Doctor of Philosophy / School of Family Studies and Human Services / Walter Schumm / Farrell J. Webb / There is considerable research on concepts of Blackness in America. Much of this research is conducted within a Eurocentric as opposed to an Afrocentric perspective. Social research has established that ideals, social norms, and values about Black minority groups may be shaped by dominant culture premises and that the dominant culture of any society can influence the attitudes, perceptions, and behaviors of minority group members coexisting within that culture. The White racial frame holds that over time a dominant cultural perspective in the U.S. has installed a positive orientation to “White” and whiteness and a strong negative orientation toward racial “others”, particularly toward Black Americans. The present research explores this phenomenon from an Afrocentric perspective, assessing propinquity preferences of non-native Immigrant and native-born American Blacks toward native-born Blacks. Utilizing data drawn from The National Survey on American Life 2001-2003 (Jackson, 2007) the study assessed the degree of Black propinquity (i.e., self-identified feelings of closeness and identity preferences with native-born Blacks) expressed within and between subsamples of native-born African American (n = 3,464) and non-native (chiefly Afro-Caribbean) Blacks (n = 1,118). More specifically, it hypothesized that native-born Blacks would display greater propinquity preferences than Immigrant Blacks for native-American Blacks depicted as more economically-challenged as well as socially affluent and elite; also, it expected they would report greater support for socially undesirable as well as socially desirable Blacks than would Immigrant Blacks. A series of hierarchical regression analyses modeled the unique and joint predictive variance of socio-demographic, socio-economic, and Black (derived) target characteristics within each Black subpopulation against the primary outcome variable (propinquity). Overall regression models for each Black group were highly similar in the proportion of explained variance (27% for native Blacks; 26% for Immigrant Blacks) and weighted contributions of three blocks of variables; derived variables for Black target characteristics contributed most of the total variance within each group. No statistically reliable differences for R score values were found between the two Black subpopulations on these derived variables. Findings are discussed in the context of the White racial frame perspective, secondary data methodology, and future research.

In many areas of science one often has a given matrix, representing for example a measured data set and is required to find a matrix that is closest in a suitable norm to the matrix and possesses additionally a structure, inherited from the model used or coming from the application. We call these problems structured matrix nearness problems. We look at three different groups of these problems that come from real applications, analyze the properties of the corresponding matrix structure, and propose algorithms to solve them efficiently. The first part of this thesis concerns the nearness problem of finding the nearest k factor correlation matrix C(X) = diag(I_n -XX T)+XX T to a given symmetric matrix, subject to natural nonlinear constraints on the elements of the n x k matrix X, where distance is measured in the Frobenius norm. Such problems arise, for example, when one is investigating factor models of collateralized debt obligations (CDOs) or multivariate time series. We examine several algorithms for solving the nearness problem that differ in whether or not they can take account of the nonlinear constraints and in their convergence properties. Our numerical experiments show that the performance of the methods depends strongly on the problem, but that, among our tested methods, the spectral projected gradient method is the clear winner. In the second part we look at two two-sided optimization problems where the matrix of unknowns Y ε R {n x p} lies in the Stiefel manifold. These two problems come from an application in atomic chemistry where one is looking for atomic orbitals with prescribed occupation numbers. We analyze these two problems, propose an analytic optimal solution of the first and show that an optimal solution of the second problem can be found by solving a convex quadratic programming problem with box constraints and p unknowns. We prove that the latter problem can be solved by the active-set method in at most 2p iterations. Subsequently, we analyze the set of optimal solutions C}= {Y ε R n x p:Y TY=I_p,Y TNY=D} of the first problem for N symmetric and D diagonal and find that a slight modification of it is a Riemannian manifold. We derive the geometric objects required to make an optimization over this manifold possible. We propose an augmented Lagrangian-based algorithm that uses these geometric tools and allows us to optimize an arbitrary smooth function over C. This algorithm can be used to select a particular solution out of the latter set C by posing a new optimization problem. We compare it numerically with a similar algorithm that ,however, does not apply these geometric tools and find that our algorithm yields better performance. The third part is devoted to low rank nearness problems in the Q-norm, where the matrix of interest is additionally of linear structure, meaning it lies in the set spanned by s predefined matrices U₁,..., U_s ε {0,1} n x p. These problems are often associated with model reduction, for example in speech encoding, filter design, or latent semantic indexing. We investigate three approaches that support any linear structure and examine further the geometric reformulation by Schuermans et al. (2003). We improve their algorithm in terms of reliability by applying the augmented Lagrangian method and show in our numerical tests that the resulting algorithm yields better performance than other existing methods.

