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In recent years, two-sample testing problems with one sample from a mixture distribution have been studied in the literature. Some of these studies ignore an auxiliary information that the exposure or treatment involved in the two-sample problems may have a positive (or negative) effect on the response variable if the effect exists. The positive (or negative) effect implies an inequality constraint. In this paper, we establish the homogeneity tests for the two-sample problem with a mixture structure by considering the inequality constraint, and their null limiting distributions are shown to be a mixture of chi-square distributions. Simulation studies and real data analysis show that the proposed tests have better performance than the existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a nonconcave penalized M-estimation of the least absolute relative errors (penalized M-LARE) method for a sparse multiplicative regression model, where the dimension of model can increase with the sample size. Under certain appropriate conditions, the consistency and asymptotic normality for the penalized M-LARE estimator are established. Simulations and a real data analysis are in support of our theoretical results and illustrate that the proposed method performs well. [ABSTRACT FROM AUTHOR]

Variable selection approaches are often employed in high-dimensionality and multicollinearity problems. Since lasso selects variables by shrinking the coefficients, it has extensive use in many fields. On the other, we may sometime have extra information on the model. In this case, the extra information should be considered in the estimation procedure. In this paper, we propose a stochastic restricted lasso estimator in linear regression model which uses the extra information as stochastic linear restrictions. The estimator is a generalization of mixed estimator with L1 type penalization. We give the coordinate descent algorithm to estimate the coefficient vector of the proposed method and strong rules for the coordinate descent algorithm to discard variables from the model. Also, we propose a method to estimate the tuning parameter. We conduct two real data analyses and simulation studies to compare the new estimator with several estimators including the ridge, lasso and stochastic restricted ridge. The real data analyses and simulation studies show that the new estimator enjoys the automatic variable selection property of the lasso while outperforms standard methods, achieving lower test mean squared error. [ABSTRACT FROM AUTHOR]

The penalized regression is an important technique for high-dimensional data analysis, but penalized estimation method hinge on finding a suitable choice of tuning parameter. In this paper, a simple modified L curve method is proposed to select the tuning parameter for penalized estimation including Lasso, SCAD and MCP in linear regression models. Through data simulation and actual data analysis, we find that the modified L curve method can be simpler and more accurate than traditional tuning parameter selection schemes such as CV and BIC. Furthermore, the method is able to identify the true model consistently and has the less model error, especially for the cases where there is a high correlation between predictors. [ABSTRACT FROM AUTHOR]

Tecator dataset has been widely used in the content of functional data analysis. As far as we know, this dataset is only considered under mean regression, which is easily affected by outliers. However, there are 8 more fat samples and 17 more protein samples in this dataset, so, in this paper, we explore this dataset by quantile regression, which is a robust method. Single-index partially functional linear quantile regression is proposed, and B-splines are used to estimate the unknown link function in the single-index component and the unknown slope function in the functional linear component. We establish the convergence rates and asymptotic normality of the estimators. Simulation studies and a real data application are presented to illustrate the performance of the proposed methodologies. [ABSTRACT FROM AUTHOR]

In the context of reliability theory, Eginhard J. Muth introduced in 1977 a continuous probability distribution that has been overlooked in the statistical literature. This paper is devoted to that model. Some statistical measures of the distribution are expressed in closed form and it is shown that the model has increasing failure rate and strictly positive memory. Moreover, the members of this family of distributions can be ordered in terms of the hazard rate order. With respect to the parameter estimation, a problem of identifiability was found via Monte Carlo simulation, which is due to the existence of two shape parameters. Such a problem is overcome if one of the parameters is assumed to be known and then the maximum likelihood method provides accurate estimates. Rainfall data sets from the Australian Bureau of Meteorology are used to illustrate that the model under consideration may be an interesting alternative to other probability distributions commonly used for modeling non-negative real data. [ABSTRACT FROM AUTHOR]

In this paper, we model the daily volatility curve as a realization of functional data. We implement the spline technique to estimate the mean and covariance functions. Uniform convergence of the estimated mean and covariance functions are established. Simulation and real data studies justify that our estimation of the mean and covariance functions is accurate. [ABSTRACT FROM AUTHOR]

Identification of influential observations is crucial in data analysis, particularly with high dimensional datasets, where the number of predictors is higher than the sample size. These rich datasets with extensive detail are increasingly exploited and analyzed in multiple fields of science, e.g., genomics, neuroscience, finance, etc. Unfortunately, classical diagnostic statistical tools are not tailored for identifying influential observations in high dimensional setup. In this paper, we use the concept of expectiles to develop an influence measure in high dimensional regression. The influence measure is based on the asymmetric marginal correlation, and its derived asymptotic distribution is used to define a threshold based on statistical principles. Our comprehensive simulation results display the favorable qualities of this influence measure under various scenarios. The usefulness of the proposed measure is illustrated through the analysis of a neuroimaging dataset. An R package implementing the procedure is publicly available on GitHub (). [ABSTRACT FROM AUTHOR]

