The empirical analysis of the -bilateral optimized combinatorial auction model

This study proposes a new and highly efficient dynamic combinatorial auction mechanism—the N-bilateral optimized combinatorial auction (N-BOCA). N-BOCA is a flexible iterative combinatorial auction model that offers more optimized trading for multiple suppliers and purchasers in the supply chain than one-sided combinatorial auction. We design the N-BOCA model from the perspectives of market architecture, trading rules, and decision strategy for winner determination, the decision strategy for winner determination needs flexible optimization modeling capability. Thus rule-based reasoning was applied for reflecting the flexible decision strategies. We also show the viability of N-BOCA through Paired Samples T-test experimentation. It shows that N-BOCA yields higher purchase efficiency and effectiveness than the one-auctioneer to multi-bidders (1-to-N) combinatorial auction mechanism.     

Likelihood ratio ordering of order statistics,mixtures and systems

Let X=(_X1,_X2,…,_Xn)$\mathit{X}=(X_1,X_2,\dots ,X_n)$ be an exchangeable random vector, and denote _X1:i=min{_X1,_X2,…,_Xi}$X_{1:i}=\min \{X_1,X_2,\dots ,X_i\}$ and _Xi:i=max{_X1,_X2,…,_Xi}$X_{i:i}=\max \{X_1,X_2,\dots ,X_i\}$, 1?i?n$1?i?n$. These order statistics represent the lifetimes of the series and the parallel systems, respectively, with component lifetimes _Xi$X_i$. In this paper we obtain conditions under which _X1:i$X_{1:i}$ (or _Xi:i$X_{i:i}$) decreases (increases) in i in the likelihood ratio (lr) order. An even more general result involving general (that is, not necessary exchangeable) random vectors is also derived for general series (or parallel) systems. We show that the series (parallel) systems are not necessarily lr-ordered even if the components are independent.     

Prediction in moving average processes

For the stationary invertible moving average process of order one with unknown innovation distribution F, we construct root-n   consistent plug-in estimators of conditional expectations E(h(_Xn+1)|_X1,…,_Xn)$E(h(X_{n+1})|X_1,\dots ,X_n)$. More specifically, we give weak conditions under which such estimators admit Bahadur-type representations, assuming some smoothness of h or of F. For fixed h it suffices that h   is locally of bounded variation and locally Lipschitz in _L2(F)$L_2(F)$, and that the convolution of h and F   is continuously differentiable. A uniform representation for the plug-in estimator of the conditional distribution function P(_Xn+1?·|_X1,…,_Xn)$P(X_{n+1}?·|X_1,\dots ,X_n)$ holds if F has a uniformly continuous density. For a smoothed version of our estimator, the Bahadur representation holds uniformly over each class of functions h that have an appropriate envelope and whose shifts are F-Donsker, assuming some smoothness of F. The proofs use empirical process arguments.     

Characterizations based on record values and order statistics

Consider a sequence of independent and identically distributed random variables {_Xi,i?1}$\{X_i,i?1\}$ with a common absolutely continuous distribution function F  . Let _X1:n?_X2:n???_Xn:n$X_{1:n}?X_{2:n}???X_{n:n}$ be the order statistics of {_X1,_X2,…,_Xn}$\{X_1,X_2,\dots ,X_n\}$ and {_Yl,l?1}$\{Y_l,l?1\}$ be the sequence of record values generated by {_Xi,i?1}$\{X_i,i?1\}$. In this work, the conditional distribution of _Yl$Y_l$ given _Xn:n$X_{n:n}$ is established. Some characterizations of F   based on record values and _Xn:n$X_{n:n}$ are then given.     

On characterizations of the logistic distribution

We modify and extend George and Mudholkar's [1981. A characterization of the logistic distribution by a sample median. Ann. Inst. Statist. Math. 33, 125–129] characterization result about the logistic distribution, which is in terms of the sample median and Laplace distribution. Moreover, we give some new characterization results in terms of the smallest order statistics and the exponential distribution.     

Asymptotic results in canonical discriminant analysis when the dimension is large compared to the sample size

This paper deals with the distributions of test statistics for the number of useful discriminant functions and the characteristic roots in canonical discriminant analysis. These asymptotic distributions have been extensively studied when the number p   of variables is fixed, the number q+1$q+1$ of groups is fixed, and the sample size N tends to infinity. However, these approximations become increasingly inaccurate as the value of p increases for a fixed value of N. On the other hand, we encounter to analyze high-dimensional data such that p is large compared to n. The purpose of the present paper is to derive asymptotic distributions of these statistics in a high-dimensional framework such that q   is fixed, p→∞$p\to \infty$, m=n-p+q→∞$m=n-p+q\to \infty$, and p/n→c∈(0,1)$p/n\to c\in (0,1)$, where n=N-q-1$n=N-q-1$. Numerical simulation revealed that our new asymptotic approximations are more accurate than the classical asymptotic approximations in a considerably wide range of (n,p,q)$(n,p,q)$.     

Asymptotical improvement of maximum likelihood estimators on Kullback–Leibler loss

We discuss the general form of a first-order correction to the maximum likelihood estimator which is expressed in terms of the gradient of a function, which could for example be the logarithm of a prior density function. In terms of Kullback–Leibler divergence, the correction gives an asymptotic improvement over maximum likelihood under rather general conditions. The theory is illustrated for Bayes estimators with conjugate priors. The optimal choice of hyper-parameter to improve the maximum likelihood estimator is discussed. The results based on Kullback–Leibler risk are extended to a wide class of risk functions.     

Ordered ranked set samples and applications to inference

Ranked set sampling (RSS) was first proposed by McIntyre [1952. A method for unbiased selective sampling, using ranked sets. Australian J. Agricultural Res. 3, 385–390] as an effective way to estimate the unknown population mean. Chuiv and Sinha [1998. On some aspects of ranked set sampling in parametric estimation. In: Balakrishnan, N., Rao, C.R. (Eds.), Handbook of Statistics, vol. 17. Elsevier, Amsterdam, pp. 337–377] and Chen et al. [2004. Ranked Set Sampling—Theory and Application. Lecture Notes in Statistics, vol. 176. Springer, New York] have provided excellent surveys of RSS and various inferential results based on RSS. In this paper, we use the idea of order statistics from independent and non-identically distributed (INID) random variables to propose ordered ranked set sampling (ORSS) and then develop optimal linear inference based on ORSS. We determine the best linear unbiased estimators based on ORSS (BLUE-ORSS) and show that they are more efficient than BLUE-RSS for the two-parameter exponential, normal and logistic distributions. Although this is not the case for the one-parameter exponential distribution, the relative efficiency of the BLUE-ORSS (to BLUE-RSS) is very close to 1. Furthermore, we compare both BLUE-ORSS and BLUE-RSS with the BLUE based on order statistics from a simple random sample (BLUE-OS). We show that BLUE-ORSS is uniformly better than BLUE-OS, while BLUE-RSS is not as efficient as BLUE-OS for small sample sizes (n<5$n<5$).     

On the distribution of quadratic functionals of the ordinary and fractional Brownian motions

In this paper we discuss some distributional properties of quadratic functionals of the ordinary and fractional Brownian motions (fBms). As far as the ordinary Brownian motion (Bm) is concerned, those properties have been established extensively. A transition from the Bm to the fBm is not straightforward. Some difficulties associated with dealing with the fBm are explained, and a way to solving the problem is indicated, and some conjectures are given.