This research was supported by funds granted to. the Institute for Research on Poverty pursuant to the provisions of the Economic Opportunity Act of 1964. We wish to t~ank the Office of Economic Opportunity, the Planning Research Corporation, and the Census Bureau for providing the data necessary for this study. John Conlisk, Robinson Hollister and Arthur Goldberger offered valuable suggestions...

The function f : F2 → F2 is k-linear if it returns the sum (over F2) of exactly k coordinates of its input. We introduce strong lower bounds on the query complexity for testing whether a function is k-linear. We show that for any k ≤ n 2 , at least k−o(k) queries are required to test k-linearity, and we show that when k ≈ n 2 , this lower bound is nearly tight since 4 3 k+o(k) queries are suffi...

‎let $g$ be a finite group and $d_2(g)$ denotes the probability‎ ‎that $[x,y,y]=1$ for randomly chosen elements $x,y$ of $g$‎. ‎we‎ ‎will obtain lower and upper bounds for $d_2(g)$ in the case where‎ ‎the sets $e_g(x)={yin g:[y,x,x]=1}$ are subgroups of $g$ for‎ ‎all $xin g$‎. ‎also the given examples illustrate that all the‎ ‎bounds are sharp‎.

This is a sequel of the article by Borichev–Golinskii– Kupin [2] where the authors obtain Blaschke-type conditions for special classes of analytic functions in the unit disk which satisfy certain growth hypotheses. These results were applied to get Lieb–Thirring inequalities for complex compact perturbations of a selfadjoint operator with a simply connected resolvent set. The first result of th...

Understanding moments of families of L-functions has long been an important subject with many number theoretic applications. Quite often, the application is to bound the error term in an asymptotic expression of the average of an arithmetic function. Also, a good bound for a moments can be used to obtain a point-wise bound for an individual L-function in the family; strong enough bounds of this...

In a wide range of practical problems correlation matrices are formed in such a way that, while symmetry and a unit diagonal are assured, they may lack semidefiniteness. We derive a variety of new upper bounds for the distance from an arbitrary symmetric matrix to the nearest correlation matrix. The bounds are of two main classes: those based on the eigensystem and those based on a modified Cho...

This bound is optimal in the sense that a matching lower bound holds under mild assumptions, and the constants are sufficiently sharp that we can often capture the precise edge of the spectrum. Analogous results are obtained for rectangular matrices and for more general subgaussian or heavy-tailed distributions of the entries, and we derive tail bounds in addition to bounds on the expected norm...

We present the clrbound, clr2bound, clr3bound, and clrtest commands for estimation and inference on intersection bounds as developed by Chernozhukov et al. (2013). The commands clrbound, clr2bound, and clr3bound provide bound estimates that can be used directly for estimation or to construct asymptotically valid confidence sets. The command clrbound provides bound estimates for one-sided lower ...

We study the fundamental problems of identity testing (goodness of fit), and closeness testing (two sample test) of distributions over k elements, under differential privacy. While the problems have a long history in statistics, finite sample bounds for these problems have only been established recently. In this work, we derive upper and lower bounds on the sample complexity of both the problem...

Transductive learning considers a training set of m labeled samples and a test set of u unlabeled samples, with the goal of best labeling that particular test set. Conversely, inductive learning considers a training set of m labeled samples drawn iid from P (X,Y ), with the goal of best labeling any future samples drawn iid from P (X). This comparison suggests that transduction is a much easier...