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On July 1 2010 new rules regarding cross-border group deductions came into force in Sweden. The rules are based on a series of judgements which were delivered by the Court of Justice of the European Union and subsequent rulings deriving from the Swedish Supreme Administrative Court. The new set of rules is supposed to make the Swedish group consolidation system in line with EU law in the area of cross-border group consolidations. The new rules allow a resident parent to deduct the losses stemming from its non-resident subsidiary but only if the subsidiary has exhausted all the possibilities to take those losses into account in its own state of origin and the losses cannot be utilized in the future by the subsidiary or a third party. Furthermore, the non-resident subsidiary needs to be liquidated for the parent to be able to show that the possibilities have been exhausted. However, before even considering whether the subsidiary has exhausted the losses there is one criterion that need to be fulfilled; the criterion of a wholly owned subsidiary. The criterion of a wholly owned subsidiary requires a resident parent to directly own its non-resident subsidiary without any intermediate companies and that shareholding must correspond to more than 90 percent. It is the requirement of a direct shareholding which post a concern to whether that criterion can be seen as in compliance with the case-law stemming from The Court of Justice of the European Union and the Swedish Supreme Administrative Court. After revising and analysing the case-law stemming from the Court of Justice and the Swedish Supreme Administrative Court it is the author’s belief that the criterion of a wholly owned subsidiary, due to the requirement of a direct shareholding, is not in conformity with EU law and cannot be justified by the justification grounds put forward by the Swedish government.

This thesis contributes to the field of Gaussian Graphical Models by exploring either numerically or theoretically various topics of Bayesian Methods in Gaussian Graphical Models and by providing a number of interesting results, the further exploration of which would be promising, pointing to numerous future research directions. Gaussian Graphical Models are statistical methods for the investigation and representation of interdependencies between components of continuous random vectors. This thesis aims to investigate some issues related to the application of Bayesian methods for Gaussian Graphical Models. We adopt the popular $G$-Wishart conjugate prior $W_G(\delta,D)$ for the precision matrix. We propose an efficient sampling method for the $G$-Wishart distribution based on the Metropolis Hastings algorithm and show its validity through a number of numerical experiments. We show that this method can be easily used to estimate the Deviance Information Criterion, providing a computationally inexpensive approach for model selection. In addition, we look at the marginal likelihood of a graphical model given a set of data. This is proportional to the ratio of the posterior over the prior normalizing constant. We explore methods for the estimation of this ratio, focusing primarily on applying the Monte Carlo simulation method of path sampling. We also explore numerically the effect of the completion of the incomplete matrix $D^{\mathcal{V}}$, hyperparameter of the $G$-Wishart distribution, for the estimation of the normalizing constant. We also derive a series of exact and approximate expressions for the Bayes Factor between two graphs that differ by one edge. A new theoretical result regarding the limit of the normalizing constant multiplied by the hyperparameter $\delta$ is given and its implications to the validity of an improper prior and of the subsequent Bayes Factor are discussed.

The purpose of this action research is to discover how self-evaluation training affects students’ knowledge and understanding about their writing and needs for improvement. In this study of 46 fifth and sixth graders, students underwent a four-stage self-evaluation training process. This involved students in defining criteria for their stories, teaching them how to apply the criteria using a variety of samples, giving students feedback about their self-evaluations, and developing action plans The study showed that after the self-evaluation process was set into place, students had an increased awareness of what made a good fictional writing piece. The self-evaluation process helped students become more aware of writing practices and of themselves as a writer. The study also found that the self-evaluation process set clear guidelines for students, focused student attention on important writing criteria, and opened up the conversation between students and teachers about evaluation, goal setting and the writing process.

The purpose of this action research is to discover how self-evaluation training affects students’ knowledge and understanding about their writing and needs for improvement. In this study of 46 fifth and sixth graders, students underwent a four-stage self-evaluation training process. This involved students in defining criteria for their stories, teaching them how to apply the criteria using a variety of samples, giving students feedback about their self-evaluations, and developing action plans The study showed that after the self-evaluation process was set into place, students had an increased awareness of what made a good fictional writing piece. The self-evaluation process helped students become more aware of writing practices and of themselves as a writer. The study also found that the self-evaluation process set clear guidelines for students, focused student attention on important writing criteria, and opened up the conversation between students and teachers about evaluation, goal setting and the writing process.

This thesis contributes to the field of Gaussian Graphical Models by exploring either numerically or theoretically various topics of Bayesian Methods in Gaussian Graphical Models and by providing a number of interesting results, the further exploration of which would be promising, pointing to numerous future research directions. Gaussian Graphical Models are statistical methods for the investigation and representation of interdependencies between components of continuous random vectors. This thesis aims to investigate some issues related to the application of Bayesian methods for Gaussian Graphical Models. We adopt the popular $G$-Wishart conjugate prior $W_G(\delta,D)$ for the precision matrix. We propose an efficient sampling method for the $G$-Wishart distribution based on the Metropolis Hastings algorithm and show its validity through a number of numerical experiments. We show that this method can be easily used to estimate the Deviance Information Criterion, providing a computationally inexpensive approach for model selection. In addition, we look at the marginal likelihood of a graphical model given a set of data. This is proportional to the ratio of the posterior over the prior normalizing constant. We explore methods for the estimation of this ratio, focusing primarily on applying the Monte Carlo simulation method of path sampling. We also explore numerically the effect of the completion of the incomplete matrix $D^{\mathcal{V}}$, hyperparameter of the $G$-Wishart distribution, for the estimation of the normalizing constant. We also derive a series of exact and approximate expressions for the Bayes Factor between two graphs that differ by one edge. A new theoretical result regarding the limit of the normalizing constant multiplied by the hyperparameter $\delta$ is given and its implications to the validity of an improper prior and of the subsequent Bayes Factor are discussed.

