Bayes quadratic unbiased estimator of spatial covariance parameters

This work presents Bayes invariant quadratic unbiased estimator, for short BAIQUE. Bayesian approach is used here to estimate the covariance functions of the regionalized variables which appear in the spatial covariance structure in mixed linear model. Firstly a brief review of spatial process, variance covariance components structure and Bayesian inference is given, since this project deals with these concepts. Then the linear equations model corresponding to BAIQUE in the general case is formulated. That Bayes estimator of variance components with too many unknown parameters is complicated to be solved analytically. Hence, in order to facilitate the handling with this system, BAIQUE of spatial covariance model with two parameters is considered. Bayesian estimation arises as a solution of a linear equations system which requires the linearity of the covariance functions in the parameters. Here the availability of prior information on the parameters is assumed. This information includes apriori distribution functions which enable to find the first and the second moments matrix. The Bayesian estimation suggested here depends only on the second moment of the prior distribution. The estimation appears as a quadratic form y'Ay , where y is the vector of filtered data observations. This quadratic estimator is used to estimate the linear function of unknown variance components. The matrix A of BAIQUE plays an important role. If such a symmetrical matrix exists, then Bayes risk becomes minimal and the unbiasedness conditions are fulfilled. Therefore, the symmetry of this matrix is elaborated in this work. Through dealing with the infinite series of matrices, a representation of the matrix A is obtained which shows the symmetry of A. In this context, the largest singular value of the decomposed matrix of the infinite series is considered to deal with the convergence condition and also it is connected with Gerschgorin Discs and Poincare theorem. Then the BAIQUE model for some experimental designs is computed and compared. The comparison deals with different aspects, such as the influence of the position of the design points in a fixed interval. The designs that are considered are those with their points distributed in the interval [0, 1]. These experimental structures are compared with respect to the Bayes risk and norms of the matrices corresponding to distances, covariance structures and matrices which have to satisfy the convergence condition. Also different types of the regression functions and distance measurements are handled. The influence of scaling on the design points is studied, moreover, the influence of the covariance structure on the best design is investigated and different covariance structures are considered. Finally, BAIQUE is applied for real data. The corresponding outcomes are compared with the results of other methods for the same data. Thereby, the special BAIQUE, which estimates the general variance of the data, achieves a very close result to the classical empirical variance.

Dress- and Auto- Makers in the “Free Trade” Arena

Even though there have been many studies on the impact of trade liberalisation on labour standards, most of the studies are at national level, and there is a lack of research at industry level. This paper examines the impact of free trade on labour standards in capital- and labour-intensive industries in a developing country. For empirical findings, I take the case of the garment industry, representing labour-intensive industry, and automotive industry, representing capital-intensive industry, in Indonesia in the face of ASEAN Free Trade Area (AFTA). Since the garment industry is a women-dominated industry, while the automotive industry is a men-dominated industry, this paper also employs a feminist perspective. As such, this paper also investigates whether free trade equally affects men and women workers. Besides free trade, other independent variables are also taken into account. Employing quantitative and qualitative methods, empirical evidence shows that there is an indication that free trade has a negative relationship with labour standards in the garment industry, whereas a positive relationships with labour standards in the automotive industry. This implies that free trade might result in decreasing labour standards in labour-intensive industry, while increasing standards in capital-intensive industry. It can also be inferred that free trade unequally affect men and women workers, in that women workers bear the brunt of free trade. The results also show that other internal and external independent variables are indicated to have relationships with labour standards in the garment and automotive industries. Therefore, these variables need to be considered in examining the extent of the impact of free trade on labour standards in labour- and capital-intensive industries.