A class of improved heteroskedasticity-consistent covariance matrix estimators

The heteroskedasticity-consistent covariance matrix estimator proposed by White (1980), also known as HC0, is commonly used in practical applications and is implemented into a number of statistical software. Cribari–Neto, Ferrari & Cordeiro (2000) have developed a bias-adjustment scheme that delivers bias-corrected White estimators. There are several variants of the original White estimator that also commonly used by practitioners. These include the HC1, HC2 and HC3 estimators, which have proven to have superior small-sample behavior relative to White’s estimator. This paper defines a general bias-correction mechamism that can be applied not only to White’s estimator, but to variants of this estimator as well, such as HC1, HC2 and HC3. Numerical evidence on the usefulness of the proposed corrections is also presented. Overall, the results favor the sequence of improved HC2 estimators.

Control charts for monitoring the mean vector and the covariance matrix of bivariate processes

In this article, we propose new control charts for monitoring the mean vector and the covariance matrix of bivariate processes. The traditional tools used for this purpose are the T (2) and the |S| charts. However, these charts have two drawbacks: (1) the T (2) and the |S| statistics are not easy to compute, and (2) after a signal, they do not distinguish the variable affected by the assignable cause. As an alternative to (1), we propose the MVMAX chart, which only requires the computation of sample means and sample variances. As an alternative to (2), we propose the joint use of two charts based on the non-central chi-square statistic (NCS statistic), named as the NCS charts. Once the NCS charts signal, the user can immediately identify the out-of-control variable. In general, the synthetic MVMAX chart is faster than the NCS charts and the joint T (2) and |S| charts in signaling processes disturbances.

Monitoring the mean vector and the covariance ­matrix of multivariate processes with sample means and sample ranges

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A single chart with supplementary runs rules for monitoring the mean vector and the covariance matrix of multivariate processes

The MRMAX chart is a single chart based on the standardized sample means and sample ranges for monitoring the mean vector and the covariance matrix of multivariate processes. User's familiarity with the computation of these statistics is a point in favor of the MRMAX chart. As a single chart, the recently proposed MRMAX chart is very appropriate for supplementary runs rules. In this article, we compare the supplemented MRMAX chart and the synthetic MRMAX chart with the standard MRMAX chart. The supplementary and the synthetic runs rules enhance the performance of the MRMAX chart. © 2013 Elsevier Ltd.

Genetic Variants in Matrix Metalloproteinase-9 Gene Modify Metalloproteinase-9 Levels in Black Subjects

Altered matrix metalloproteinases (MMPs) levels are involved in cardiovascular diseases and increased MMP-9 levels enhance the cardiovascular risk in apparently healthy subjects. We investigated the effects of MMP-9 gene polymorphisms and haplotypes on the circulating MMP-9 levels in healthy black subjects and the effects of an MMP-2 polymorphism on the plasma MMP-2 concentrations. We studied 190 healthy subjects, nonsmokers, self-reported as blacks (18-63 years). Genotypes for the MMP-2 C-1306T polymorphism and the MMP-9 C-1562T, 90(CA)(14-24) and Q279R polymorphisms (rs243865, rs3918242, rs2234681, and rs17576, respectively) were determined by TaqMan (R) Allele Discrimination assay and real-time polymerase chain reaction or restriction fragment length polymorphism. Alleles for the 90(CA)(14-24) polymorphism were grouped as low (L) when there were < 21 and high (H) when there were >= 21 CA repeats. The plasma levels of MMP-2 and MMP-9 were determined by gelatin zymography. The software PHASE 2.1 was used to estimate the haplotypes frequencies. Although we found no effects of the MMP-9 C-1562T or the Q279R polymorphisms on MMP-9 levels, higher MMP-9 levels were associated with the HH genotype for the -90(CA)(14-24) polymorphism compared with the HL or LL genotypes. Lower MMP-9 levels were found in carriers of the CRL haplotype (combining the C, R, and L alleles for the MMP-9 polymorphisms) compared with the CRH haplotype. Consistent with this finding, the CRL haplotype was more commonly found in subjects with low MMP-9 levels. The MMP-2 C-1306T polymorphism had no effects on the plasma MMP-2 levels. Our results show that MMP-9 genetic variations modify MMP-9 levels in black subjects and may offer biochemical evidence implicating MMP-9 in the pathogenesis of cardiovascular diseases in blacks.

The spatial sign covariance matrix and its application for robust correlation estimation

8 pages, 2 figures, to be published in the conference proceedings of 11th international conference "Computer Data Analysis & Modeling 2016"

Direct genetic analysis by matrix-assisted laser desorption/ionization mass spectrometry

An approach to analyzing single-nucleotide polymorphisms (SNPs) found in the human genome has been developed that couples a recently developed invasive cleavage assay for nucleic acids with detection by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS). The invasive cleavage assay is a signal amplification method that enables the analysis of SNPs by MALDI-TOF MS directly from human genomic DNA without the need for initial target amplification by PCR. The results presented here show the successful genotyping by this approach of twelve SNPs located randomly throughout the human genome. Conventional Sanger sequencing of these SNP positions confirmed the accuracy of the MALDI-TOF MS analysis results. The ability to unambiguously detect both homozygous and heterozygous genotypes is clearly demonstrated. The elimination of the need for target amplification by PCR, combined with the inherently rapid and accurate nature of detection by MALDI-TOF MS, gives this approach unique and significant advantages in the high-throughput genotyping of large numbers of SNPs, useful for locating, identifying, and characterizing the function of specific genes.

