Semisupervised data classification via the Mumford–Shah–Potts-type model

More and more high dimensional data are widely used in many real world applications. This kind of data are obtained from different feature extractors, which represent distinct perspectives of the data. How to classify such data efficiently is a challenge. Despite of existence of millions of unlabeled data samples, it is believed that labeling a handful of data such as the semisupervised scheme will remarkably improve the searching performance. However, the performance of semisupervised data classification highly relies on proposed models and related numerical methods. Following from the extension of the Mumford–Shah–Potts-type model in the spatially continuous setting, we propose some efficient data classification algorithms based on the alternating direction method of multipliers and the primal-dual method to efficiently deal with the nonsmoothing problem in the proposed model. The convergence of the proposed data classification algorithms is established under the framework of variational inequalities. Some balanced and unbalanced classification problems are tested, which demonstrate the efficiency of the proposed algorithms.     

Bernstein Polynomial Estimation in the Partially Linear Model under Monotonicity Constraints

In this paper, a Bernstein-polynomial-based likelihood method is proposed for the partially linear model under monotonicity constraints. Monotone Bernstein polynomials are employed to approximate the monotone nonparametric function in the model. The estimator of the regression parameter is shown to be asymptotically normal and efficient, and the rate of convergence of the estimator of the nonparametric component is established, which could be the optimal under the smooth assumptions. A simulation study and a real data analysis are conducted to evaluate the finite sample performance of the proposed method.     

关于两总体均值差的一种半参数假设检验方法

近年来, 已有一些在半参数密度函数比模型下建立半参数统计分析方法的报道, 这些方法往往比参数方法稳健, 比非参数方法有效. 在本文里, 我们提出一种半参数的假设检验方法用于对两总体均值差进行假设检验. 该方法主要建立在对两总体均值差进行半参数估计的基础上. 我们报告了一些理论和统计模拟的结果, 得出该方法在数据符合正态性假设时, 比常用的参数和非参数方法略好; 而在数据不符合正态性假设时, 它的优势就非常明显. 我们还将提出的方法用到了两组真实数据的分析上.     

A multi-objective-ACO-based data association method for bearings-only multi-target tracking

The study is concerned with data association of bearings-only multi-target tracking using two stationary observers in a 2-D scenario. In view of each target moving with a constant speed, two objective functions, i.e., distance and slope differences, are proposed and a multi-objective-ant-colony-optimization-based algorithm is then introduced to execute data association by minimizing the two objective functions. Numerical simulations are conducted to evaluate the effectiveness of the proposed algorithm in comparison with the data association results of the joint maximum likelihood (ML) method under different noise levels and track figurations.     

Parameter Estimation for a Mixture of Generalized Exponential Distributions under Grouped and Right-Censored Samples

Parameter estimation of mixed generalized exponential distribution model under grouped and right-censored data is considered by using EM algorithm in this paper. The estimation formulae are obtained and some simulations are presented to illustrate the proposed method. Finally, a set of medicine data is analyzed.     

Kernel Smoothing Estimation for Varying Coefficient EV Models with Longitudinal Data

Varying coefficient EV models with longitudinal data are considered. The local bias-corrected kernel estimators for the unknown coefficient functions are proposed. It is shown that the proposed estimators are asymptotically normal under some suitable conditions, and hence it can be used to construct the pointwise confidence regions of the coefficient functions. The finite-sample properties of the proposed procedures are studied through a simulation study.     

A more powerful test identifying the change in mean of functional data

An existence of change point in a sequence of temporally ordered functional data demands more attention in its statistical analysis to make a better use of it. Introducing a dynamic estimator of covariance kernel, we propose a new methodology for testing an existence of change in the mean of temporally ordered functional data. Though a similar estimator is used for the covariance in finite dimension, we introduce it for the independent and weakly dependent functional data in this context for the first time. From this viewpoint, the proposed estimator of covariance kernel is more natural one when the sequence of functional data may possess a change point. We prove that the proposed test statistics are asymptotically pivotal under the null hypothesis and consistent under the alternative. It is shown that our testing procedures outperform the existing ones in terms of power and provide satisfactory results when applied to real data.     

