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In this paper, we consider the estimated weights of the tangency portfolio. We derive analytical expressions for the higher order non-central and central moments of these weights when the returns are assumed to be independently and multivariate normally distributed. Moreover, the expressions for mean, variance, skewness and kurtosis of the estimated weights are obtained in closed forms. Later, we complement our results with a simulation study where data from the multivariate normal and t-distributions are simulated, and the first four moments of estimated weights are computed by using the Monte Carlo experiment. It is noteworthy to mention that the distributional assumption of returns is found to be important, especially for the first two moments. Finally, through an empirical illustration utilizing returns of four financial indices listed in NASDAQ stock exchange, we observe the presence of time dynamics in higher moments., Funding Agency:Örebro University

We propose asymptotic approximations for the probabilities of misclassification in linear discriminant analysis when the group means follow a growth curve structure. The discriminant function can classify a new observation vector of p repeated measurements into one of several multivariate normal populations with equal covariance matrix. We derive certain relations of the statistics under consideration in order to obtain asymptotic approximation of misclassification errors for the two group case. Finally, we perform Monte Carlo simulations to evaluate the reliability of the proposed results., Funding Agencies|Swedish Research CouncilSwedish Research CouncilEuropean Commission [2017-03003]

We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the discriminant function coefficients is derived, which is then used to obtain their asymptotic distribution under the high-dimensional asymptotic regime. We investigate the performance of the classification analysis based on the discriminant function in both small and large dimensions. A stochastic representation is established, which allows to compute the error rate in an efficient way. We further compare the calculated error rate with the optimal one obtained under the assumption that the covariance matrix and the two mean vectors are known. Finally, we present an analytical expression of the error rate calculated in the high-dimensional asymptotic regime. The finite-sample properties of the derived theoretical results are assessed via an extensive Monte Carlo study., Funding Agencies:Swedish International Development Cooperation Agency (SIDA) through the TZ-Sweden Programme for Research, Higher Education and Institutional Advancement Örebro University project "Models for macro and financial economics after the financial crisis" - Jan Wallander and Tom Hedelius Foundation P18-0201

We study the distributional properties of the linear discriminant function under the assumption of normality by comparing two groups with the same covariance matrix but different mean vectors. A stochastic representation for the discriminant function coefficients is derived, which is then used to obtain their asymptotic distribution under the high-dimensional asymptotic regime. We investigate the performance of the classification analysis based on the discriminant function in both small and large dimensions. A stochastic representation is established, which allows to compute the error rate in an efficient way. We further compare the calculated error rate with the optimal one obtained under the assumption that the covariance matrix and the two mean vectors are known. Finally, we present an analytical expression of the error rate calculated in the high-dimensional asymptotic regime. The finite-sample properties of the derived theoretical results are assessed via an extensive Monte Carlo study.

This thesis consists of two papers which take a critical look on functions of an inverse Wishart matrix and a Gaussian vector. In the first paper, the product expression, of which the inverse of the pooled estimator of the covariance matrix is inverse Wishart distributed and the difference of sample means is multivariate normally distributed, is investigated by exploring the distributional properties via a stochastic representation for both the finite sample case and the infinite sample case under the large-dimensional asymptotic regime. A test theory is developed to study the contribution of population coefficients in the discriminant function. Furthermore, we investigate the performance of the classification analysis based on the discriminant function. In the second paper, the expression of the product of the inverse sample covariance matrix and the sample mean vector with regard to the derivation of moments of the estimated tangency portfolio weights is studied. In particular, higher order central and non-central moments of the elements of such a product are obtained. Moreover, the closed-form expressions of the second, the third and the fourth central moments are provided whose expressions do not depend on special mathematical functions, like the confluent hypergeometric function. Furthermore, we deduce analytical expressions for the mean, the variance, the skewness, and the kurtosis from the higher-order central and non-central moments of the tangency portfolio weights. Finally, the developed results have been successfully applied to real weekly data of eight stocks traded on NASDAQ.

In this paper we consider the estimated weights of tangency portfolio. The returns are assumed to be independently and multivariate normally distributed. We derive analytical expressions for the higher order non-central and central moments of these weights. Moreover, the expressions for mean, variance, skewness and kurtosis of the estimated weights are obtained in closed-forms. Finally, we complement our result with an empirical study where we analyze a portfolio with actual returns of eight financial indexes listed in NASDAQ stock exchange.

In this paper we consider the estimated tangency portfolio weights. We derive analytical expressions for the higher central and non-central moments of these weights. Main focus has been given to skewness and kurtosis due to the importance of asymmetry and heavy tails of the data. We complement our results with an empirical study where we analyze an international diversified portfolio.