The local Walsh-average regression has been shown to be a comparable method to the others in nonparametric regression. In this paper, we develop a new estimation procedure based on local Walsh-average regression for single index varying coefficient models. Under some general assumptions, we establish the asymptotic properties of the proposed estimators for both the parametric and nonparametric parts. We further demonstrate that the proposed estimates have great efficiency gains across a wide spectrum of non-normal error distributions and almost not lose any efficiency for the normal error compared with that of local polynomial regression estimates under the least squares loss. Even in the worst case scenarios, the asymptotic relative efficiency owns a lower bound equaling to 0.864 for estimating the single-index parameter and a lower bound being 0.8896 for estimating the nonparametric link functions respectively, versus the least squares estimators. A simulation study is conducted to assess the finite sample properties of the proposed procedure, and a real data analysis is followed to further illustrate the application of the proposed methodology. [ABSTRACT FROM AUTHOR]

The reversed hazard rate, defined as the ratio of the density to the distribution function, has recently drawn great interest in reliability and survival analysis due to its usefulness in the analysis of left-censored data. This paper develops the mixture model of discrete reversed hazard rates and studies its main properties. Similar to the continuous case, results of the bending property for the reversed hazard rate in discrete case are studied. In addition, mixtures of the mean inactivity time, which are closely related to the reversed hazard rate, are discussed and the corresponding results of its bending property are also investigated. Preservation of aging properties under both mixtures of reversed hazard rate and mean inactivity time is discussed as well. As a special case, the proportional discrete reversed hazard rate model is presented and the bending properties for this case are also discussed. Finally, stochastic comparisons of the mixture discrete reversed hazard rates of two mixed populations are addressed. [ABSTRACT FROM AUTHOR]

Weibull distribution is widely used in engineering because of its flexibility to take on many different shapes. For different application fields, people put forward different estimation methods, including grey estimation method. The purpose of this paper is to improve the existing grey estimation method of Weibull distribution as its some serious shortcomings. Firstly, a grey three-parameter Weibull model is proposed in a discrete form. Then, by means of the grey Weibull model, a two-stage hybrid method for estimating the three-parameter Weibull distribution is proposed, which is composed of the linear and nonlinear least square principles. To demonstrate the feasibility of the proposed grey Weibull model, a simulation study was conducted and compared the results with the modified MLE method, and a comparison study on the frequency analysis of four breakdown data sets of epoxy resins is also carried out. Moreover, as a practical application, Weibull model based on the grey estimation approach is applied to the frequency analysis of monthly wind speed of Hohhot in 2018, and compared with a series of existing estimation methods. Results show that the proposed grey Weibull estimation improves the existing grey estimation and can be well applied to the frequency analysis of Weibull data. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the variable selection for varying coefficient errors-in-variables (EV) models with longitudinal data when some covariates are measured with additive errors. A variable selection method based on bias-corrected penalized quadratic inference function (pQIF) is proposed by combining the basis function approximation to coefficient functions and bias-corrected quadratic inference function (QIF) with shrinkage estimations. The proposed method can handle the measurement errors of covariates and within-subject correlation, estimate and select non-zero nonparametric coefficient functions. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection method and the sparsity properties of the regularized estimators. The finite sample performance of the proposed method is assessed by simulation studies. The utility of the method is further demonstrated via a real data analysis. [ABSTRACT FROM AUTHOR]

This paper proposes a new efficient composite quantile regression (CQR) estimating function for the semivarying models with longitudinal data, which can incorporate the correlation structure between repeated measures via the Gaussian copula. Because the objective function is non-smooth and non-convex, the induced smoothing method is used to reduce computational burdens. It is proved that the smoothed estimator is asymptotically equivalent to the original estimator. Furthermore, a smooth-threshold efficient CQR estimating equation variable selection method is proposed. Because the new method can incorporate the correlation structure and inherit the good properties of CQR, it has the advantages of both robustness and high estimation efficiency. Simulation studies and real data analysis are also included to illustrate the finite sample performance of our methods. [ABSTRACT FROM AUTHOR]