Testing quasi-independence for truncation data

Quasi-independence is a common assumption for analyzing truncated data. To verify this condition, we propose a class of weighted log-rank type statistics that include existing tests proposed by Tsai (1990) and Martin and Betensky (2005) as special cases. To choose an appropriate weight function that may lead to a more power test, we derive a score test when the dependence structure under the alternative hypothesis is modeled via the odds ratio function proposed by Chaieb, Rivest and Abdous (2006). Asymptotic properties of the proposed tests are established based on the functional delta method which can handle more general situations than results based on rank-statistics or U-statistics. Extension of the proposed methodology under two different censoring settings is also discussed. Simulations are performed to examine finite-sample performances of the proposed method and its competitors. Two datasets are analyzed for illustrative purposes.     

Generalized constrained co-inertia analysis

In this paper a method for generalized constrained co-inertia analysis is proposed. This approach is based on a suitable decomposition of each set of variables which incorporates external information on both rows and columns of data matrices. These external information are incorporated in the analysis in order to improve the interpretability of the phenomenon under investigation. Once both matrices are decomposed according to the external information, we propose to apply the co-inertia analysis to any pair of obtainable submatrices in order to study relationships between them. A variety of existing and new extensions of COA are then realized. According to the nature of the data, this approach subsumes also several generalized constrained methods proposed in literature. An example is given to illustrate the proposed method.     

A Bayesian approach for analyzing case 2 interval-censored data under the semiparametric proportional odds model

Analyzing interval-censored data is difficult due to its complex data structure containing left-, interval-, and right-censored observations. An easy-to-implement Bayesian approach is proposed under the proportional odds (PO) model for analyzing such data. The nondecreasing baseline log odds function is modeled with a linear combination of monotone splines. Two efficient Gibbs samplers are developed based on two different data augmentations using the relationship between the PO model and the logistic distribution. In the first data augmentation, the logistic distribution is achieved by the scaled normal mixture with the scale parameter related to the Kolmogorov-Smirnove distribution. In the second data augmentation, the logistic distribution is approximated by a Student’s t distribution up to a scale constant. The proposed methods are evaluated by simulation studies and illustrated with an application of an HIV data set.     

Properties of finite-difference schemes for singular integrodifferential equations of index 1

Systems of integrodifferential equations with a singular matrix multiplying the highest derivative of the unknown vector function are considered. An existence theorem is formulated, and a numerical solution method is proposed. The solutions to singular systems of integrodifferential equations are unstable with respect to small perturbations in the initial data. The influence of initial perturbations on the behavior of numerical processes is analyzed. It is shown that the finite-difference schemes proposed for the systems under study are self-regularizing.     

Imputation of mean of ratios for missing data and its application to PPSWR sampling

In practical survey sampling, nonresponse phenomenon is unavoidable. How to impute missing data is an important problem. There are several imputation methods in the literature. In this paper, the imputation method of the mean of ratios for missing data under uniform response is applied to the estimation of a finite population mean when the PPSWR sampling is used. The imputed estimator is valid under the corresponding response mechanism regardless of the model as well as under the ratio model regardless of the response mechanism. The approximately unbiased jackknife variance estimator is also presented. All of these results are extended to the case of non-uniform response. Simulation studies show the good performance of the proposed estimators.     

Formalization of a synthesis problem and methods for its solution

A formal formulation is proposed for the synthesis problem of finding objects with certain properties described only by a collection of precedents. A key feature of this formalization is that it is closely related to the pattern recognition theory. A general approach to solving the synthesis problem is described, and particular solution methods are presented in two important cases. For this purpose, a new recognition method is proposed that exhibits a high speed as applied to the data of the structure under study. The performance of the methods is demonstrated on actual data.     

Estimation of the Common Mean of a Bivariate Normal Population

In this paper we discuss the problem of estimating the common mean of a bivariate normal population based on paired data as well as data on one of the marginals. Two double sampling schemes with the second stage sampling being either a simple random sampling (SRS) or a ranked set sampling (RSS) are considered. Two common mean estimators are proposed. It is found that under normality, the proposed RSS common mean estimator is always superior to the proposed SRS common mean estimator and other existing estimators such as the RSS regression estimator proposed by Yu and Lam (1997, Biometrics, 53, 1070–1080). The problem of estimating the mean Reid Vapor Pressure (RVP) of regular gasoline based on field and laboratory data is considered.     

