Variance estimation is a fundamental problem in statistical modeling. In ultrahigh dimensional linear regressions where the dimensionality is much larger than sample size, traditional variance estimation techniques are not applicable. Recent advances on variable selection in ultrahigh dimensional linear regressions make this problem more accessible. One of the major problems in ultrahigh dimens...

Association rule mining finds interesting associations or correlations in a large pool of transactions. Apriori based algorithms are two step algorithms for mining association rules from large datasets. They find the frequent item sets from transactions as the first step and then construct the association rules. Though these algorithms generate multiple rules, most of the rules become irrelevan...

While finite cop-win finite graphs possess a good structural characterization, none is known for infinite cop-win graphs. As evidence that such a characterization might not exist, we provide as large as possible classes of infinite graphs with finite cop number. More precisely, for each infinite cardinal and each positive integer k, we construct 2 non-isomorphic k-cop-win graphs satisfying addi...

Assuming elliptically contoured distribution for portfolio asset returns, we derive the exact marginal and joint densities of the global minimum variance portfolio variance, and weights estimators. We also construct a test for the hypothesis that the global minimum variance is less then or equal to a certain value. A stochastic representation and moments of its estimator is provided. We illustr...

This paper examines the notion of ‘irrelevant’alternatives in the context of social choice problems. It is shown that seemingly irrelevant alternatives could be relevant because of their information content. This leads to a consideration of aggregation rules where an endogenous condition of independence of irrelevant alternatives is imposed. The analysis leads to the characterization of a uniqu...

We present a general result giving us families of incomplete and boundedly complete families of discrete distributions. For such families, the classes of unbiased estimators of zero with finite variance and of parametric functions which will have uniformly minimum variance unbiased estimators with finite variance are explicitly characterized. The general result allows us to construct a large nu...