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In this paper the problem of classification of an observation into one of two Gaussian populations with different means and common variance is considered in the case when equicorrelated training sample is given. Unknown means and common variance are estimated from training sample and these estimators are pluged in the Bayes discriminant function. The maximum likelihood estimators are used. The approximation of the expected error rate associated with Bayes plug-in discriminant function is derived. Numerical analysis of the accuracy of that approximation for various values of correlation is presented.

Paper deals with statistical classification of spatial data as a part of widely applicable statistical approach to pattern recognition. Error rates in supervised classification of Gaussian random field observation into one of two populations specified by different constant means and common stationary geometric anisotropic covariance are considered. Formula for the exact Bayesian error rate is derived. The influence of the ratio of anisotropy to the error rates is evaluated numerically for the case of complete parametric certainty.

Shear stresses in planes perpendicular to the grain, so-called rolling shear stresses, need to be considered in the ultimate and serviceability limit state design of many timber structural elements. Knowledge about the rolling shear modulus and strength has further gained in importance since the invention and increased use of cross laminated timber (CLT). As a result of the orthogonal orientation of adjacent layers within CLT, rolling shear stresses develop when CLT is subjected to out-of-plane bending. Previous numerical and experimental studies on rolling shear are largely restricted to Norway spruce ( Picea abies (L.) Karst.). In the present study, experimental investigations on the rolling shear properties were carried out on six timber species. The two investigated coniferous species were Norway spruce ( Picea abies (L.) Karst.) and pine ( Pinus sylvestris L.). Four deciduous species, namely European beech ( Fagus sylvatica L.), European ash ( Fraxinus excelsior L.), poplar ( Populus tremula L.), and European birch ( Betula pendula R.) were investigated. Furthermore, different board geometries and sawing patterns were investigated. In comparison to Norway spruce, all other investigated species featured higher rolling shear properties. In particular, these of European beech and European ash were roughly three-times higher. In agreement with previous findings, the aspect ratio (board width vs. board thickness) as well as sawing pattern were identified as main influencing parameters on the rolling shear properties. In addition to single board segments, multi-segment systems were experimentally tested and numerically investigated. Parallel systems consisting of either two or four board segments were tested to obtain information on potential system effects of laminations within single CLT cross layers regarding rolling shear strength and rolling shear modulus, i.e. stresses may be distributed depending on the local stiffness. This system effect may influence the shear strength, the shear modulus, and the failure behaviour compared to the results of single segment testing. Often, CLT elements consist of more than one cross layer. Layups can also feature parallel layers, however, usually with grain in direction of the main span direction. Some of these layups have a remarkable potential for two-dimensional load transfer. Thus, these commonly double or triple layers are exposed to rolling shear by stresses in the weak load transfer direction. As rolling shear failure of one of the cross layers in layups featuring alternating orthogonal layers as well as layups featuring some parallel layers leads to the ultimate failure of the entire element, such elements can be considered as serial systems with regard to the rolling shear strength and rolling shear modulus. In order to investigate the serial-parallel system behaviour, multi-segment systems consisting of 4 × 3 board segments were tested. The investigated systems should allow linking the results obtained from single element testing to the actual behaviour of CLT laminations and, subsequently, to give recommendations for rolling shear test configurations as well as related rolling shear properties. The outcomes show a good comparability between the results from out-of-plane bending tests on CLT elements featuring rolling shear failures and EN 408-alike shear tests conducted on board segments. The analysis of the within- and between-boards variation of rolling shear properties and density is also a part of this paper. The results of this study provide an overview of the rolling shear properties of tested European softwood and hardwood species. The investigated species are already in use, or have a significant potential to be used for construction purposes in the near future. The findings regarding the influential material- and product-related parameters contribute to a better understanding of the mechanical behaviour of timber subjected to rolling shear. [ABSTRACT FROM AUTHOR]

A systematic investigation is still lacking for tension out-of-plane in cross laminated timber (CLT), as a planar timber construction product. The objectives of the present study are the determination of the tensile properties of CLT made of Norway spruce, the identification of essential product-specific influencing parameters and a comparative analysis with glulam. For this purpose, seven test series were defined, which allowed the determination of the tensile properties on board segments and thereof produced glulam and CLT specimens by varying the number of layers, layer orientation and number of elements within a layer. The orthogonal laminated structure of CLT led to between 50% and 70% higher tensile properties out-of-plane, which is explained by the different stress distribution compared to glulam; the regulation of 30% higher properties than for glulam is suggested. In addition, the lognormal distribution turned out to be a more representative distribution model for characterizing the tensile strength out-of-plane than the Weibull distribution. This was also confirmed with regard to the investigated serial and parallel system effects, in which a clearly more homogeneous behavior was found in CLT compared to glulam, which in turn can be attributed again to the different stress distributions. [ABSTRACT FROM AUTHOR]

A new covariance matrix estimator is proposed under the assumption that at every time period all pairwise correlations are equal. This assumption, which is pragmatically applied in various areas of finance, makes it possible to estimate arbitrarily large covariance matrices with ease. The model, called DECO, involves first adjusting for individual volatilities and then estimating correlations. A quasi-maximum likelihood result shows that DECO provides consistent parameter estimates even when the equicorrelation assumption is violated. We demonstrate how to generalize DECO to block equicorrelation structures. DECO estimates for U.S. stock return data show that (block) equicorrelated models can provide a better fit of the data than DCC. Using out-of-sample forecasts, DECO and Block DECO are shown to improve portfolio selection compared to an unrestricted dynamic correlation structure. [ABSTRACT FROM PUBLISHER]

Certification of crop seeds from a seed lot requires determination of the seed germination rate through tests governed by the International Seed Testing Association (ISTA) and the Association of Official Seed Analysts (AOSA). The results from four tests of 100 seeds each are compared with published tolerances to determine whether seed lots concur with a labeled germination rate. Examination of results from numerous corn and soybean seed lots sent to more than 30 member laboratories of the AOSA and the Society of Commercial Seed Technologists (SCST) suggested that, in aggregate, counts reported by the laboratories frequently show less sample variability than expected under independentbinomial sampling due to positive correlation among the individual test results. Whereas much of the recent literature on correlated binomial data is concerned with efficient methods for estimating the binomial success probabilities, comparatively little attention is paid to the problem of diagnosing whether correlations exist and are significant. Considering the replicate tests as clusters, we propose an estimator for the intercluster (interreplicate count) correlation coefficient and examine its statistical properties. Results from applying the estimator in unblinded and blinded seed tests are presented. The results are revealing; the estimates tend to be larger and significant in the unblinded seed tests. [ABSTRACT FROM AUTHOR]

Violation of sphericity of covariance across repeated measures inflates Type I error rates in univariate repeated-measures analysis of variance. Hence the use of Geisser--Greenhouse epsilon or Huynh-Feldt epsilon is now common (to provide improved Type I error rate), With nonsphericity, no method has been available to compute power. A convenient method is suggested for approximating power and test size under nonsphericity. New approximations are suggested for (a) a weighted sum of independent noncentral chi[sup 2]'s, (b) the trace of a noncentral Wishart (or pseudo-Wishart)matrix, (c) the expected values of epsilon and epsilon, and (d) the noncentral test statistic, whether corrected or uncorrected, The new approximations are extensions of the work of Box (1954a,b) and Satterthwaite (194l), The method performed well when evaluated against published and new simulations. [ABSTRACT FROM AUTHOR]