半定规划鲁棒不可行性研究

本文给出了一种判别半定规划鲁棒不可行的准则,通过该准则我们可判断模型对输入数据是否敏感,进而决定是否应该利用鲁棒优化建模的方法对模型进行重新建模,使其所求解具有鲁棒性.避免了所给模型在实际应用中存在较大的风险性,为更好的应用鲁棒优化建模方法提供了理论依据.     

Tests of Independence and Zero Correlations Among P Random Variables

Suppose it is desired to determine whether there is an association between any pair of p random variables. A common approach is to test H₀ : R = I, where R is the usual population correlation matrix. A closely related approach is to test H₀ : R_pb = I, where R_pb is the matrix of percentage bend correlations. In so far as type I errors are a concern, at a minimum any test of H₀ should have a type I error probability close to the nominal level when all pairs of random variables are independent. Currently, the Gupta-Rathie method is relatively successful at controlling the probability of a type I error when testing H₀: R = I, but as illustrated in this paper, it can fail when sampling from nonnormal distributions. The main goal in this paper is to describe a new test of H₀: R_pb = I that continues to give reasonable control over the probability of a type I error in the situations where the Gupta-Rathie method fails. Even under normality, the new method has advantages when the sample size is small relative to p. Moreover, when there is dependence, but all correlations are equal to zero, the new method continues to give good control over the probability of a type I error while the Gupta-Rathie method does not. The paper also reports simulation results on a bootstrap confidence interval for the percentage bend correlation.     

A Note on the Theil-Sen Regression Estimator When the Regressor Is Random and the Error Term Is Heteroscedastic

In simple regression, two serious problems with the ordinary least squares (OLS) estimator are that its efficiency can be relatively poor when the error term is normal but heteroscedastic, and the usual confidence interval for the slope can have highly unsatisfactory probability coverage. When the error term is nonnormal, these problems become exacerbated. Two other concerns are that the OLS estimator has an unbounded influence function and a breakdown point of zero. Wilcox (1996) compared several estimators when there is heteroscedasticity and found two that have relatively good efficiency and simultaneously provide protection against outliers: an M-estimator with Schweppe weights and an estimator proposed by Cohen, Dalal and Tukey (1993). However, the M-estimator can handle only one outlier in the X-domain or among the Y values, and among the methods considered by Wilcox for computing confidence intervals for the slope, none performed well when working with the Cohen-Dalal-Tukey estimator. This note points out that the small-sample efficiency of theTheil-Sen estimator competes well with the estimators considered by Wilcox, and a method for computing a confidence interval was found that performs well in simulations. The Theil-Sen estimator has a reasonably high breakdown point, a bounded influence function, and in some cases its small-sample efficiency offers a substantial advantage over all of the estimators compared in Wilcox (1996).     

Pairwise Comparisons Using Trimmed Means or M-Estimators when Working with Dependent Groups

For J dependent groups, let θ_j, j = 1, …, J, be some measure of location associated with the jth group. A common goal is computing confidence intervals for the pairwise differences, θ_j — θ_k, j < k, such that the simultaneous probability coverage is 1 — α. If means are used, it is well known that slight departures from normality (as measured by the Kolmogorov distance) toward a heavy-tailed distribution can substantially inflate the standard error of the sample mean, which in turn can result in relatively low power. Also, when distributions differ in shape, or when sampling from skewed distributions with relatively light tails, practical problems arise when the goal is to obtain confidence intervals with simultaneous probability coverage reasonably close to the nominal level. Extant theoretical and simulation results suggest replacing means with trimmed means. The Tukey-McLaughlin method is easily adapted to the problem at hand via the Bonferroni inequality, but this paper illustrates that practical concerns remain. Here, the main result is that the percentile t bootstrap method, used in conjunction with trimmed means, gives improved probability coverage and substantially better power. A method based on a one-step M-estimator is also considered but found to be less satisfactory.     