This paper presents a new efficient and robust inference method by combing the robust generalized estimating equations and the well-known empirical likelihood method in longitudinal data analysis. Based on a bounded exponential score function and leverage-based weights, robust auxiliary random vectors are constructed to achieve robustness against outliers both in the response and the covariate domains. Moreover, the additional tuning parameter in the exponential score function can be automatically selected by the observed data. Finally, some simulation studies and a real data analysis are carried out to demonstrate the performances of the proposed method. [ABSTRACT FROM AUTHOR]

This paper focuses on robust estimation for varying coefficient partially functional linear regression model (VCPFLM) without specification of the error distributions. The proposed estimators of the nonparametric coefficients and slope function are based on B-spline approximation and rank regression, which demonstrates that the proposed estimation is robust for non-normal error distributions compared with that of least square estimate. In addition, the optimal convergence rates of the estimators are established under some mild regularity conditions. Finally, simulation study and a real data analysis are conducted to illustrate the finite sample performance of the proposed method. [ABSTRACT FROM AUTHOR]

Empirical likelihood has been widely used in survival data analysis recently. In this paper, we combine Bayesian idea with empirical likelihood and develop a Bayesian empirical likelihood method to analyze current status data based on the linear regression model. By constructing unbiased transformation of current status data, we derive an empirical log-likelihood function. The normal prior distribution and a Metro-Hastings method are presented to make Bayesian posterior inference. The theoretical properties of the estimators are proposed. Extensive simulation studies indicate that Bayesian empirical likelihood method performs much better than the empirical likelihood method in terms of coverage probability. Finally, we apply two real data to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

In network data analysis, one of the fundamental data mining tasks is to find dense subgraphs, which has wide applications in biology, finance, graph compression and so on. In practice, given network data, it's unknown whether a dense subgraph exists or not. Statistically, this problem can be formulated as a hypothesis testing problem: under the null distribution, there is no dense subgraph while under the alternative hypothesis, a dense subgraph exists. In the graph regime, this problem has been well studied. However, in the hypergraph case, to our knowledge, it's still open. In this paper, we study the problem in the context of uniform hypergraphs. Specifically, we propose a test statistic, derive its asymptotic distributions under the null and alternative hypothesis, and show the power may approach one when the sample size goes to infinity. Then we use simulation and real data to evaluate the finite sample performance of our test. [ABSTRACT FROM AUTHOR]

In this study, we propose an improved matrix-based computational method of the Gini index. The proposed method is ideal for large datasets since it calculates the value of the Gini index effectively with high computational speed satisfying the needs of the modern data analysis. In the first part of the study, we introduce the matrix-based computational method for non grouped data and the proposed decomposable form of the Gini index in case of grouped data. The second part of the study validates the proposed methodology comparing the elapsed time for the calculation of the Gini index between the methods. The experimental results prove that the proposed method is superior in terms of the calculation of the index since the elapsed time is significantly reduced in comparison with the methods that already exist. [ABSTRACT FROM AUTHOR]

This article addresses the issue of multicollinearity for the distributed lag model via Bayesian approach. We introduce the Bayes Almon ridge estimator under this approach by employing prior information. Specifically, the resulting estimator is a new Bayesian estimator that is the mean of posterior density function for the coefficient of the Almon model. Also, a restricted version of this estimator is proposed by using Lagrange multipliers to optimize the coefficients under the additional exact linear constraints. In mathematical sense, theoretical comparisons are carried out by employing mean squared error utilizing matrix theory. Additionally, we investigate a selection method for the biasing parameter of the new estimators with the help of the mean squared error comparisons. To test the theoretical suggestions, we perform a real-life data analysis as a means of applied mathematics. Moreover, we benefit from Monte Carlo simulation techniques where we use several levels of different parameters. The outcomes of numerical example and simulation study favor the new estimators and, hence we succeed in eliminating the multicollinearity. [ABSTRACT FROM AUTHOR]

It has become an increasingly common practice in modern science and engineering to collect samples of multiple network data in which a network serves as a basic data object. The increasing prevalence of multiple network data calls for developments of models and theories that can deal with inference problems for populations of networks. In this work, we propose a general procedure for hypothesis testing of networks and in particular, for differentiating distributions of two samples of networks. We consider a very general framework which allows us to perform test on large and sparse networks. Our contribution is two-fold: (1) We propose a test statistics based on the singular value of a generalized Wigner matrix. The asymptotic null distribution of the statistics is shown to follow the Tracy–Widom distribution as the number of nodes tends to infinity. The test also yields asymptotic power guarantee with the power tending to one under the alternative; (2) The test procedure is adapted for change-point detection in dynamic networks which is proven to be consistent in detecting the change-points. In addition to theoretical guarantees, another appealing feature of this adapted procedure is that it provides a principled and simple method for selecting the threshold that is also allowed to vary with time. Extensive simulation studies and real data analyses demonstrate the superior performance of our procedure with competitors. [ABSTRACT FROM AUTHOR]

