Asymptotics for Marginal Generalized Linear Models With Sparse Correlations

Marginal generalized linear models can be used for clustered and longitudinal data by fitting a model as if the data were independent and using an empirical estimator of parameter standard errors. We extend this approach to data where the number of observations correlated with a given one grows with sample size and show that parameter estimates are consistent and asymptotically Normal with a slower convergence rate than for independent data, and that an information sandwich variance estimator is consistent. We present two problems that motivated this work, the modelling of patterns of HIV genetic variation and the behavior of clustered data estimators when clusters are large.

On the use of Cramér-Rao minimum variance bounds for the design of magnetic resonance spectroscopy experiments

Localized Magnetic Resonance Spectroscopy (MRS) is in widespread use for clinical brain research. Standard acquisition sequences to obtain one-dimensional spectra suffer from substantial overlap of spectral contributions from many metabolites. Therefore, specially tuned editing sequences or two-dimensional acquisition schemes are applied to extend the information content. Tuning specific acquisition parameters allows to make the sequences more efficient or more specific for certain target metabolites. Cramér-Rao bounds have been used in other fields for optimization of experiments and are now shown to be very useful as design criteria for localized MRS sequence optimization. The principle is illustrated for one- and two-dimensional MRS, in particular the 2D separation experiment, where the usual restriction to equidistant echo time spacings and equal acquisition times per echo time can be abolished. Particular emphasis is placed on optimizing experiments for quantification of GABA and glutamate. The basic principles are verified by Monte Carlo simulations and in vivo for repeated acquisitions of generalized two-dimensional separation brain spectra obtained from healthy subjects and expanded by bootstrapping for better definition of the quantification uncertainties.

Cross-Country Evidence on Output Growth Volatility: Nonstationary Variance and GARCH Models

This paper revisits the issue of conditional volatility in real GDP growth rates for Canada, Japan, the United Kingdom, and the United States. Previous studies find high persistence in the volatility. This paper shows that this finding largely reflects a nonstationary variance. Output growth in the four countries became noticeably less volatile over the past few decades. In this paper, we employ the modified ICSS algorithm to detect structural change in the unconditional variance of output growth. One structural break exists in each of the four countries. We then use generalized autoregressive conditional heteroskedasticity (GARCH) specifications modeling output growth and its volatility with and without the break in volatility. The evidence shows that the time-varying variance falls sharply in Canada, Japan, and the U.K. and disappears in the U.S., excess kurtosis vanishes in Canada, Japan, and the U.S. and drops substantially in the U.K., once we incorporate the break in the variance equation of output for the four countries. That is, the integrated GARCH (IGARCH) effect proves spurious and the GARCH model demonstrates misspecification, if researchers neglect a nonstationary unconditional variance.

Bayesian generalized linear models for meta-analysis of diagnostic tests

With the recognition of the importance of evidence-based medicine, there is an emerging need for methods to systematically synthesize available data. Specifically, methods to provide accurate estimates of test characteristics for diagnostic tests are needed to help physicians make better clinical decisions. To provide more flexible approaches for meta-analysis of diagnostic tests, we developed three Bayesian generalized linear models. Two of these models, a bivariate normal and a binomial model, analyzed pairs of sensitivity and specificity values while incorporating the correlation between these two outcome variables. Noninformative independent uniform priors were used for the variance of sensitivity, specificity and correlation. We also applied an inverse Wishart prior to check the sensitivity of the results. The third model was a multinomial model where the test results were modeled as multinomial random variables. All three models can include specific imaging techniques as covariates in order to compare performance. Vague normal priors were assigned to the coefficients of the covariates. The computations were carried out using the 'Bayesian inference using Gibbs sampling' implementation of Markov chain Monte Carlo techniques. We investigated the properties of the three proposed models through extensive simulation studies. We also applied these models to a previously published meta-analysis dataset on cervical cancer as well as to an unpublished melanoma dataset. In general, our findings show that the point estimates of sensitivity and specificity were consistent among Bayesian and frequentist bivariate normal and binomial models. However, in the simulation studies, the estimates of the correlation coefficient from Bayesian bivariate models are not as good as those obtained from frequentist estimation regardless of which prior distribution was used for the covariance matrix. The Bayesian multinomial model consistently underestimated the sensitivity and specificity regardless of the sample size and correlation coefficient. In conclusion, the Bayesian bivariate binomial model provides the most flexible framework for future applications because of its following strengths: (1) it facilitates direct comparison between different tests; (2) it captures the variability in both sensitivity and specificity simultaneously as well as the intercorrelation between the two; and (3) it can be directly applied to sparse data without ad hoc correction. ^

