Constructing optimal designs for fitting pharmacokinetic models

We consider some computational issues that arise when searching for optimal designs for pharmacokinetic (PK) studies. Special factors that distinguish these are (i) repeated observations are taken from each subject and the observations are usually described by a nonlinear mixed model (NLMM), (ii) design criteria depend on the model fitting procedure, (iii) in addition to providing efficient parameter estimates, the design must also permit model checking, (iv) in practice there are several design constraints, (v) the design criteria are computationally expensive to evaluate and often numerical integration is needed and finally (vi) local optimisation procedures may fail to converge or get trapped at local optima.We review current optimal design algorithms and explore the possibility of using global optimisation procedures. We use these latter procedures to find some optimal designs.For multi-purpose designs we suggest two surrogate design criteria for model checking and illustrate their use.     

有序拓扑空间上多元函数的连续性定理

本文在有序拓扑空间上建立了[1]中的问题Ⅰ之逆命题,并把它推广到n元情形。     

奥尔里奇空间L_φ(μ,X)内的最佳逼近问题

设X是一实巴拿赫空间，（Ω，μ）是[O，1]上的勒贝格测度空间，φ是定义在[0，+∞）上具φ（O）＝0的严格增加的连续凸函数。L_φ（μ，X）={可测函数f:Ω→X；存在c＞0使得∫f（t）||)dμ（t）＜+∞｝。本文的主要结果之一为：若Y是X的闭子空间，则L_φ（μ，Y）是L_φ（μ，X）的存在性集充要条件为L'（μ,Y）是L'(μ，X)的存在性集；同时也给出了有关L_φ(μ，X）子空间存在性集的其他结果。     

凸函数的一个等价定义

本文讨论了定义在区间上的凸函数与其单调性之间的内在联系，并给出了凸函数的一个等价定义．     

A Compressive Sensing Based Analysis of Anomalies in Generalized Linear Models

In this article, we present a compressive sensing based framework for generalized linear model regression that employs a two-component noise model and convex optimization techniques to simultaneously detect outliers and determine optimally sparse representations of noisy data from arbitrary sets of basis functions. We then extend our model to include model order reduction capabilities that can uncover inherent sparsity in regression coefficients and achieve simple, superior fits. Second, we use the mixed ?₂/?₁ norm to develop another model that can efficiently uncover block-sparsity in regression coefficients. By performing model order reduction over all independent variables and basis functions, our algorithms successfully deemphasize the effect of independent variables that become uncorrelated with dependent variables. This desirable property has various applications in real-time anomaly detection, such as faulty sensor detection and sensor jamming in wireless sensor networks. After developing our framework and inheriting a stable recovery theorem from compressive sensing theory, we present two simulation studies on sparse or block-sparse problems that demonstrate the superior performance of our algorithms with respect to (1) classic outlier-invariant regression techniques like least absolute value and iteratively reweighted least-squares and (2) classic sparse-regularized regression techniques like LASSO.     

Lasso with convex loss: Model selection consistency and estimation

Abstract

Variable selection is a fundamental challenge in statistical learning if one works with data sets containing huge amount of predictors. In this artical we consider procedures popular in model selection: Lasso and adaptive Lasso. Our goal is to investigate properties of estimators based on minimization of Lasso-type penalized empirical risk with a convex loss function, in particular nondifferentiable. We obtain theorems concerning rate of convergence in estimation, consistency in model selection and oracle properties for Lasso estimators if the number of predictors is fixed, i.e. it does not depend on the sample size. Moreover, we study properties of Lasso and adaptive Lasso estimators on simulated and real data sets.     

求凸二次函数极值的一种递推算法

本文通过讨论凸二次函数的几个结论,给出了求凸二次函数极值的一种递推算法．     

Inhomogeneous Markov Chains and Ergodicity Coefficients: John Hajnal (1924–2008)

In 1958, a paper by John Hajnal, a demographer and mathematical statistician, was fundamental in the revival of the theory of inhomogeneous Markov chains. Hajnal made his contribution by the development of tools for the analysis of weak ergodicity, and proofs of fundamental theorems. This article reviews Hajnal's career, and then focuses on the four topics: 1. ergodicity coefficients and the weak ergodicity theorem; 2. scrambling matrices; 3. the coupling theorem; and 4. non-negative matrix products. Related work by other authors, especially Wolfgang Doeblin, is mentioned in context. Attention is given to some recent surveys and applications of ergodicity coefficients, including the Google matrix.     

Optimal consumption and portfolio selection with negative wealth constraints,subsistence consumption constraints,and CARA utility

We consider the optimal consumption and portfolio selection problem with constant absolute risk aversion (CARA) utility. The economic agent in this model receives constant labor income, and her economic behavior is restricted on consumption and wealth, which are called the subsistence consumption constraint and the negative wealth constraint. We use the convex duality method to derive the value function and the optimal policies in closed-form solutions. Also we illustrate some numerical examples.