The process of parameter estimation in order to characterize a population using algorithms is in constant development and perfection. Recent years show that data-based decision-making is complex when there is uncertainty generated by statistical censoring. The purpose of this article is to evaluate the effect of statistical censoring on the normal distribution, which is common in many processes. Parameter estimation properties will be characterized with the conditional expected value algorithm, using different censoring percentages and sample sizes. The estimation properties chosen for the study will focus on the monitoring and decision-making related to industrial processes with the presence of censoring. [ABSTRACT FROM AUTHOR]

Existing studies on spatial linear mixed models typically assume a normal distribution for the random error components. However, such an assumption may not be appropriate in many applications. This work relaxes the normality assumption of a generalized linear mixed model with spatial correlated by using an unrestricted multivariate skew-normal distribution, which includes the normal distribution as a special case. For parameter estimation, a Bayesian inference algorithm is developed. A simulation study and the analysis of a real data set of cigarette consumption observed between 1963 and 1992 located in 46 states of the US are conducted to compare the proposed skew normal spatial mixed model with the normal spatial mixed model. [ABSTRACT FROM AUTHOR]

Motivated by applications in microarray data analysis, we consider the problem of estimating the row sparsity of the coefficient matrix in multivariate regression. The problem is formulated as a row-wise multiple testing problem. A new test statistic is constructed for each row of the coefficient matrix, and a row-wise multiple testing procedure is proposed. Our approach takes advantage of the row sparsity of the coefficient matrix to gain high power and handles the correlation structure of the error vector. Asymptotic distribution of the test statistic and asymptotic false discovery control of the row-wise multiple testing procedure are provided. Numerical results are also presented to evaluate the performance of the proposed method in both simulation studies and real data analysis. [ABSTRACT FROM AUTHOR]

Post-selection inference has been an active research topic recently. A lot of work provided different ways to solve practical problems in many fields such as medicine, finance, and so on. In particular, post-selection inference under the linear model is widely discussed. We extend it to generalized linear model and present new approaches for post-selection inference for penalized least squares method. The core of this framework is the distribution function of the post-selection estimation conditioned on the selection event. Then, lasso and elastic net are used to select models to construct the effective confidence interval of the selected coefficient. The theoretical results and the numerical comparisons show that our methods are better than the existing ones. Finally, the proposed methods are applied to the analysis of real data sets. [ABSTRACT FROM AUTHOR]

A quantile-quantile (Q–Q) plot is derived from a characterization for the multivariate normal distribution and the Shapiro–Wilk's (1965) S–W statistic. The normal characterization results in some independent spherical distributions. The affine invariance of the S–W statistic and a simple property of spherical distributions are employed to construct the Q–Q plot. Easy simulation of the empirical distribution of the S–W statistic avoids the complicated exact null distribution of S-W statistic. The Q–Q plot can be easily implemented for detecting a possible departure from multivariate normality in high dimensional data analysis. Two examples are illustrated for real application. [ABSTRACT FROM AUTHOR]

Fused Lasso is one of extensions of Lasso to shrink differences of parameters. We focus on a general form of it called generalized fused Lasso (GFL). The optimization problem for GFL can be came down to that for generalized Lasso and can be solved via a path algorithm for generalized Lasso. Moreover, the path algorithm is implemented via the genlasso package in R. However, the genlasso package has some computational problems. Then, we apply a coordinate descent algorithm (CDA) to solve the optimization problem for GFL. We give update equations of the CDA in closed forms, without considering the Karush-Kuhn-Tucker conditions. Furthermore, we show an application of the CDA to a real data analysis. [ABSTRACT FROM AUTHOR]

In order to improve the accuracy and the precision of estimation in a sample survey, the ratio estimator and the regression estimator using auxiliary information have been widely used. The ratio estimator is simple in its form, convenient to use. However, the ratio estimator gives good results only when the variance structure is suitable for the use. On the other hand, even though the regression estimator is relatively complex in form, it gives highly accurate and robust result for the various distribution types. In this study, we propose a generalized ratio-type estimator obtained by approximating a ratio-type estimator to the regression estimator in case with several auxiliary variables. Therefore, the generalized ratio-type estimator has the features of the multiple regression estimator and it has the form of the ratio-type estimator which is simple and easy to use. Through simulation studies, we confirm the theoretical results and the Korea financial statement analysis data are used for real data analysis. [ABSTRACT FROM AUTHOR]