Variance and covariance of actual relationship between relatives at one locus.

The relationship between pairs of individuals is an important topic in many areas of population and quantitative genetics. It is usually measured as the proportion of thegenome identical by descent shared by the pair and it can be inferred from pedigree information. But there is a variance in actual relationships as a consequence of Mendelian sampling, whose general formula has not been developed. The goal of this work is to develop this general formula for the one-locus situation,. We provide simple expressions for the variances and covariances of all actual relationships in an arbitrary complex pedigree. The proposed method relies on the use of the nine identity coefficients and the generalized relationship coefficients; formulas have been checked by computer simulation. Finally two examples for a short pedigree of dogs and a long pedigree of sheep are given.

Response of Catch-Per-Unit-Effort to Spatial and Environmental Factors: an Exploratory Data Analysis Using Generalized Additive Models

Understanding spatial distributions and how environmental conditions influence catch-per-unit-effort (CPUE) is important for increased fishing efficiency and sustainable fisheries management. This study investigated the relationship between CPUE, spatial factors, temperature, and depth using generalized additive models. Combinations of factors, and not one single factor, were frequently included in the best model. Parameters which best described CPUE varied by geographic region. The amount of variance, or deviance, explained by the best models ranged from a low of 29% (halibut, Charlotte region) to a high of 94% (sablefish, Charlotte region). Depth, latitude, and longitude influenced most species in several regions. On the broad geographic scale, depth was associated with CPUE for every species, except dogfish. Latitude and longitude influenced most species, except halibut (Areas 4 A/D), sablefish, and cod. Temperature was important for describing distributions of halibut in Alaska, arrowtooth flounder in British Columbia, dogfish, Alaska skate, and Aleutian skate. The species-habitat relationships revealed in this study can be used to create improved fishing and management strategies.

Variance-balanced designs under interference for dependent observations

It is shown that variance-balanced designs can be obtained from Type I orthogonal arrays for many general models with two kinds of treatment effects, including ones for interference, with general dependence structures. These designs can be used to obtain optimal and efficient designs. Some examples and design comparisons are given. (C) 2002 Elsevier B.V. All rights reserved.

Analysis of Melanoma Onset: Assessing Familial Aggregation by Using Estimating Equations and Fitting Variance Components via Bayesian Random Effects Models

We investigate whether relative contributions of genetic and shared environmental factors are associated with an increased risk in melanoma. Data from the Queensland Familial Melanoma Project comprising 15,907 subjects arising from 1912 families were analyzed to estimate the additive genetic, common and unique environmental contributions to variation in the age at onset of melanoma. Two complementary approaches for analyzing correlated time-to-onset family data were considered: the generalized estimating equations (GEE) method in which one can estimate relationship-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modeled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov Chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the free ware package BUGS. In addition, we also used a Bayesian model to investigate the relative contribution of genetic and environmental effects on the expression of naevi and freckles, which are known risk factors for melanoma.

A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.

The distribution of the sample minimum-variance frontier

In this paper, we present a finite sample analysis of the sample minimum-variance frontier under the assumption that the returns are independent and multivariate normally distributed. We show that the sample minimum-variance frontier is a highly biased estimator of the population frontier, and we propose an improved estimator of the population frontier. In addition, we provide the exact distribution of the out-of-sample mean and variance of sample minimum-variance portfolios. This allows us to understand the impact of estimation error on the performance of in-sample optimal portfolios. Key Words: minimum-variance frontier; efficiency set constants; finite sample distribution