An analysis of australopithecine dentition

The means and variances of dental length, breadth, and area measurements of South and East African gracile and robust australopithecines are analyzed to determine the existence of statistically significant differences due possibly to different niche utilization and divergent evolution. The study material is divided into four groups: South African gracile, South African robust, East African gracile, and East African robust. Comparison of East and South African graciles, East African robusts and graciles, and South African robusts and graciles shows few significant F-ratios; a high frequency of significance is observed between East and South African robusts. High frequencies of significance are observed in t tests between all groups. Probit analysis, carried out on each of the four groups separately for each measurement, shows little or no significant deviation from normality; similar results are obtained when the groups are combined, suggesting the joint-normal distribution of the total australopithecine sample. High frequencies of significant t tests and low frequencies of significant F-ratios are observed when all graciles are compared with all robusts; yet few significant t tests and many significant F-ratios occur when all East African forms are combined with all South African forms. Observed differences in dental measurements in australopithecines tend to occur on a regional rather than a morphologic basis, especially with regard to robust samples from South and East Africa. While analysis of variance and probit analysis cannot be used to establish taxonomic divisions, results suggest the inappropriateness of dental measurements in establishing an australopithecine taxonomy.     

时滞大系统鲁棒稳定性补充结果

利用代数Ｒｉｃｃａｔｉ方法和Ｌｙａｐｕｎｏｖ稳定性,本文分别得到带有匹配条件和非匹配条件的时滞大系统的鲁棒稳定性判别准则,通过仿真实例进一步说明本文所得稳定性的容许界限优于文献中的结论。     

Biodiversity dynamics and their driving factors during the Cretaceous diversification of Spatangoida (Echinoidea, Echinodermata)

Variations in recorded diversity over time present a scrambled signal that is modulated by a large number of variables: the potential of particular life forms to generate evolutionary innovations, external constraints induced by the environment in its broad sense, the heterogeneity of the fossil record and the analytical artefacts due to sampling bias. A key question is how to characterise and quantify the separate input of any given factor in the overall diversity signal. This paper explores the structure of diversity data for spatangoid heart urchins and the sensitivity of recorded diversity to different factors of analytical bias (length of geological periods, proportion of palaeogeographical realms explored, accessible area of outcrops and historical determinism). Unexpectedly, recorded diversity of spatangoids is not proportional to the duration of stages. Bias implied by time scale is negligible compared to bias of sampling or historical determinism. Diversity at any given time is dependent on its recent history (autocorrelation). For spatangoids, a high correlation between diversity at time t_i and t_i−1 suggests that recorded diversity has an evolutionary significance. A nearly constant rate of diversification is hypothesised for the Cretaceous. A relative poor fossil record during the Turonian and the Coniacian interrupts the main trend of diversification. The number of species counted for a single time interval depends on the number of palaeogeographical realms considered. In conjunction with ecological and phylogenetic data, this relation suggests an evolutionary signal in which western Tethys acted as a centre of origination. Diversity at a single location is constrained ecologically and diversification is controlled by migration into new realms. Recorded diversity and available area of outcrop seem to be correlated, but alternative interpretations can be drawn, including large-scale bias in the fossil record or operation of similar causes (e.g., effect of sea-level fluctuation). Comparing recorded diversity with separate factors independently leads to conflicting results. A multivariate approach suggests that the main trend in recorded diversity might be partially related to evolutionary signal or biases connected with the heterogeneity of the fossil record. Results from other approaches (phylogeny, morphological disparity) are consistent with and emphasise the evolutionary significance of the recorded diversity of spatangoids.     

Median percent change: A robust alternative for assessing temporal trends

A typical summary statistic for temporal trends is the average percent change (APC). The APC is estimated by using a generalized linear model, usually under the assumption of linearity on the logarithmic scale. A serious limitation of least-squares type estimators is their sensitivity to outliers. The goal of this study is twofold: firstly, we propose a robust and easy-to-compute measure of the temporal trend based on the median of the rates (median percent change – MPC), rather than their mean, under the hypothesis of constant relative change; secondly, we investigate the performance of several models for estimating the rate of change when some of the most common model assumptions are violated. We provide some guidance on the practices of the estimation of temporal trends when using different models under different circumstances. The robustness property of the median is assessed in a simulation study, which shows that the MPC provides strong reductions in estimation bias and variance in presence of outliers. We also demonstrate how a mathematical property of the median helps addressing the issue of zero counts when estimating trends on the log-scale. Finally, we analyzed an English cancer registration dataset to illustrate the proposed method. We believe that, as a good practice, both APC and MPC should be presented when sensitivity issues arise.     

