Nested Inequalities Among Divergence Measures

In this paper we have considered a single inequality having 11 known divergence measures. This inequality include measures like: Jeffryes-Kullback-Leiber J-divergence, Jensen-Shannon divergence (Burbea-Rao, 1982), arithmetic-geometric mean divergence (Taneja, 1995), Hellinger discrimination, symmetric chi-square divergence, triangular discrimination, etc. All these measures are well-known in the literature on Information theory and Statistics. This sequence of 11 measures also include measures due to Kumar and Johnson (2005) and Jain and Srivastava (2007). Three measures arising due to some mean divergences also appears in this inequality. Based on non-negative differences arising due to this single inequality of 11 measures, we have put more than 40 divergence measures in nested or sequential form. Idea of reverse inequalities is also introduced

A distributionally robust perspective on uncertainty quantification and chance constrained programming

The objective of uncertainty quantification is to certify that a given physical, engineering or economic system satisfies multiple safety conditions with high probability. A more ambitious goal is to actively influence the system so as to guarantee and maintain its safety, a scenario which can be modeled through a chance constrained program. In this paper we assume that the parameters of the system are governed by an ambiguous distribution that is only known to belong to an ambiguity set characterized through generalized moment bounds and structural properties such as symmetry, unimodality or independence patterns. We delineate the watershed between tractability and intractability in ambiguity-averse uncertainty quantification and chance constrained programming. Using tools from distributionally robust optimization, we derive explicit conic reformulations for tractable problem classes and suggest efficiently computable conservative approximations for intractable ones

Adaptive estimation of covariance matrices via Cholesky decomposition

This paper studies the estimation of a large covariance matrix. We introduce a novel procedure called ChoSelect based on the Cholesky factor of the inverse covariance. This method uses a dimension reduction strategy by selecting the pattern of zero of the Cholesky factor. Alternatively, ChoSelect can be interpreted as a graph estimation procedure for directed Gaussian graphical models. Our approach is particularly relevant when the variables under study have a natural ordering (e.g. time series) or more generally when the Cholesky factor is approximately sparse. ChoSelect achieves non-asymptotic oracle inequalities with respect to the Kullback-Leibler entropy. Moreover, it satisfies various adaptive properties from a minimax point of view. We also introduce and study a two-stage procedure that combines ChoSelect with the Lasso. This last method enables the practitioner to choose his own trade-off between statistical efficiency and computational complexity. Moreover, it is consistent under weaker assumptions than the Lasso. The practical performances of the different procedures are assessed on numerical examples

Regional income inequality in China and Indonesia: A comparative analysis

This study examines the extent and trends of regional income inequality in China and Indonesia, and performs a comparative analysis between these two countries in terms of factors determining regional income inequality. There are a number of studies that have analyzed the relationship between economic development and regional income inequality in China and Indonesia. However, most previous studies employed provincial income and population data to measure regional income inequality and were thus unable to measure inequality within provinces. In order to rectify this drawback, we will use district-level income and population data, rather than provincial data, to measure regional income inequality, and examine not only between-province inequalities but also within-province inequalities by using the two-stage nested Theil decomposition method developed by Akita (2002). China and Indonesia are still at a relatively early stage of economic development; therefore, income-enhancing economic activities tend to have concentrated in a few districts in each province to enjoy agglomeration economies. We will show that a very large regional income inequality exists among the districts of China and Indonesia. This study will also conduct a regression analysis to explore possible determinants of within-province income inequality, in which the following variables are considered: foreign direct investment, economic dualism, and migration.

Urbanization, educational expansion, and expenditures inequality in Indonesia in 1996, 1999, and 2002:

"This paper considers urban-rural location and education as the main causes of expenditure inequality and attempts to examine inequality changes associated with urbanization and educational expansion in Indonesia from 1996 to 2002, using Indonesian monthly household consumption expenditure data. It introduces a hierarchical framework of inequality decomposition by population subgroups, which enables researchers to analyze inequality resulting from differences in educational attainment as well as inequality within each educational group, after the effects on inequality of urban–rural differences in the composition of educational attainments are removed. It finds that the urban sector's higher educational group contributes significantly to overall inequality. Inequality within the group increased significantly once Indonesia recovered from the financial crisis of 1998. This, together with educational expansion in urban areas, led to a conspicuous rise in urban inequality. Overall expenditure inequality has increased markedly, due not only to the rise in urban inequality but also a widening urban-rural disparity, accompanied by a population shift from the rural to the urban sector. Since more people will obtain higher education as the economy continues to develop, and more jobs requiring specialized skills become available in urban areas, urban inequality is likely to remain high. In order to mitigate urban inequality and thus overall inequality, the government needs to introduce policies that could reduce inequality among households whose heads have a tertiary education." from Authors' AbstractExpenditure inequality, Urbanization, Educational expansion, Theil index, Two-stage nested inequality decomposition analysis, Public investment,