Martin Singull

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In this paper we consider the problem of testing (a) sphericity and (b) intraclass covariance structure under a Growth Curve model. The maximum likelihood estimator (MLE) for the mean in a Growth Curve model is a weighted estimator with the inverse of the sample covariance matrix which is unstable for large p close to N and singular for p larger than N .(More)
In this paper the extended growth curve model with two terms and a linearly structured covariance matrix is considered. We propose an estimation procedure that handles linearly structured covariance matrices. The idea is first to estimate the covariance matrix when finding the inner product in a regression space and thereafter reestimate it when it should(More)
The goal of this paper is to present and prove a cumulantmoment recurrent relation formula in free probability theory. It is convenient tool to determine underlying compactly supported distribution function. The existing recurrent relations between these objects require the combinatorial understanding of the idea of non-crossing partitions, which has been(More)
In this paper we consider the extended generalized multivariate analysis of variance (GMANOVA) with a linearly structured covariance matrix. The main theme is to find explicit estimators for the mean and for the linearly structured covariance matrix. We show how to decompose the residual space, the orthogonal complement to the mean space, into m + 1(More)
There is a growing interest in the analysis of multi-way data. In some studies the inference about the dependencies in three-way data is done using the third order tensor normal model, where the focus is on the estimation of the variance-covariance matrix which has a Kronecker product structure. Little attention is paid to the structure of the mean, though,(More)
Two regime switching models for predicting temperature dynamics are presented in this study for the purpose to be used for weather derivatives pricing. One is an existing model in the literature (Elias model) and the other is presented in this paper. The new model we propose in this study has a mean reverting heteroskedastic process in the base regime and a(More)
In this paper, the issue of analysis of multivariate repeated measures data that follow a monotonic sample pattern for small area estimation is addressed. Random effects growth curve models with covariates for both complete and incomplete data are formulated. A conditional likelihood based approach is proposed for estimation of the mean parameters and(More)
In this paper, we consider the problem of estimating and testing a general linear hypothesis in a general multivariate linear model, the so called Growth Curve model, when the p×N observation matrix is normally distributed with an unknown covariance matrix. The maximum likelihood estimator (MLE) for the mean is a weighted estimator with the inverse of the(More)
In this paper, we discuss an application of Small Area Estimation (SAE) techniques under a multivariate linear regression model for repeated measures data to produce district level estimates of crop yield for beans which comprise two varieties, bush beans and climbing beans in Rwanda during agricultural seasons 2014. By using the micro data of National(More)
The problem of estimating mean and covariances of a multivariate normally distributed random vector has been studied in many forms. This paper focuses on the estimators proposed by Ohlson et al. (2011) for a banded covariance structure with m-dependence. We rewrite the estimator when m = 1, which makes it easier to analyze. This leads to an adjustment, and(More)