The Singularity of the Information Matrix of the Mixed Proportional Hazard Model

This paper presents new identification conditions for the mixed proportional hazard model. In particular, the baseline hazard is assumed to be bounded away from 0 and ∞ near t = 0. These conditions ensure that the information matrix is nonsingular. The paper also presents an estimator for the mixed proportional hazard model that converges at rate N^−1/2.     

Generalized discrete discrepancy and its applications in experimental designs

In recent years, there has been increasing interest in the study of discrete discrepancy. In this paper, the popular discrete discrepancy is extended to the so-called generalized discrete discrepancy. Connections among generalized discrete discrepancy and other optimality criteria, such as orthogonality, generalized minimum aberration and minimum moment aberration, are investigated. These connections provide strong statistical justification of generalized discrete discrepancy. A lower bound of generalized discrete discrepancy is also obtained, which serves as an important benchmark of design uniformity.     

Column generation with free replicability in DEA

The evaluation of efficiency scores in data envelopment analysis is based on the construction of artificial decision making units subject to some assumptions, usually requiring convexity of the production possibility set. This demands divisibility in input and output, which is not always possible. The so-called free replicability model, proposed by Henry Tulkens, permits input and output to enter in only discrete amounts. The model is of a mixed integer programming type, for which the number of variables, here corresponding to the decision making units, may be critical in order to reach an optimal solution.     

A Lagrangian relaxation approach for the multiple sequence alignment problem

We present a branch-and-bound (bb) algorithm for the multiple sequence alignment problem (MSA), one of the most important problems in computational biology. The upper bound at each bb node is based on a Lagrangian relaxation of an integer linear programming formulation for MSA. Dualizing certain inequalities, the Lagrangian subproblem becomes a pairwise alignment problem, which can be solved efficiently by a dynamic programming approach. Due to a reformulation w.r.t. additionally introduced variables prior to relaxation we improve the convergence rate dramatically while at the same time being able to solve the Lagrangian problem efficiently. Our experiments show that our implementation, although preliminary, outperforms all exact algorithms for the multiple sequence alignment problem. Furthermore, the quality of the alignments is among the best computed so far.     

Optimal Berry–Esseen bound for parameter estimation of SPDE with small noise

We investigate a rate of convergence on asymptotic normality of the maximum likelihood estimator (MLE) for parameter $\theta$ appearing in parabolic SPDEs of the form

$d{u}^{?}(t,x)=(A_0+\theta A_1)u^{?}(t,x)dt+?dW(t,x),$

where $A_0$ and$A_1$ are partial differential operators, $W$ is a cylindrical Brownian motion (CBM) and $?\downarrow 0$. We find an optimal Berry–Esseen bound for central limit theorem (CLT) of the MLE. It is proved by developing techniques based on combining Malliavin calculus and Stein’s method.     

Computing the conditional stationary distribution in Markov chains of level-dependent M/G/1-type

This paper considers the computation of the conditional stationary distribution in Markov chains of level-dependent M/G/1-type, given that the level is not greater than a predefined threshold. This problem has been studied recently and a computational algorithm is proposed under the assumption that matrices representing downward jumps are nonsingular. We first show that this assumption can be eliminated in a general setting of Markov chains of level-dependent G/G/1-type. Next we develop a computational algorithm for the conditional stationary distribution in Markov chains of level-dependent M/G/1-type, by modifying the above-mentioned algorithm slightly. In principle, our algorithm is applicable to any Markov chain of level-dependent M/G/1-type, if the Markov chain is irreducible and positive-recurrent. Furthermore, as an input to the algorithm, we can set an error bound for the computed conditional distribution, which is a notable feature of our algorithm. Some numerical examples are also provided.     

A new per-field classification method using mixture discriminant analysis

In this study, a new per-field classification method is proposed for supervised classification of remotely sensed multispectral image data of an agricultural area using Gaussian mixture discriminant analysis (MDA). For the proposed per-field classification method, multivariate Gaussian mixture models constructed for control and test fields can have fixed or different number of components and each component can have different or common covariance matrix structure. The discrimination function and the decision rule of this method are established according to the average Bhattacharyya distance and the minimum values of the average Bhattacharyya distances, respectively. The proposed per-field classification method is analyzed for different structures of a covariance matrix with fixed and different number of components. Also, we classify the remotely sensed multispectral image data using the per-pixel classification method based on Gaussian MDA.     

Uniformity pattern and related criteria for q-level factorials

The objective of this paper is to study the issue of the projection discrepancy along the line of Liu (2002) and Fang and Qin (2005) based on discrete discrepancy measure proposed in Qin and Fang (2004), which has wide application to the field of fractional factorials. Here we also study the projection properties for q-level factorials and provide connection between minimum projection uniformity and other optimality criteria. A lower bound to projection discrepancy for q-level factorials is presented here.     

Local asymptotic minimax theory for block-decreasing densities

In this paper, we study Lebesgue densities on (0,∞)^d$(0,\infty {)}^d$ that are non-increasing in each coordinate, while keeping all other coordinates fixed, from the perspective of local asymptotic minimax lower bound theory. In particular, we establish a local optimal rate of convergence of the order n^−1/(d+2)$n^{-1/(d+2)}$.