On Asymptotic Strategy-Proofness of Classical Social Choice Rules

We show that, when the number of participating agents n tends to infinity, all classical social choice rules are asymptotically strategy-proof with the proportion of manipulable profiles being of order O (1/n).     

Center and Distinguisher for Strings with Unbounded Alphabet

Consider two sets and of strings of length L with characters from an unbounded alphabet , i.e., the size of is not bounded by a constant and has to be taken into consideration as a parameter for input size. A closest string s* of is a string that minimizes the maximum of Hamming¹ distance(s, s*) over all string s : s . In contrast, a farthest string t* from maximizes the minimum of Hamming distance(t*,t) over all elements t: t . A distinguisher of from is a string that is close to every string in and far away from any string in . We obtain polynomial time approximation schemes to settle the above problems.     

Improved Approximation for Breakpoint Graph Decomposition and Sorting by Reversals

Sorting by Reversals (SBR) is one of the most widely studied models of genome rearrangements in computational molecular biology. At present, is the best known approximation ratio achievable in polynomial time for SBR. A very closely related problem, called Breakpoint Graph Decomposition (BGD), calls for a largest collection of edge disjoint cycles in a suitably-defined graph. It has been shown that for almost all instances SBR is equivalent to BGD, in the sense that any solution of the latter corresponds to a solution of the former having the same value. In this paper, we show how to improve the approximation ratio achievable in polynomial time for BGD, from the previously known to for any > 0. Combined with the results in (Caprara, Journal of Combinatorial Optimization, vol. 3, pp. 149–182, 1999b), this yields the same approximation guarantee for n! – O((n – 5)!) out of the n! instances of SBR on permutations with n elements. Our result uses the best known approximation algorithms for Stable Set on graphs with maximum degree 4 as well as for Set Packing where the maximum size of a set is 6. Any improvement in the ratio achieved by these approximation algorithms will yield an automatic improvement of our result.     

The densest <Emphasis Type="Italic">k</Emphasis>-subgraph problem on clique graphs

The Densest k-Subgraph (DkS) problem asks for a k-vertex subgraph of a given graph with the maximum number of edges. The problem is strongly NP-hard, as a generalization of the well known Clique problem and we also know that it does not admit a Polynomial Time Approximation Scheme (PTAS). In this paper we focus on special cases of the problem, with respect to the class of the input graph. Especially, towards the elucidation of the open questions concerning the complexity of the problem for interval graphs as well as its approximability for chordal graphs, we consider graphs having special clique graphs. We present a PTAS for stars of cliques and a dynamic programming algorithm for trees of cliques. M.L. is co-financed within Op. Education by the ESF (European Social Fund) and National Resources. V.Z. is partially supported by the Special Research Grants Account of the University of Athens under Grant 70/4/5821.     

Landau多项式算子与无界函数逼近

利用扩展乘数法构造了 Landau型多项式算子逼近全空间或有界集上无界函数的若干收敛定理 ,给出了具有一般性的结论 ,从而推广了已有文献的若干结果 .     

On shrinkage least squares estimation in a parallelism problem

In a multi-sample simple regression model, generally, homogeneity of the regression slopes leads to improved estimation of the intercepts. Analogous to the preliminary test estimators, (smooth) shrinkage least squares estimators of Intercepts based on the James-Stein rule on regression slopes are considered. Relative pictures on the (asymptotic) risk of the classical, preliminary test and the shrinkage least squares estimators are also presented. None of the preliminary test and shrinkage least squares estimators may dominate over the other, though each of them fares well relative to the other estimators.     

On asymptotic distribution of the test statistic for the mean of the non-isotropic principal component

In this paper, the authors derived the large sample distribution of the t statistic based upon the observations on the first principal component instead of the original variables. It is shown that the above statistic is distributed asymptotically as Student's t distribution.     

On an application of the diffusion approximation of the generalized birth and death process for stochastic population projection

Assuming that both birth and death rates are density and time dependent, a diffusion approximation of the generalized birth and death process has been considered in this paper to obtain a suitable stochastic population model describing the population size and its moments. A simple method of estimating the parameters of the model Is discussed. The predictions of the expected size of the population, and the variance are made and compared with the corresponding census figures as well as with another deterministic projection series made for the corresponding period.     

Recursive location and scale estimators

It is shown that a recursive estimator with the same asymptotic properties as the median has convergence properties in finite samples which depend heavily on the scale of the data. A simple modification which adjusts for the scale is suggested and its application illustrated on simulated data. The modified estimator has much improved properties which are similar to those of the sample (non-recursive) median.     

Model Averaging for Prediction With Fragmentary Data

ABSTRACT

One main challenge for statistical prediction with data from multiple sources is that not all the associated covariate data are available for many sampled subjects. Consequently, we need new statistical methodology to handle this type of “fragmentary data” that has become more and more popular in recent years. In this article, we propose a novel method based on the frequentist model averaging that fits some candidate models using all available covariate data. The weights in model averaging are selected by delete-one cross-validation based on the data from complete cases. The optimality of the selected weights is rigorously proved under some conditions. The finite sample performance of the proposed method is confirmed by simulation studies. An example for personal income prediction based on real data from a leading e-community of wealth management in China is also presented for illustration.