150,684 research outputs found
Distribution-Free Tests of Independence in High Dimensions
We consider the testing of mutual independence among all entries in a
-dimensional random vector based on independent observations. We study
two families of distribution-free test statistics, which include Kendall's tau
and Spearman's rho as important examples. We show that under the null
hypothesis the test statistics of these two families converge weakly to Gumbel
distributions, and propose tests that control the type I error in the
high-dimensional setting where . We further show that the two tests are
rate-optimal in terms of power against sparse alternatives, and outperform
competitors in simulations, especially when is large.Comment: to appear in Biometrik
Witten Genus and String Complete Intersections
In this note, we prove that the Witten genus of nonsingular string complete
intersections in product of complex projective spaces vanishes. Our result
generalizes a known result of Landweber and Stong (cf. [HBJ]).Comment: Some materials and references are adde
Studying Maximum Information Leakage Using Karush-Kuhn-Tucker Conditions
When studying the information leakage in programs or protocols, a natural
question arises: "what is the worst case scenario?". This problem of
identifying the maximal leakage can be seen as a channel capacity problem in
the information theoretical sense. In this paper, by combining two powerful
theories: Information Theory and Karush-Kuhn-Tucker conditions, we demonstrate
a very general solution to the channel capacity problem. Examples are given to
show how our solution can be applied to practical contexts of programs and
anonymity protocols, and how this solution generalizes previous approaches to
this problem
Smooth local solutions to weingarten equations and -equations
In this paper, we study the existence of smooth local solutions to Weingarten
equations and -equations. We will prove that, for ,
the Weingarten equations and the -equations always have smooth local
solutions regardless of the sign of the functions in the right-hand side of the
equations. We will demonstrate that the associate linearized equations are
uniformly elliptic if we choose the initial approximate solutions
appropriately
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