Balanced augmented jackknife empirical likelihood for two sample U-statistics

In this paper, we investigate the two sample U-statistics by jackknife empirical likelihood(JEL),a versatile nonparametric approach. More precisely, we propose the method of balanced augmented jackknife empirical likelihood(BAJEL) by adding two artificial points to the original pseudo-value dataset, and we prove that the log likelihood ratio based on the expanded dataset tends to the χ~2 distribution.     

WEAK INVARIANCE PRINCIPLE FOR FINITE-POPULATION U-STATISTICS

Under the weakest possible conditions,we establish the weak invariance principle for finite-population U-statistics in this paper.It is worth while to point out that,for the sampling withoutreplacement,the sequence of random elements in C[0,1],associated with the sample partial sums orthe U-statistics,converges in law to the standard Brown bridge,but not to the Brown motion as inthe usual case of replacement sampling.     

Delete-group Jackknife Estimate in Partially Linear Regression Models with Heteroscedasticity

Abstract Consider a partially linear regression model with an unknown vector parameter β,an unknownfunction g(.),and unknown heteroscedastic error variances.Chen,You proposed a semiparametric generalizedleast squares estimator(SGLSE)for β,which takes the heteroscedasticity into account to increase efficiency.Forinference based on this SGLSE,it is necessary to construct a consistent estimator for its asymptotic covariancematrix.However,when there exists within-group correlation, the traditional delta method and the delete-1jackknife estimation fail to offer such a consistent estimator.In this paper, by deleting grouped partial residualsa delete-group jackknife method is examined.It is shown that the delete-group jackknife method indeed canprovide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations.This result is an extension of that in[21].     

Short Cycle Structure of Graphs on Surfaces （1） -the Uniqueness Theorems

In this paper we investigate cycle base structures of a （weighted） graph and show that much information of short cycles is contained in a MCB （minimum cycle base）. After setting up a Hall type theorem for base-transformation, we give a sufficient and necessary condition for a cycle base to be a MCB. Further more, we show that the structure of MCB in a （weighted） graph is unique. In the case of nonnegative weight, every pair of MCB have the same number of k-cycles for each integer k ≥ 3. The property is also true for those having longest length （although much work has been down in evaluating MCB, little is known for those having longest length）.     

Jackknifed random weighting for Cox proportional hazards model

The Cox proportional hazards model is the most used statistical model in the analysis of survival time data.Recently,a random weighting method was proposed to approximate the distribution of the maximum partial likelihood estimate for the regression coefficient in the Cox model.This method was shown not as sensitive to heavy censoring as the bootstrap method in simulation studies but it may not be second-order accurate as was shown for the bootstrap approximation.In this paper,we propose an alternative random weighting method based on one-step linear jackknife pseudo values and prove the second accuracy of the proposed method.Monte Carlo simulations are also performed to evaluate the proposed method for fixed sample sizes.     

Jackknife empirical likelihood test for the equality of degrees of freedom in t-copulas

It has been argued that fitting a t-copula to financial data is superior to a normal copula. To overcome the shortcoming that a t-copula only has one parameter for the degrees of freedom, the t-copula with multiple parameters of degrees of freedom has been proposed in the literature, which generalizes both the t-copulas and the grouped t-copulas. Like the inference for a t-copula, a computationally efficient inference procedure is to first estimate the correlation matrix via Kendall's τ and then to estimate the parameters of degrees of freedom via pseudo maximum likelihood estimation. This paper proposes a jackknife empirical likelihood test for testing the equality of some parameters of degrees of freedom based on this two-step inference procedure, and shows that the Wilks theorem holds.     

The diffeomorphic types of the complements of arrangements in CP~3Ⅱ

For any arrangement of hyperplanes in CP~3,we introduce the soul of this arrangement. The soul,which is a pseudo-complex,is determined by the combinatorics of the arrangement of hyper- planes.In this paper,we give a sufficient combinatoric condition for two arrangements of hyperplanes to be diffeomorphic to each other.In particular we have found sufficient conditions on combinatorics for the arrangement of hyperplanes whose moduli space is connected.This generalizes our previous result on hyperplane point arrangements in CP~3.     

Purely Hom-Lie bialgebras

In this paper, we first show that there is a Hom-Lie algebra structure on the set of(σ, σ)-derivations of an associative algebra. Then we construct the dual representation of a representation of a Hom-Lie algebra.We introduce the notions of a Manin triple for Hom-Lie algebras and a purely Hom-Lie bialgebra. Using the coadjoint representation, we show that there is a one-to-one correspondence between Manin triples for Hom-Lie algebras and purely Hom-Lie bialgebras. Finally, we study coboundary purely Hom-Lie bialgebras and construct solutions of the classical Hom-Yang-Baxter equations in some special Hom-Lie algebras using Hom-O-operators.     

STEINER MINIMAL TREES FOR BAR WAVES

A Steiner minimal tree (SMT) for a set of points P in the plane is a shortest networkinterconnecting P.The construction of a SMT for a general set P is known to be an NP-completeproblem.Recently,SMTs have been constructed for special sets P such as ladders,splitting trees,zigzag lines and co-circular points.In this paper we study SMTs for a wide class of point-sets calledmild bar wave.We show that a SMT for a mild bar wave must assume a special form,thus the numberof trees needed to be inspected is greatly reduced.Furthermore if a mild bar wave is also a mild rectan-gular wave,then we produce a Steiner tree constructible in linear time whose length can exceed thatof a SMT by an amount bounded by the difference in heights of the two endpoints of the rectangularwave,thus independent of the number of points.When a rectangular wave satisfies some otherconditions (including ladders as special cases),then the Steiner tree we produced is indeed a SMT.     

A NEW FRAMEWORK OF PRIMAL-DUAL INFEASIBLE INTERIOR-POINT METHOD FOR LINEAR PROGRAMMING*

On the basis of the formulations of the logarithmic barrier function and the idea of following the path of minimizers for the logarithmic barrier family of problems the so called "centralpath" for linear programming, we propose a new framework of primal-dual infeasible interiorpoint method for linear programming problems. Without the strict convexity of the logarithmic barrier function, we get the following results: (a) if the homotopy parameterμcan not reach to zero,then the feasible set of these programming problems is empty; (b) if the strictly feasible set is nonempty and the solution set is bounded, then for any initial point x, we can obtain a solution of the problems by this method; (c) if the strictly feasible set is nonempty and the solution set is unbounded, then for any initial point x, we can obtain a (?)-solution; and(d) if the strictly feasible set is nonempty and the solution set is empty, then we can get the curve x(μ), which towards to the generalized solutions.