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In this paper, we present a statistical approach to evaluate the relationship between variables observed in a two-factors experiment. We consider a three-level model with covariance structure Σ ⊗ Ψ 1 ⊗ Ψ 2 , where Σ is an arbitrary positive definite covariance matrix, and Ψ 1 and Ψ 2 are both correlation matrices with a compound symmetric structure corresponding to two different factors. The Rao's score test is used to test the hypotheses that observations grouped by one or two factors are uncorrelated. We analyze a fermentation process to illustrate the results. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

Starting from a simple Gauss–Markov model, this paper presents notes about criteria for the estimability of parametric functions of the vector of interest in linear models. The results obtained for the transformed models are compared with known results from the literature. [ABSTRACT FROM AUTHOR]

In this paper we present properties of an algorithm to determine the maximum likelihood estimators of the covariance matrix when two processes jointly affect the observations. Additionally, one process is partially modeled by a compound symmetry structure. We perform a simulation study of the properties of an iteratively determined estimator of the covariance matrix. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the association between two random vectors related to two groups of characteristics. To analyze the multivariate association, the ρV coefficient and distance correlation are used. Two methods (classical and recent) are compared and illustrated with real data. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the association between two random vectors related to two groups of characteristics. To analyze the multivariate association, the ρV coefficient and distance correlation are used. Two methods (classical and recent) are compared and illustrated with real data. [ABSTRACT FROM AUTHOR]

The aim of the paper is to determine maximum-likelihood estimation equations. Observations follow a multivariate normal distribution,, where,anddescribe the unknown covariance structure between rows and columns of, respectively. Imposing restrictions onandfour types of covariance structures will be considered. [ABSTRACT FROM AUTHOR]

In the article, properties of the Bennett test and Miller test are analyzed. Assuming that the sample size is the same for each sample and considering the null hypothesis that the coefficients of variation forkpopulations are equal against the hypothesis thatk− 1 coefficients of variation are the same but differ from the coefficient of variation for thekth population, the empirical significance level and the power of the test are studied. Moreover, the dependence of the test statistic and the power of the test on the ratio of coefficients of variation are considered. The analyses are performed on simulated data. [ABSTRACT FROM AUTHOR]

Logit and probit models belong to the class of generalised linear models. A few applications of both models have been documented in the field of forestry. The objective of this paper was to test the parallel use of these models to discover the differences in damage to a spruce stand after thinning using the full tree system, the long wood system and the short wood system. In particular the aim was to ascertain the general damage probability caused by the harvesting systems (HS) and the particular damage class probability in each HS. When the general damage probability was calculated the logit model was used. When nine damage classes were taken into account, however, the probit model was found to fit the data better. In this case, the results obtained gave accurate information on the probability of the appearance of a particular damage class for each HS. It was concluded that the probit and logit models should be considered in parallel in order to obtain the best possible goodness of fit and to get accurate information on the distribution of damage classes. [ABSTRACT FROM AUTHOR]

In general, varieties of any cultivated species can differ in many aspects. One of the desirable traits in breeding new varieties is high yield, which can be significantly reduced by plant diseases. This study is an extension of previous research about the resistance of seed pea lines to downy mildew, and provides an extended analysis of this type of experiment. The probability of a degree of infection is determined based on a logistic model with a multinomial distribution. In the analysis the impact of a fixed effect of variety and random environmental effects is considered. It is shown that the environmental effects (combinations of years and location – macro-environments) significantly influence the resistance to diseases, and the differences among environments are larger than the variability of differences among genotypes over all environments. For two types of soils (light and rich) the most resistant varieties, which are significantly different from the control variety, are indicated. [ABSTRACT FROM AUTHOR]