A penalty method for nonparametric estimation of the intensity function of a counting process

Nonparametric estimators are proposed for the logarithm of the intensity function of some univariate counting processes. An Aalen multiplicative intensity model is specified for our counting process and the estimators are derived by a penalized maximum likelihood method similar to the method introduced by Silverman for probability density estimation. Asymptotic properties of the estimators, such as uniform consistency and normality, are investigated and some illustrative examples from survival theory are analyzed.This work was conducted while the author was visiting the Department of Mathematics, University of California at Irvine.     

电声技术近年进展

本文讨论近年电声技术的进展，综述电声器件概况，介绍高保真立体声中的环境声和数字声频，并总结迅速发展的声场电声控制技术，最后讨论了主观电声测量方面的动态．     

A Trust Region SQP Algorithm for Equality Constrained Parameter Estimation with Simple Parameter Bounds

We describe a new algorithm for a class of parameter estimation problems, which are either unconstrained or have only equality constraints and bounds on parameters. Due to the presence of unobservable variables, parameter estimation problems may have non-unique solutions for these variables. These can also lead to singular or ill-conditioned Hessians and this may be responsible for slow or non-convergence of nonlinear programming (NLP) algorithms used to solve these problems. For this reason, we need an algorithm that leads to strong descent and converges to a stationary point. Our algorithm is based on Successive Quadratic Programming (SQP) and constrains the SQP steps in a trust region for global convergence. We consider the second-order information in three ways: quasi-Newton updates, Gauss-Newton approximation, and exact second derivatives, and we compare their performance. Finally, we provide results of tests of our algorithm on various problems from the CUTE and COPS sets.     

一个除数问题的推广

本文推广了Ｒ．Ａ．Ｓｍｉｔｈ，Ｍ．Ｖ．Ｓｕｂｂａｒａｏ和Ｇ．Ｎｏｗａｋ所考虑的一个除数问题．令Ｓ＝｛（ａｉ，ｑｉ）｜ａｉ≤ｑｉ｝（ｒ≥３）．定义ｄ（ｎ；Ｓ）＝Σ（１）１，Σ（１）表示对满足ｎ＝ｍ１…ｍｒ，ｍｊ≡ａｊ（ｍｏｄｑｊ），ｊ＝１，２，…，ｒ的诸ｍｊ求和．我们求出了Σｎ≤ｘｄ（ｎ；Ｓ）的渐近公式，并得到了余项估计．     

Nonparametric Estimation for Gibbs Random Fields Specified Through One‐Point Systems

The problem of nonparametric estimation for Gibbs random fields is considered. The field is supposed to be specified through a translation invariant quasilocal one‐point system. An estimator of one‐point system is constructed by the method of sieves, and its exponential and L^p consistencies are proved in different setups. The results hold regardless of non‐uniqueness and translation invariance breaking. This revised version was published online in June 2006 with corrections to the Cover Date.     

Parameter cascades and profiling in functional data analysis

A data smoothing method is described where the roughness penalty depends on a parameter that must be estimated from the data. Three levels of parameters are involved in this situation: Local parameters are the coefficients of the basis function expansion defining the smooth, global parameters define low-dimensional trend and the roughness penalty, and a complexity parameter controls the amount of roughness in the smooth. By defining local parameters as regularized functions of global parameters, and global parameters in turn as functions of complexity parameter, we define a parameter cascade, and show that the accompanying multi-criterion optimization problem leads to good estimates of all levels of parameters and their precisions. The approach is illustrated with real and simulated data, and this application is a prototype for a wide range of problems involving nuisance or local parameters.     

Estimating the distance to a monotone function

In standard property testing, the task is to distinguish between objects that have a property 𝒫 and those that are ε‐far from 𝒫, for some ε > 0. In this setting, it is perfectly acceptable for the tester to provide a negative answer for every input object that does not satisfy 𝒫. This implies that property testing in and of itself cannot be expected to yield any information whatsoever about the distance from the object to the property. We address this problem in this paper, restricting our attention to monotonicity testing. A function f : {1,…,n} ↦ R is at distance ε_f from being monotone if it can (and must) be modified at ε_fn places to become monotone. For any fixed δ > 0, we compute, with probability at least 2/3, an interval [(1/2 − δ)ε,ε] that encloses ε_f. The running time of our algorithm is O(ε_f⁻¹ log log ε_f^{− 1} log n), which is optimal within a factor of loglog ε_f⁻¹ and represents a substantial improvement over previous work. We give a second algorithm with an expected running time of O(ε_f⁻¹ log nlog log log n). Finally, we extend our results to multivariate functions. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

失效率的综合E-Bayes估计

该文提出了可靠性参数的一种新估计方法综合E-Bayes估计法.在无失效数据情形下给出了失效率的E-Bayes估计的定义,并给出了失效率的E-Bayes估计。在引进失效信息后，给出了失效率的E-Bayes估计，并在此基础上给出了失效率和其它参数的综合E-Bayes估计。最后，结合实际问题进行计算，结果表明该文提出的方法可行且便于应用。     

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??This paper constructs a penalized empirical likelihood estimation method via quadratic inference function method, filter method and empirical likelihood estimation method. Under some regular conditions, we derived the large sample properties of estimators and show that the proposed empirical likelihood ratio is asymptotically to chi-square distribution. Furthermore, the infinite sample performance of the proposed method is evaluated by Monte Carlo simulation and real data analysis.     

The estimation of moments of an unknown error distribution in the discrete pulse transform

Intuition suggests that the variance of additive noise contaminating a signal can be estimated by investigation of the highest resolution level in a local Nonlinear Multiresolution Analysis. In the case of the Discrete Pulse Transforms with LULU-operators well known elegant identities between B-splines lead to some surprisingly simple and useful results.