Weyl group multiple Dirichlet series of type A_2

A Weyl group multiple Dirichlet series is a Dirichlet series in several complex variables attached to a root system Phi. The number of variables equals the rank r of the root system, and the series satisfies a group of functional equations isomorphic to the Weyl group W of Phi. In this paper we construct a Weyl group multiple Dirichlet series over the rational function field using n-th order Gauss sums attached to the root system of type A_2. The basic technique is to construct a rational function in r variables invariant under a certain action of W, and use this to build a ``local factor'' of the global series

Optimally combining Censored and Uncensored Datasets

We develop a simple semiparametric framework for combining censored and uncensored samples so that the resulting estimators are consistent, asymptotically normal, and use all information optimally. No nonparametric smoothing is required to implement our estimators. To illustrate our results in an empirical setting, we show how to estimate the effect of changes in compulsory schooling laws on age at first marriage, a variable that is censored for younger individuals. Results from a small simulation experiment suggest that the estimator proposed in this paper can work very well in finite samples.

Holographic entanglement negativity for disjoint intervals in AdS3/CFT2AdS_3/CFT_2

We advance a holographic construction for the entanglement negativity of bipartite mixed state configurations of two disjoint intervals in $(1+1)$ dimensional conformal field theories ($CFT_{1+1}$) through the $AdS_3/CFT_2$ correspondence. Our construction constitutes the large central charge analysis of the entanglement negativity for mixed states under consideration and involves a specific algebraic sum of bulk space like geodesics anchored on appropriate intervals in the dual $CFT_{1+1}$. The construction is utilized to compute the holographic entanglement negativity for such mixed states in $CFT_{1+1}$s dual to bulk pure $AdS_3$ geometries and BTZ black holes respectively. Our analysis exactly reproduces the universal features of corresponding replica technique results in the large central charge limit which serves as a consistency check.Comment: 17 pages, 4 figure

Optimally Combining Censored and Uncensored Datasets

Economists and other social scientists often face situations where they have access to two datasets that they can use but one set of data suffers from censoring or truncation. If the censored sample is much bigger than the uncensored sample, it is common for researchers to use the censored sample alone and attempt to deal with the problem of partial observation in some manner. Alternatively, they simply use only the uncensored sample and ignore the censored one so as to avoid biases. It is rarely the case that researchers use both datasets together, mainly because they lack guidance about how to combine them. In this paper, we develop a tractable semiparametric framework for combining the censored and uncensored datasets so that the resulting estimators are consistent, asymptotically normal, and use all information optimally. When the censored sample, which we refer to as the master sample, is much bigger than the uncensored sample (which we call the refreshment sample), the latter can be thought of as providing identification where it is otherwise absent. In contrast, when the refreshment sample is large and could typically be used alone, our methodology can be interpreted as using information from the censored sample to increase effciency. To illustrate our results in an empirical setting, we show how to estimate the effect of changes in compulsory schooling laws on age at first marriage, a variable that is censored for younger individuals. We also demonstrate how refreshment samples for this application can be created by matching cohort information across census datasets

India’s calorie consumption puzzle: insights from the stochastic cost frontier analysis of calorie purchases

Between the early 1970s and very nearly the present, Indians’ per capita calorie consumption declined. This decline, perplexing in the face of rising per capita income when malnutrition is rampant, has been termed India’s Calorie Consumption Puzzle. It has been partially attributed to a squeeze in the household food budget. This study employs Stochastic Cost Frontier Analysis to evaluate this explanation, upon the logic that such a squeeze shall likely result in the rising cost-efficiency of calorie purchases, that is, the more economical purchase of calories. Analysis of household expenditure data from India’s National Sample Survey reveals that Indian households’ purchase of calories did become more cost-efficient at every level of income, suggesting that there was indeed a squeeze in the household food budget, making this a viable explanation of the Calorie Consumption Puzzle. Besides thus investigating India’s Calorie Consumption Puzzle, this study demonstrates a novel application of Stochastic Cost Frontier Analysis, to consumption instead of the more common production, in that the method has not previously been applied to the consumption of multiple items treated as inputs yielding an output. Stochastic Cost Frontier Analysis applied to calorie acquisition may be a new way of gauging changes over time in food security, with a rise in cost-efficiency indicating a squeeze in the food budget or declining food security