Estimators Asymptotically Minimax in Wide Sense

Estimators of location are considered. Huber (1964) introduced estimators asymptotically minimax on the set ?? of all regular M-estimators, for a given contamination ε and for the set Q of all regular symmetric alternative data sources. We extend his concept by admitting arbitrary sets ?? of regular M-estimators and arbitrary sets Q or regular symmetric alternative sources, and also by replacing the singletons [ε] ? (0, 1) by arbitrary subsets ?? ? (0, 1). The resulting estimator cannot in general be evaluated explicitly. But for finite T it exists and, if ?? and Q are finite too, it may be chosen by a computer. This extra burden is justified in some cases since more than 100% relative efficiency gain against all Huber's Hk is achievable in this manner. Such gains are achieved for a nontrivial family Q by the estimator proposed in Vajda (1984), with redescending influence curve, which is shown to be asymptotically minimax in wide sense.     

Application of projection pursuit based robust principal component analysis to ECG enhancement

The paper presents an application of principal component analysis (PCA) to ECG processing. For this purpose the ECG beats are time-aligned and stored in the columns of an auxiliary matrix. The matrix, considered as a set of multidimensional variables, undergoes PCA. Reconstruction of the respective columns on the basis of a low dimensional principal subspace leads to the enhancement of the stored ECG beats. A few modifications of this classical approach to ECG signal filtering by means of a multivariate analysis are introduced. The first one is based on replacing the classical PCA by its robust extension. The second consists in replacing the analysis of the whole synchronized beats by the analysis of shorter signal segments. This creates the background for the third modification, which introduces the concept of variable dimensions of the subspaces corresponding to different parts of ECG beats. The experiments performed show that introduction of the respective modifications significantly improves the classical approach to ECG processing by application of principal component analysis.     

变时滞区间细胞神经网络的全局鲁棒稳定性

利用拓扑度理论和Liapunov泛函方法讨论了变时滞区间细胞神经网络的全局鲁棒稳定性．给出了实用有效的判定条件,推广了有关文献中的结果．     

A new association test based on disease allele selection for case–control genome-wide association studies

Background

Current robust association tests for case–control genome-wide association study (GWAS) data are mainly based on the assumption of some specific genetic models. Due to the richness of the genetic models, this assumption may not be appropriate. Therefore, robust but powerful association approaches are desirable.

Results

In this paper, we propose a new approach to testing for the association between the genotype and phenotype for case–control GWAS. This method assumes a generalized genetic model and is based on the selected disease allele to obtain a p-value from the more powerful one-sided test. Through a comprehensive simulation study we assess the performance of the new test by comparing it with existing methods. Some real data applications are also used to illustrate the use of the proposed test.

Conclusions

Based on the simulation results and real data application, the proposed test is powerful and robust.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2164-15-358) contains supplementary material, which is available to authorized users.     

Pseudo-Likelihood for Combined Selection and Pattern-Mixture Models for Incomplete Data

In this paper we develop pseudo-likelihood methods for the estimation of parameters in a model that is specified in terms of both selection modelling and pattern-mixture modelling quantities. Two cases are considered: (1) the model is specified directly from a joint model for the measurement and dropout processes; (2) conditional models for the measurement process given dropout and vice versa are specified directly. In the latter case, compatibility constraints to ensure the existence of a joint density are derived. The method is applied to data from a psychiatric study, where a bivariate therapeutic outcome is supplemented with covariate information.     

A point process driven multiple change point model: A robust resistant approach

Helicases are a class of enzymes involved in Ribonucleic Acid (RNA) metabolism. In this work a statistical method is proposed to analyze the individual mechanistic cycle of these motor proteins which are crucial to the understanding of their cellular functions. The RNA unwinding by NS3 helicase is hypothesized to occur in a series of discrete steps and the steps themselves occurring in accordance to an underlying point process. A point process driven multiple change point model is proposed to model the RNA unwinding mechanism. The methods are portable to other areas of applications as well. Algorithms based on robust-resistant statistical procedures are proposed to detect the change points. Both sequential and a posteriori change point models are considered. The relevant parameters of interest are estimated using a maximum likelihood approach. Simulations are performed to assess the performance of the methodology.