Age-specific inbreeding depression and components of genetic variance in relation to the evolution of senescence.

Two major theories of the evolution of senescence (mutation accumulation and antagonistic pleiotropy) make different predictions about the relationships between age, inbreeding effects, and the magnitude of genetic variance components of life-history components. We show that, under mutation accumulation, inbreeding decline and three major components of genetic variance are expected to increase with age in randomly mating populations. Under the simplest version of the antagonistic pleiotropy model, no changes in the severity of inbreeding decline, dominance variance, or the genetic variance of chromosomal homozygotes are expected, but additive genetic variance may increase with age. Age-specific survival rates and mating success were measured on virgin males, using lines extracted from a population of Drosophila melanogaster. For both traits, inbreeding decline and several components of genetic variance increase with age. The results are consistent with the mutation accumulation model, but can only be explained by antagonistic pleiotropy if there is a general tendency for an increase with age in the size of allelic effects on these life-history traits.

On the eigenvalues of the spatial sign covariance matrix in more than two dimensions

Acknowledgments Alexander Dürre was supported in part by the Collaborative Research Grant 823 of the German Research Foundation. David E. Tyler was supported in part by the National Science Foundation grant DMS-1407751. A visit of Daniel Vogel to David E. Tyler was supported by a travel grant from the Scottish Universities Physics Alliance. The authors are grateful to the editors and referees for their constructive comments.

Orthogonality defect and reduced search-space size for solving integer least-squares problems

In the context of ambiguity resolution (AR) of Global Navigation Satellite Systems (GNSS), decorrelation among entries of an ambiguity vector, integer ambiguity search and ambiguity validations are three standard procedures for solving integer least-squares problems. This paper contributes to AR issues from three aspects. Firstly, the orthogonality defect is introduced as a new measure of the performance of ambiguity decorrelation methods, and compared with the decorrelation number and with the condition number which are currently used as the judging criterion to measure the correlation of ambiguity variance-covariance matrix. Numerically, the orthogonality defect demonstrates slightly better performance as a measure of the correlation between decorrelation impact and computational efficiency than the condition number measure. Secondly, the paper examines the relationship of the decorrelation number, the condition number, the orthogonality defect and the size of the ambiguity search space with the ambiguity search candidates and search nodes. The size of the ambiguity search space can be properly estimated if the ambiguity matrix is decorrelated well, which is shown to be a significant parameter in the ambiguity search progress. Thirdly, a new ambiguity resolution scheme is proposed to improve ambiguity search efficiency through the control of the size of the ambiguity search space. The new AR scheme combines the LAMBDA search and validation procedures together, which results in a much smaller size of the search space and higher computational efficiency while retaining the same AR validation outcomes. In fact, the new scheme can deal with the case there are only one candidate, while the existing search methods require at least two candidates. If there are more than one candidate, the new scheme turns to the usual ratio-test procedure. Experimental results indicate that this combined method can indeed improve ambiguity search efficiency for both the single constellation and dual constellations respectively, showing the potential for processing high dimension integer parameters in multi-GNSS environment.

Sample size considerations and augmentation of computer experiments

Computer Experiments, consisting of a number of runs of a computer model with different inputs, are now common-place in scientific research. Using a simple fire model for illustration some guidelines are given for the size of a computer experiment. A graph is provided relating the error of prediction to the sample size which should be of use when designing computer experiments. Methods for augmenting computer experiments with extra runs are also described and illustrated. The simplest method involves adding one point at a time choosing that point with the maximum prediction variance. Another method that appears to work well is to choose points from a candidate set with maximum determinant of the variance covariance matrix of predictions.

Rank regression analysis of correlated water quality data from South East Queensland

With growing population and fast urbanization in Australia, it is a challenging task to maintain our water quality. It is essential to develop an appropriate statistical methodology in analyzing water quality data in order to draw valid conclusions and hence provide useful advices in water management. This paper is to develop robust rank-based procedures for analyzing nonnormally distributed data collected over time at different sites. To take account of temporal correlations of the observations within sites, we consider the optimally combined estimating functions proposed by Wang and Zhu (Biometrika, 93:459-464, 2006) which leads to more efficient parameter estimation. Furthermore, we apply the induced smoothing method to reduce the computational burden. Smoothing leads to easy calculation of the parameter estimates and their variance-covariance matrix. Analysis of water quality data from Total Iron and Total Cyanophytes shows the differences between the traditional generalized linear mixed models and rank regression models. Our analysis also demonstrates the advantages of the rank regression models for analyzing nonnormal data.