随机化应答调查方案的参数估计问题

随机化应答调查是一种特殊的数据采集技术,使得调查者既得到了某个敏感问题的信息又保护了被调查者的隐私,本文研究从两种随机化答调查方案采得数据后的参数估计问题,在应用Ｂａｙｅｓ估计时,给出了便于Ｍａｔｈｅｍａｔｉｃａ软件计算的后验均值和方差的公式,通过模拟实验,比较了两个方案所得估计量的优劣。     

Improving Approximate Bayesian Computation via Quasi-Monte Carlo

ABC (approximate Bayesian computation) is a general approach for dealing with models with an intractable likelihood. In this work, we derive ABC algorithms based on QMC (quasi-Monte Carlo) sequences. We show that the resulting ABC estimates have a lower variance than their Monte Carlo counter-parts. We also develop QMC variants of sequential ABC algorithms, which progressively adapt the proposal distribution and the acceptance threshold. We illustrate our QMC approach through several examples taken from the ABC literature.     

An improved approximation algorithm for the partial Latin square extension problem

Previous work on the partial Latin square extension (PLSE) problem resulted in a 2-approximation algorithm based on the LP relaxation of a three-dimensional assignment IP formulation. We present an e/(e−1)-approximation algorithm that is based on the LP relaxation of a packing IP formulation of the PLSE problem.     

On the limitation imposed by gravity on measurements of the critical viscosity of a pure fluid

Measurements of the viscosity of a fluid by means of a parallel plate torsional oscillator are conventionally limited to a plate separation that is much larger than the viscous penetration depth of the fluid contained between the plates. Here we demonstrate that, in principle, useful measurements can be carried out in the opposite regime where the thickness is smaller than the penetration depth. An alternative method, described in the last part of this paper, for alleviating the restriction imposed by the density stratification that results from the earth's gravity, is to use electrostriction, rather than the inertial force, to drive the fluid between the plates.     

OUTLIER TEST IN RANDOMIZED LINEAR MODEL

In this paper, we give an approach for detecting one or more outliers inrandomized linear model The likelihood ratio test statistic and its distributions under the null hypothesis and the alternative bypothesis are given. Furthermore, the rebustneas of the test statistic in a certain sere is proved. Finally, the optimality properties of the test are derived.     

夹紧法磨外圆

夹紧法磨外圆是一种有效的加工方法,这种方法不需要对玻璃粘接成条,而且定位准确又牢靠,简化了工序,提高了生产效率。     

I-binomial scrambling of digital nets and sequences

The computational complexity of the integration problem in terms of the expected error has recently been an important topic in Information-Based Complexity. In this setting, we assume some sample space of integration rules from which we randomly choose one. The most popular sample space is based on Owen's random scrambling scheme whose theoretical advantage is the fast convergence rate for certain smooth functions.This paper considers a reduction of randomness required for Owen's random scrambling by using the notion of i-binomial property. We first establish a set of necessary and sufficient conditions for digital (0,s)-sequences to have the i-binomial property. Then based on these conditions, the left and right i-binomial scramblings are defined. We show that Owen's key lemma (Lemma 4, SIAM J. Numer. Anal. 34 (1997) 1884) remains valid with the left i-binomial scrambling, and thereby conclude that all the results on the expected errors of the integration problem so far obtained with Owen's scrambling also hold with the left i-binomial scrambling.     

Minimizing the Stabbing Number of Matchings, Trees, and Triangulations

The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segments that can be intersected by any one (axis-parallel) line. This paper deals with finding perfect matchings, spanning trees, or triangulations of minimum stabbing number for a given set of vertices. The complexity of finding a spanning tree of minimum stabbing number is one of the original 30 questions on “The Open Problems Project” list of outstanding problems in computational geometry by Demaine, Mitchell, and O’Rourke. We show -hardness of stabbing problems by means of a general proof technique. For matchings, this also implies a nontrivial lower bound on the approximability. On the positive side, we propose a cut-based integer programming formulation for minimizing the stabbing number of matchings and spanning trees. From the corresponding linear programming relaxation we obtain polynomial-time lower bounds and show that there always is an optimal fractional solution that contains an edge of at least constant weight. We conjecture that the resulting iterated rounding scheme constitutes a constant-factor approximation algorithm. An extended abstract appeared in the Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms [11]. M.E. Lübbecke visits to Kingston and Stony Brook were supported by a DFG travel grant. H. Meijer partially supported by NSERC while visiting Braunschweig in 2002.     

On the Nyström and Column-Sampling Methods for the Approximate Principal Components Analysis of Large Datasets

In this article, we analyze approximate methods for undertaking a principal components analysis (PCA) on large datasets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the leading eigenvectors of the covariance matrix. This projection can be used either for exploratory purposes or as an input for further analysis, for example, regression. If the data have billions of entries or more, the computational and storage requirements for saving and manipulating the design matrix in fast memory are prohibitive. Recently, the Nyström and column-sampling methods have appeared in the numerical linear algebra community for the randomized approximation of the singular value decomposition of large matrices. However, their utility for statistical applications remains unclear. We compare these approximations theoretically by bounding the distance between the induced subspaces and the desired, but computationally infeasible, PCA subspace. Additionally we show empirically, through simulations and a real data example involving a corpus of emails, the trade-off of approximation accuracy and computational complexity.