alternatives are considered in the same vein. It is also shown that the UI score test is Bahadur deficiency of order O(log n).

On the power superiority of likelihood ratio tests for restricted alternatives

For the multivariate normal mean vector testing problem, it is shown that in the light of power comparison, the restricted likelihood ratio test (LRT) is uniformly more powerful than the blobal version for the entire restricted parameter space in many cases.

Asymptotic optimality of nonparametric tests for restricted alternatives in some multivariate mixed models

For some mixed models (involving both stochastic and nonstochastic predictors), a general class of permutationally distribution-free rank tests for some restricted alternative problems is considered. The proposed tests are asymptotically optimal in the light of the restricted likelihood ratio tests. For an ordered alternative problem in a two-way analysis of covariance model, the proposed tests are asymptotically optimal.

Behavior of fluorides in the preservation of wood: R. Nowotny. ( Oester. Chem. Zeit., igro, xiii)

Most statistical methods for microarray data analysis consider one gene at a time, and they may miss subtle changes at the single gene level. This limitation may be overcome by considering a set of genes simultaneously where the gene sets are derived from prior biological knowledge. We call a pathway as a predefined set of genes that serve a particular cellular or physiological function. Limited work has been done in the regression settings to study the effects of clinical covariates and expression levels of genes in a pathway on a continuous clinical outcome. A semiparametric regression approach for identifying pathways related to a continuous outcome was proposed by Liu et al. (2007), who demonstrated the connection between a least squares kernel machine for nonparametric pathway effect and a restricted maximum likelihood (REML) for variance components. However, the asymptotic properties on a semiparametric regression for identifying pathway have never been studied. In this paper, we study the asymptotic properties of the parameter estimates on semiparametric regression and compare Liu et al.'s REML with our REML obtained from a profile likelihood. We prove that both approaches provide consistent estimators, have n convergence rate under regularity conditions, and have either an asymptotically normal distribution or a mixture of normal distributions. However, the estimators based on our REML obtained from a profile likelihood have a theoretically smaller mean squared error than those of Liu et al.'s REML. Simulation study supports this theoretical result. A profile restricted likelihood ratio test is also provided for the non-standard testing problem. We apply our approach to a type II diabetes data set (Mootha et al., 2003).