Information and asymptotic efficiency of the case-cohort sampling design in Cox's regression model

Efficiencies of the maximum pseudolikelihood estimator and a number of related estimators for the case-cohort sampling design in the proportional hazards regression model are studied. The asymptotic information and lower bound for estimating the parametric regression parameter are calculated based on the effective score, which is obtained by determining the component of the parametric score orthogonal to the space generated by the infinite-dimensional nuisance parameter. The asymptotic distributions of the maximum pseudolikelihood and related estimators in an i.i.d. setting show that these estimators do not achieve the computed asymptotic lower bound. Simple guidelines are provided to determine in which instances such estimators are close enough to efficient for practical purposes.     

Analysis of blockwise shrinkage wavelet estimates via lower bounds for no-signal setting

A blockwise shrinkage is a popular procedure of adaptation that has allowed the statisticians to establish an impressive bouquet of asymptotic mathematical results and develop softwares for solving practical problems. Traditionally risks of the estimates are studied via upper bounds that imply sufficient conditions for a blockwise shrinkage procedure to be minimax. This article suggests to analyze the estimates via exact (non-asymptotic) lower bounds established for a no-signal setting. The approach complements the familiar minimax, Bayesian and numerical analysis, it allows to find necessary conditions for a procedure to attain desired rates, and it sheds a new light on popular choices of blocks and thresholds recommended in the literature. Mathematical results are complemented by a numerical study. Supported in part by NSF Grants DMS-9971051 and DMS-0243606.     

Sequential Estimation of the Parameters in a Trigonometric Regression Model with the Gaussian Coloured Noise

This paper considers the estimation problem for a trigonometric regression model with the noise specified by the Ornstein–Uhlenbeck process with unknown parameter. We propose a sequential procedure which ensures a prescribed mean square precision uniformly in the nuisance parameter. The asymptotic behaviour of the procedure duration mean has been studied. This revised version was published online in August 2006 with corrections to the Cover Date.     

10瓦级双包层光纤激光器

考虑到所用大功率激光二极管的光谱特性，对光纤激光器的基本法布里-珀罗腔型稍加改变，研制出激光二极管抽运的10w级双包层光纤激光器，获得最高功率为11．8w、波长1100mm的单模激光输出。     

应用无衍射贝塞尔光束的固体线膨胀系数测量系统

测量固体线膨胀系数是工程设计中的一项重要工作。这套非接触固体线膨胀系数测量系统利用激光三角法进行了设计。通过采用线阵CCD作为信号传感器来实现自动化测量。通过采用无衍射贝塞尔光束来提高测量精度和增大测量范围。     

Une méthode de calcul des coefficients de réflexion et de transmission d'une houle bidimensionnelle en milieu confinéA new method for the calculation of transmission and reflection coefficients for water waves in a small basin

This paper presents a method to estimate reflected and transmitted wave amplitude spectra in a bounded domain such as a wave tank, when available data signals must be shortened due to interferences and wall effects. This paper extends the well known Goda and Suzuki two-probe method to three probes. The paper also suggests solutions to compute reliable transmission and reflection coefficients in spite of problems linked to higher harmonics and to the interference between different wave trains propagating in the tank. To cite this article: G. Duclos, A.H. Clément, C. R. Mecanique 331 (2003).     

Minimum Disparity Estimation in Linear Regression Models: Distribution and Efficiency

This paper deals with the minimum disparity estimation in linear regression models. The estimators are defined as statistical quantities which minimize the blended weight Hellinger distance between a weighted kernel density estimator of errors and a smoothed model density of errors. It is shown that the estimators of the regression parameters are asymptotic normally distributed and efficient at the model if the weights of the density estimators are appropriately chosen.     

Second Order Representations of the Least Absolute Deviation Regression Estimator

We consider exact weak and strong Bahadur-Kiefer representations of the least absolute deviation estimator for the linear regression model. The precise behavior of these representations is obtained under minimal conditions.     

Extension of multivariate regression trees to interval data. Application to electricity load profiling

Summary  Several data can be presented as interval curves where intervals reflect a within variability. In particular, this representation is well adapted for load profiles, which depict the electricity consumption of a class of customers. Electricity load profiling consists in assigning a daily load curve to a customer based on their characteristics such as energy requirement. Within the load profiling scope, this paper investigates the extension of multivariate regression trees to the case of interval dependent (or response) variables. The tree method aims at setting up simultaneously load profiles and their assignment rules based on independent variables. The extension of multivariate regression trees to interval responses is detailed and a global approach is defined. It consists in a first stage of a dimension reduction of the interval response variables. Thereafter, the extension of the tree method is applied to the first principal interval components. Outputs are the classes of the interval curves where each class is characterized both by an interval load profile (e.g. the class prototype) and an assignment rule based on the independent variables.     

Some Properties of an Operator on L^∞（△） and Its Applications

In this paper, we introduce an operator Hμ（z） on L^∞（△） and obtain some of its properties. Some applications of this operator to the extremal problem of quasiconformal mappings are given. In particular, a sufficient condition for a point r in the universal Teichmfiller space T（△） to be a Strebel point is obtained.