A Minimax-condition for the Characteristic Center of a Tree
نویسنده
چکیده
Let L be the Laplacian matrix of a tree. We present a graph-theoretic interpretation of the cofactors of order 2 of L. From this, we deduce a description for the inverse of the rooted Laplacian, reflecting the geometry of a branch. Defining the thickness of a branch as the Perron root of this matrix, we present a minimaxcharacterization of the characteristic center of the tree based on the thickness of its branches.
منابع مشابه
FINITENESS PROPERTIES OF LOCALE COHOMOLOGY MODULES FOR (I;J)- MINIMAX MODULES
ABSTRACT. Let R be a commutative noetherian ring, I and J are two ideals of R. Inthis paper we introduce the concept of (I;J)- minimax R- module, and it is shown thatif M is an (I;J)- minimax R- module and t a non-negative integer such that HiI;J(M) is(I;J)- minimax for all i
متن کاملAdmissible and Minimax Estimator of the Parameter $theta$ in a Binomial $Bin( n ,theta)$ distribution under Squared Log Error Loss Function in a Lower Bounded Parameter Space
Extended Abstract. The study of truncated parameter space in general is of interest for the following reasons: 1.They often occur in practice. In many cases certain parameter values can be excluded from the parameter space. Nearly all problems in practice have a truncated parameter space and it is most impossible to argue in practice that a parameter is not bounded. In truncated parameter...
متن کاملOn the Minimax Optimality of Block Thresholded Wavelets Estimators for ?-Mixing Process
We propose a wavelet based regression function estimator for the estimation of the regression function for a sequence of ?-missing random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator based on block thresholding are investigated. It is found that the estimators achieve optimal minimax convergence rates over large class...
متن کاملMinimax Estimation of the Scale Parameter in a Family of Transformed Chi-Square Distributions under Asymmetric Squared Log Error and MLINEX Loss Functions
This paper is concerned with the problem of finding the minimax estimators of the scale parameter ? in a family of transformed chi-square distributions, under asymmetric squared log error (SLE) and modified linear exponential (MLINEX) loss functions, using the Lehmann Theorem [2]. Also we show that the results of Podder et al. [4] for Pareto distribution are a special case of our results for th...
متن کاملTruncated Linear Minimax Estimator of a Power of the Scale Parameter in a Lower- Bounded Parameter Space
Minimax estimation problems with restricted parameter space reached increasing interest within the last two decades Some authors derived minimax and admissible estimators of bounded parameters under squared error loss and scale invariant squared error loss In some truncated estimation problems the most natural estimator to be considered is the truncated version of a classic...
متن کامل