Η παρούσα μεταπτυχιακή διατριβή εντάσσεται ερευνητικά στην περιοχή της Στατιστικής Θεωρίας Αποφάσεων και ειδικότερα στην εκτίμηση των παραμέτρων στο μοντέλο της διπαραμετρικής εκθετικής κατανομής με παράμετρο θέσης μ και παράμετρο κλίμακος σ. Θεωρούμε το πρόβλημα εκτίμησης των παραμέτρων κλίμακας μ και θέσης σ, όταν μ≤c, όπου c είναι μία γνωστή σταθερά. Αποδεικνύουμε ότι σε σχέση με το κριτήριο του Μέσου Τετραγωνικού Σφάλματος (ΜΤΣ), οι βέλτιστοι αναλλοίωτοι εκτιμητές των μ και σ, είναι μη αποδεκτοί όταν μ≤c, και προτείνουμε βελτιωμένους. Επίσης συγκρίνουμε του εκτιμητές αυτούς σε σχέση με το κριτήριο του Pitman. Επιπλέον, προτείνουμε εκτιμητές που είναι καλύτεροι από τους βέλτιστους αναλλοίωτους εκτιμητές, όταν μ≤c, ως προς την συνάρτηση ζημίας LINEX. Τέλος, η θεωρία που αναπτύσσεται εφαρμόζεται σε δύο ανεξάρτητα δείγματα προερχόμενα από εκθετική κατανομή. / The present master thesis deals with the estimation of the location parameter μ and the scale parameter σ of the two-parameter exponential distribution. We consider the problem of estimation of locasion parameter μ and the scale parameter σ, when it is known apriori that μ≤c, where c is a known constant. We establish that with respect to the mean square error (mse) criterion the best affine estimators of μ and σ in the absence of information μ≤c are inadmissible and we propose estimators which are better than these estimators. Also, we compare these estimators with respect to the Pitman Nearness criterion. We propose estimators which are better than the standard estimators in the unrestricted case with respect to the suitable choise of LINEX loss. Finally, the theory developed is applied to the problem of estimating the location and scale parameters of two exponential distributions when the location parameters are ordered.

Abstract Station-nearness principles as we will discuss in this paper, deals with the coordination of urban functions with the public transportation network. When we talk about functions, we mean residences, workplaces, commercial services, entertainment venues, places of culture, etc. These functions should be high density, there should be a mix of them and they should be pedestrian friendly in nature. Effective integration of functions around train stations brings many benefits and is one of the best means by which you can increase public transport use and increase the accessibility for people in a region. More and more, cities in North America, Europe and other places, are exploring the idea of how this concept can be applied. The Copenhagen region as we will discuss, has placed station-nearness principles at the forefront of their finger plan. Since the Copenhagen region has applied these principles, they have seen clear results with increased public transit ridership, as well on the overall, an increase in the standard of living. As many places are exploring the concept, not everyplace has been able to make the concept work. When we look at Scania, the concept is under utilized to a degree. There continues to be many populated and dense areas in Scania where the coordination of urban functions with public transit is lacking. The automobile is also gaining stronger competition over public transportation; this is a concern in terms of the sustainable future and quality of life for the region. It is not always the solution to simply expand the public transportation network, rather it can be significant to explore more upon the concept of station-nearness principles so that the existing public transit network can be made more effective. It is important to compare places, see in our case study how the concept has worked in the Copenhagen region and look into why the concept is lacking in Scania, as well, what can be done to implement it more in Scania. It is also important how the Öresund region as whole, can play a role with developing the concept, as well, how the concept can benefit the Öresund region vice versa.