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Data depth measures the centrality of a point with respect to a given distribution or data cloud. It provides a natural center-outward ordering of multivariate data points and yields a systematic nonparametric multivariate analysis scheme. In particular, the halfspace depth is shown to have many desirable properties and broad applicability. However, the empirical halfspace depth is zero outside the convex hull of the data. This property has rendered the empirical halfspace depth useless outside the data cloud, and limited its utility in applications where the extreme outlying probability mass is the focal point, such as in classification problems and control charts with very small false alarm rates. To address this issue, we apply extreme value statistics to refine the empirical halfspace depth in “the tail”. This provides an important linkage between data depth, which is useful for inference on centrality, and extreme value statistics, which is useful for inference on extremity. The refined empirical halfspace depth can thus extend all its utilities beyond the data cloud, and hence broaden greatly its applicability. The refined estimator is shown to have substantially improved upon the empirical estimator in theory and simulations. The benefit of this improvement is also demonstrated through the applications in classification and statistical process control.

The five essays in the dissertation explore the interaction between economic development in Africa and three economic concepts from different fields: decentralized agricultural innovation systems, trust and saving practices. A relatively new view to boost agricultural growth is the implementation of the innovation system approach. The Sub Saharan African Challenge Program adopted this approach through the development of local decentralized Innovation Platforms (IPs) in eight African countries. The first and the second essay respectively evaluate the impact of those platforms, on poverty and the adoption of agricultural technologies. The studies reach to mixed results concerning average impact on poverty and technology adoption. Some platforms promote the adoption of some innovations and reduce poverty level, and others do not (yet). The third essay complements these studies and investigates whether this difference in IP performance is because they may not have equally implemented the principles of the approach. The essay shows that IPs which performed better in human capacity development at the field, ceteris paribus, are more successful. Theory suggests that trust fosters economic development via reduced transaction costs and increased specialization. A vicious cycle may materialize if increased specialization, via increased market integration, also fosters trust. To shed light on the latter, the fourth essay studies whether increased market integration fosters trust by using a comprehensive survey of households living in West Africa in the early stages of market integration. The study identifies a negative and causal relationship between market integration and trust, which is contradictory to the theory. Having limited access to finance, entrepreneurs in developing countries have to utilize business profits or save in order to invest in their businesses. At the same time they keep their savings in multiple practices (e.g bank account, moneylender, etc.), which potentially may have different efficiency levels, and therefore may have varying effects on business investments. The fifth essay studies how different saving practices affect the likelihood of business profit reinvestment. The study shows that the practice of saving in a deposit account of a formal financial institution is more likely to facilitate reinvestment compared to the practice of keeping savings within the household.

A modification of the kinetic growth model in two dimensions for the polymerization of 5-membered rings is presented. The preliminary results reveal the validity of the modified model.