在迴歸分析中，若變數間具有非線性的關係時，B-Spline線性迴歸是以無母數的方式建立模型。B-Spline函數為具有節點(knots)的分段多項式，選取合適節點的位置對B-Spline的估計有重要的影響，在近年來許多的文獻中已提出一些尋找節點位置的估計方法，而本文中我們提出了一種基於Bayesian information criterion(BIC)的節點估計方式。 我們想要深入了解在不同類型的迴歸函數間，各種選取節點方法的配適效果與模擬時間，並且加以比較，在使用B-Spline函數估計時，能夠使用合適的方法尋找節點。 / In regression analysis, when the relation between the response variable and the explanatory variable is nonlinear, one can use nonparametric methods to estimate the regression function. B-Spline regression is one of the popular nonparametric regression methods. B-Splines are piecewise polynomial joint at knots, and the choice of knot locations is crucial. Zhou and Shen (2001) proposed to use spatially adaptive regression splines (SARS), where the knots are estimated using a selection scheme. Dimatteo, Genovese, and Kass (2001) proposed to use Bayesian adaptive regression splines (BARS), where certain priors for knot locations are considered. In this thesis, a knot estimation method based on the Bayesian information criterion (BIC) is proposed, and simulation studies are carried out to compare BARS, SARS and the proposed BIC-based method.

In this dissertation we first consider a parallel linear model with correlated dual responses on a symmetric compact design region and construct locally optimal designs for estimating the location-shift parameter. These locally optimal designs are variant under linear transformation of the design space and depend on the correlation between the dual responses in an interesting and sensitive way. Subsequently, minimax and maximin efficient designs for estimating the location-shift parameter are derived. A comparison of the behavior of efficiencies between the minimax and maximin efficient designs relative to locally optimal designs is also provided. Both minimax or maximin efficient designs have advantage in terms of estimating efficiencies in different situations. Thirdly, we consider a linear regression model with a one-dimensional control variable x and an m-dimensional response variable y=(y_1,...,y_m). The components of y are correlated with a known covariance matrix. The calibration problem discussed here is based on the assumed regression model. It is of interest to obtain a suitable estimation of the corresponding x for a given target T=(T_1,...,T_m) on the expected responses. Due to the fact that there is more than one target value to be achieved in the multiresponse case, the m expected responses may meet their target values at different respective control values. Consideration includes the deviation of the expected response E(y_i) from its corresponding target value T_i for each component and the optimal value of calibration point x, say x_0, is considered to be the one which minimizes the weighted sum of squares of such deviations within the range of x. The objective of this study is to find a locally optimal design for estimating x_0, which minimizes the mean square error of the difference between x_0 and its estimator. It shows the optimality criterion is approximately equivalent to a c-criterion under certain conditions and explicit solutions with dual responses under linear and quadratic polynomial regressions are obtained.

In this thesis, symbol timing recovery based on matched filtering in Gaussian Minimum Shift Keying (GMSK) with bandwidth-bit period product (BT) of 0.3 is investigated. GMSK is the standard modulation type for GSM. Although GMSK modulation is non-linear, it is approximated to Offset Quadrature Amplitude Modulation (OQAM), which is a linear modulation, so that Maximum Likelihood Sequence Estimation (MLSE) method is possible in the receiver part. In this study Typical Urban (TU) channel model developed in COST 207 is used. Two methods are developed on the construction of the matched filter. In order to obtain timing recovery for GMSK signals, these methods are investigated. The fractional time delays are acquired by using interpolation and an iterative maximum search process. The performance of the proposed symbol timing recovery (STR) scheme is assessed by using computer simulations. It is observed that the STR tracks the variations of the frequency selective multipath fading channels almost the same as the Mazo criterion.

Consider the D-optimal designs for the dth-degree polynomial regression model with a bounded and positive weight function on a compact interval. As the degree of the model goes to infinity, we show that the D-optimal design converges weakly to the arcsin distribution. If the weight function is equal to 1, we derive the formulae of the values of the D-criterion for five classes of designs including (i) uniform density design; (ii) arcsin density design; (iii) J_{1/2,1/2} density design; (iv) arcsin support design and (v) uniform support design. The comparison of D-efficiencies among these designs are investigated; besides, the asymptotic expansions and limits of their D-efficiencies are also given. It shows that the D-efficiency of the arcsin support design is the highest among the first four designs.