On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.

Non-product related environmental process and production methods (NPR-PPMs): a view from international trade law and international environmental governance

The primary aim of this thesis is to analyse legal and governance issues in the use of Environmental NPR-PPMs, particularly those aiming to promote sustainable practices or to protect natural resources. NPR-PPMs have traditionally been thought of as being incompatible with the rules of the World Trade Organization (WTO). However, the issue remains untouched by WTO adjudicatory bodies. One can suggest that WTO adjudicatory bodies may want to leave this issue to the Members, but the analysis of the case law also seems to indicate that the question of legality of NPR-PPMs has not been brought ‘as such’ in dispute settlement. This thesis advances the argument that despite the fact that the legal status of NPR-PPMs remains unsettled, during the last decades adjudicatory bodies have been scrutinising environmental measures based on NPR-PPMs just as another expression of the regulatory autonomy of the Members. Though NPR-PPMs are regulatory choices associated with a wide range of environmental concerns, trade disputes giving rise to questions related to the legality of process-based measures have been mainly associated with the protection of marine wildlife (i.e., fishing techniques threatening or affecting animal species). This thesis argues that environmental objectives articulated as NPR-PPMs can indeed qualify as legitimate objectives both under the GATT and the TBT Agreement. However, an important challenge for the their compatibility with WTO law relate to aspects associated with arbitrary or unjustifiable discrimination. In the assessment of discrimination procedural issues play an important role. This thesis also elucidates other important dimensions to the issue from the perspective of global governance. One of the arguments advanced in this thesis is that a comprehensive analysis of environmental NPR-PPMs should consider not only their role in what is regarded as trade barriers (governmental and market-driven), but also their significance in global objectives such as the transition towards a green economy and sustainable patterns of consumption and production.