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A universal approximate cross-validation criterion and its asymptotic distribution
AIC cross entropy crossvalidation estimator choice Kullback-Leibler risk model selection ordered categorical observations psychometric tests
2012/6/29
A general framework is that the estimators of a distribution are obtained by minimizing a function (the estimating function) and they are assessed through another function (the assessment function). T...
The asymptotic distribution of the length of Beta-coalescent trees
Beta-coalescent coupling, point process stable distribution Probability
2011/9/6
Abstract: We derive the asymptotic distribution of the total length $L_n$ of a Beta($2-\alpha,\alpha$)-coalescent tree for $1<\alpha < 2$, starting from $n$ individuals. There are two regimes: If $\al...
Asymptotic Distribution Of The Roots Of The Ehrhart Polynomial Of The Cross-Polytope
Asymptotic Distribution Roots Of The Ehrhart Polynomial eCross-Polytope
2011/1/20
We use the method of steepest descents to study the root distribution of the Ehrhart polynomial of the d-dimensional cross-polytope, namely Ld, as d ! 1. We prove that the distribution function of the...
On the asymptotic distribution of the singular values of powers of random matrices
asymptotic distribution singular values of powers of random matrices
2011/1/21
We consider powers of random matrices with independent entries. Let Xij , i, j ≥ 1,be independent complex random variables with EXij = 0 and E|Xij |2 = 1 and let X denote an n×n matrix with [X]ij = Xi...
On the asymptotic distribution of singular values of products of large rectangular random matrices
asymptotic distribution of singular values of products large rectangular random matrices
2011/1/21
We consider products of independent large random rectangular matrices with independent entries. The limit distribution of the expected empirical distribution of singular values of such products is com...
On Jiang's asymptotic distribution of the largest entry of a sample correlation matrix
On Jiang's asymptotic distribution correlation matrix
2010/11/19
Let $ \{X, X_{k,i}; i \geq 1, k \geq 1 \}$ be a double array of nondegenerate i.i.d. random variables and let $\{p_{n}; n \geq 1 \}$ be a sequence of positive integers such that $n/p_{n}$ is bounded a...