An equitable DEA-based approach for assigning fixed resources along with targets

A typical problem in organization management is how to divide a fixed resource along with a target among decision making units (DMUs) of an organization equitably. By using the data envelopment analysis technique, this paper concerns the problem from the perspective of efficiency analysis and proposes a new sharing model. In the proposed method, the fixed resource and target are divided among DMUs such that the efficiencies of DMUs remain unchanged after assigning the fixed cost and target. The proposed method is unit-invariant; it eliminates resource waste and target insufficiency brought by slacks. Also, every DMU is assigned a positive resource and a positive target under this method. Two corresponding algorithms are designed to yield a unique allocation. The proposed approach can be developed under both constant returns to scale and variable returns to scale. Two examples are presented to illustrate the validity and superiorities of our method.     

A non-linear thermo-viscoelastic rheological model based on fractional derivatives for high temperature creep in concrete

In this paper, a novel non-linear thermo-viscoelastic rheological model based on fractional derivatives for high temperature creep in concrete is proposed. The rheological model consists of a linear springpot unit placed in series with a second springpot used for non-linear creep which activates under high stress and temperature. The model parameters which include the dynamic viscosities of the springpots and the fractional exponent are calibrated using existing experimental data of basic creep strain in concrete under constant stress and temperatures for various aggregate types. The power law form of the naturally resulting creep compliance allows an accurate representation of experimental data with the use of only a few model parameters. Furthermore, the variable-order fractional differential stress-strain equation provides a compact method for analytical and numerical modelling of basic creep under conditions of time-varying stress and temperature. In addition, applications of the proposed model to determine axial deformations in columns and transverse deflections in beams under constant and varying temperatures are demonstrated.     

Bayesian inference on longitudinal-survival data with multiple features

The modeling of longitudinal and survival data is an active research area. Most of researches focus on improving the estimating efficiency but ignore many data features frequently encountered in practice. In this article, we develop a joint model that concurrently accounting for longitudinal-survival data with multiple features. Specifically, our joint model handles skewness, limit of detection, missingness and measurement errors in covariates which are typical observed in the collection of longitudinal-survival data from many studies. We employ a Bayesian approach for making inference on the joint model. The proposed model and method are applied to an AIDS study. A few alternative models under different conditions are compared. Some interesting results are reported. Simulation studies are conducted to assess the performance of the proposed methods.     

Covariate-Adjusted Nonparametric Regression for Time Series

The covariate-adjusted regression model was initially proposed for the situations where both the predictors and the response variables are not directly observed, but are distorted by some common observable covariates. In this paper, we investigate a covariate-adjusted nonparametric regression (CANR) model and consider the proposed model on time series setting. We develop a two-step estimation procedure to estimate the regression function. The asymptotic property of the proposed estimation is investigated under the -mixing conditions. Both the real data and simulated examples are provided for illustration.     

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In this article, we develop efficient robust method for estimation of mean and covariance simultaneously for longitudinal data in regression model. Based on Cholesky decomposition for the covariance matrix and rewriting the regression model, we propose a weighted least square estimator, in which the weights are estimated under generalized empirical likelihood framework. The proposed estimator obtains high efficiency from the close connection to empirical likelihood method, and achieves robustness by bounding the weighted sum of squared residuals. Simulation study shows that, compared to existing robust estimation methods for longitudinal data, the proposed estimator has relatively high efficiency and comparable robustness. In the end, the proposed method is used to analyse a real data set.     

Nonparametric Estimation of the Dependence Function in Bivariate Extreme Value Distributions

The paper considers the problem of estimating the dependence function of a bivariate extreme survival function with standard exponential marginals. Nonparametric estimators for the dependence function are proposed and their strong uniform convergence under suitable conditions is demonstrated. Comparisons of the proposed estimators with other estimators are made in terms of bias and mean squared error. Several real data sets from various applications are used to illustrate the procedures.