COMPARISONS AND SELECTION OF TWO-PARAMETER EXPONENTIAL POPULATIONS

For two-parameter exponential populations with the same scale parameter (known or unknown) comparisons are made between the location parameters. This is done by constructing confidence intervals, which can then be used for selection procedures. Comparisons are made with a control, and with the (unknown) “best” or “worst” population. Emphasis is laid on finding approximations to the confidence so that calculations are simple and tables are not necessary. (Since we consider unequal sample sizes, tables for exact values would need to be extensive.)     

SHOULD WE ESTIMATE THE PROBABILITY OF CORRECT SELECTION?

Various authors, given k location parameters, have considered lower confidence bounds on (standardized) dserences between the largest and each of the other k - 1 parameters. They have then used these bounds to put lower confidence bounds on the probability of correct selection (PCS) in the same experiment (as was used for finding the lower bounds on differences). It is pointed out that this is an inappropriate inference procedure. Moreover, if the PCS refers to some later experiment it is shown that if a non-trivial confidence bound is possible then it is already possible to conclude, with greater confidence, that correct selection has occurred in the first experiment. The short answer to the question in the title is therefore ‘No’, but this should be qualified in the case of a Bayesian analysis.     

Selecting the normal population with the smallest variance: A restricted subset selection rule

Consider k( ? 2) normal populations whose means are all known or unknown and whose variances are unknown. Let σ²_[1] ? ??? ? σ_[k]² denote the ordered variances. Our goal is to select a non empty subset of the k populations whose size is at most m(1 ? m ? k ? 1) so that the population associated with the smallest variance (called the best population) is included in the selected subset with a guaranteed minimum probability P* whenever σ²_[2]/σ_[1]² ? δ* > 1, where P* and δ* are specified in advance of the experiment. Based on samples of size n from each of the populations, we propose and investigate a procedure called R_BCP. We also derive some asymptotic results for our procedure. Some comparisons with an earlier available procedure are presented in terms of the average subset sizes for selected slippage configurations based on simulations. The results are illustrated by an example.     

Composite Estimation for Single‐Index Models with Responses Subject to Detection Limits

We propose a semiparametric estimator for single‐index models with censored responses due to detection limits. In the presence of left censoring, the mean function cannot be identified without any parametric distributional assumptions, but the quantile function is still identifiable at upper quantile levels. To avoid parametric distributional assumption, we propose to fit censored quantile regression and combine information across quantile levels to estimate the unknown smooth link function and the index parameter. Under some regularity conditions, we show that the estimated link function achieves the non‐parametric optimal convergence rate, and the estimated index parameter is asymptotically normal. The simulation study shows that the proposed estimator is competitive with the omniscient least squares estimator based on the latent uncensored responses for data with normal errors but much more efficient for heavy‐tailed data under light and moderate censoring. The practical value of the proposed method is demonstrated through the analysis of a human immunodeficiency virus antibody data set.     

A three-stage variable selection method for supersaturated designs

A supersaturated design (SSD) is a design whose run size is not enough for estimating all main effects. Such a design is commonly used in screening experiments to screen active effects based on the effect sparsity principle. Traditional approaches, such as the ordinary stepwise regression and the best subset variable selection, may not be appropriate in this situation. In this article, a new variable selection method is proposed based on the idea of staged dimensionality reduction. Simulations and several real data studies indicate that the newly proposed method is more effective than the existing data analysis methods.     

Hard thresholding regression

In this paper, we propose the hard thresholding regression (HTR) for estimating high‐dimensional sparse linear regression models. HTR uses a two‐stage convex algorithm to approximate the ?₀‐penalized regression: The first stage calculates a coarse initial estimator, and the second stage identifies the oracle estimator by borrowing information from the first one. Theoretically, the HTR estimator achieves the strong oracle property over a wide range of regularization parameters. Numerical examples and a real data example lend further support to our proposed methodology.     

Fast and approximate exhaustive variable selection for generalised linear models with APES

We present APproximated Exhaustive Search (APES), which enables fast and approximated exhaustive variable selection in Generalised Linear Models (GLMs). While exhaustive variable selection remains as the gold standard in many model selection contexts, traditional exhaustive variable selection suffers from computational feasibility issues. More precisely, there is often a high cost associated with computing maximum likelihood estimates (MLE) for all subsets of GLMs. Efficient algorithms for exhaustive searches exist for linear models, most notably the leaps‐and‐bound algorithm and, more recently, the mixed integer optimisation (MIO) algorithm. The APES method learns from observational weights in a generalised linear regression super‐model and reformulates the GLM problem as a linear regression problem. In this way, APES can approximate a true exhaustive search in the original GLM space. Where exhaustive variable selection is not computationally feasible, we propose a best‐subset search, which also closely approximates a true exhaustive search. APES is made available in both as a standalone R package as well as part of the already existing mplot package.     

关于Feigenbaum型泛函方程的C^1解

利用Schauder不动点定理、自同胚和紧凸子集的相关性质研究Feigenbaum型泛函方程的连续可微解的存在性和唯一性.     

遗传算法在入侵检测中的应用

介绍了基于模型推理和基于模型两种入侵检测系统,提出了一种新的基于智能体技术的入侵检测系统体系结构,解决了传统集中式入侵检测系统的弊病,将任务处理和数据分布到网络各个结点上,充分利用网络资源协同完成入侵检测任务;介绍了遗传算法在该系统中的应用,因系统安全的先验知识体现在对原始数据中有价值特征属性变量集的选择上,故利用遗传算法对特征属性变量子集的选择进行优化,找到相对最优的由特征向量表示的特征属性变量集,以降低入侵检测系统的负荷。     

Machine Learning for Drug Overdose Surveillance

ABSTRACT

We describe two recently proposed machine learning approaches for discovering emerging trends in fatal accidental drug overdoses. The Gaussian Process Subset Scan (Herlands, McFowland, Wilson, & Neill, 2017 Neill, D. B. (2017). Multidimensional tensor scan for drug overdose surveillance. Journal of Public Health Informatics, 9(1), e20. doi:10.5210/ojphi.v9i1.7598[Crossref] , [Google Scholar]) enables early detection of emerging patterns in spatio-temporal data, accounting for both the complex, correlated nature of the data and the fact that detecting subtle patterns requires integration of information across multiple spatial areas and multiple time steps. We apply this approach to 17 years of county-aggregated data for monthly opioid overdose deaths in the New York City metropolitan area, showing clear advantages in the utility of discovered patterns as compared to typical anomaly detection approaches. To detect and characterize emerging overdose patterns that differentially affect a subpopulation of the data, including geographic, demographic, and behavioral patterns (e.g., which combinations of drugs are involved), we apply the Multidimensional Tensor Scan (Neill, 2017 Neill, D. B. (2017). Multidimensional tensor scan for drug overdose surveillance. Journal of Public Health Informatics, 9(1), e20. doi:10.5210/ojphi.v9i1.7598[Crossref] , [Google Scholar]) to 8 years of case-level overdose data from Allegheny County, Pennsylvania. We discover previously unidentified overdose patterns which reveal unusual demographic clusters, show impacts of drug legislation, and demonstrate potential for early detection and targeted intervention. These approaches to early detection of overdose patterns can inform prevention and response efforts, as well as understanding the effects of policy changes.