Productivity improvement in Korean rice farming: parametric and non-parametric analysis

The published empirical literature on frontier production functions is dominated by two broadly defined estimation approaches – parametric and non‐parametric. Using panel data on Korean rice production, parametric and non‐parametric production frontiers are estimated and compared with estimated productivity. The non‐parametric approach employs two alternative measures based on the Malmquist index and the Luenberger indicator, while the parametric approach is closely related to the time‐variant efficiency model. Productivity measures differ considerably between these approaches. It is discovered that measures of efficiency change are more sensitive to the choice of the model than are measures of technical change. Both approaches reveal that the main sources of growth in Korean rice farming have been technical change and productivity improvements in regions of the country that have been associated with low efficiency.Crop Production/Industries, Productivity Analysis,

Superpotentials of N=1 Supersymmetric Gauge Theories from M-theory

We consider brane configurations in M-theory describing N=1 supersymmetric gauge theories and using the parametric representation of the brane configurations, we calculate the superpotentials for various cases including multiple gauge groups or fermions. For SU(n) N=1 SQCD with $N_f$ fermion case ($N_f < N_c)$, we find that the superpotential from M-theory and the gauge theory agree precisely. This gives a direct evidence of the validity of Witten's M-theory method for calculating the super potential.Comment: 15pages, latex, typos corrected, a line regarding M\"obius transformation in page 4 and angle dependence in page 12 correcte

A convex pseudo-likelihood framework for high dimensional partial correlation estimation with convergence guarantees

Sparse high dimensional graphical model selection is a topic of much interest in modern day statistics. A popular approach is to apply l1-penalties to either (1) parametric likelihoods, or, (2) regularized regression/pseudo-likelihoods, with the latter having the distinct advantage that they do not explicitly assume Gaussianity. As none of the popular methods proposed for solving pseudo-likelihood based objective functions have provable convergence guarantees, it is not clear if corresponding estimators exist or are even computable, or if they actually yield correct partial correlation graphs. This paper proposes a new pseudo-likelihood based graphical model selection method that aims to overcome some of the shortcomings of current methods, but at the same time retain all their respective strengths. In particular, we introduce a novel framework that leads to a convex formulation of the partial covariance regression graph problem, resulting in an objective function comprised of quadratic forms. The objective is then optimized via a coordinate-wise approach. The specific functional form of the objective function facilitates rigorous convergence analysis leading to convergence guarantees; an important property that cannot be established using standard results, when the dimension is larger than the sample size, as is often the case in high dimensional applications. These convergence guarantees ensure that estimators are well-defined under very general conditions, and are always computable. In addition, the approach yields estimators that have good large sample properties and also respect symmetry. Furthermore, application to simulated/real data, timing comparisons and numerical convergence is demonstrated. We also present a novel unifying framework that places all graphical pseudo-likelihood methods as special cases of a more general formulation, leading to important insights