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Abstract: Abstract In literature, the idea of kernel machine was introduced to quantile regression, resulting kernel quantile regression (KQR) model, which is capable to fit nonlinear models with flexibility. However, the formulation of KQR leads to a quadratic programming which is computationally expensive to solve. This paper proposes a fast training algorithm for KQR based on majorization-minimization approach, in which an upper bound for the objective function is derived in each iteration which is easier to be minimized. The proposed approach is easy to implement, without requiring any special computing package other than basic linear algebra operations. Numerical studies on simulated and real-world datasets show that, compared to the original quadratic programming based KQR, the proposed approach can achieve essentially the same prediction accuracy with substantially higher time efficiency in training. PubDate: 2022-06-01
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Abstract: Abstract We consider a Bayesian framework for clustering the high-dimensional data and learning sparse multiple graphical models simultaneously. Different from most previous multiple graphs learning methods which assume that the cluster information is known in advance, we impose a multi-distribution prior for the cluster labels. Then a joint spike-and-slab graphical lasso prior is imposed for the precision matrices, which can induce a sparsity and homogeneity of the heterogeneous graphical models across all clusters adaptively. Additionally, by imposing a structural Markov random field (MRF) prior, the proposed method can also cluster the network-linked data without the independence assumption of the samples. Then a fast Expectation Maximization (EM) algorithm is utilized for the posterior inference. The proposed model can get a significant improvement both in clustering error and graphical selection precision. The simulations and real data analysis are shown to demonstrate the performance of our method. PubDate: 2022-06-01
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Abstract: Abstract This paper proposes and investigates the bivariate, the marginal distribution functions and quantiles estimators and their asymptotic properties for naïve, ratio, and difference estimators based on the bivariate stratified simple random sampling (BVSSRS) and bivariate stratified ranked set sampling designs (BVSRSS). We demonstrate that the proposed estimators using BVSRSS and BVSSRS are consistent and asymptotically normally distributed. Improved performance of the proposed estimators using BVSRSS compared to BVSSRS supported through an intensive simulation study. The derivation of the optimal allocation based on BVSSRS and BVSRSS is provided. The National Health and Nutrition Examination Survey (NHANES) data is used to illustrate the methods. PubDate: 2022-06-01
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Abstract: Abstract One of the fundamental topics in statistical inference is constructing a confidence interval for a binomial proportion p. It is well known that commonly used asymptotic confidence intervals, such as the Wilson and Agresti–Coull confidence intervals, suffer from systematic bias and oscillations in their coverage probabilities. We generalize asymptotic confidence intervals, including the Wald, Wilson and Agresti–Coull intervals, and propose a generalized Agresti–Coull type confidence interval by adjusting the bias with the saddlepoint approximation. We compare the coverage probabilities and lengths of the proposed confidence interval with those of other popular asymptotic confidence intervals. We show that the proposed confidence interval is more stable than the Wilson interval at the boundaries of p and has a shorter length than the Agresti–Coull interval. PubDate: 2022-06-01
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Abstract: Abstract In this paper, we propose a smoothed estimator and variable selection method for partially linear quantile regression models with nonignorable missing responses. To address the identifiability problem, a parametric propensity model and an instrumental variable are used to construct sufficient instrumental estimating equations. Subsequently, the nonparametric function is approximated by B-spline basis functions and the kernel smoothing idea is used to make estimation statistically and computationally efficient. To accommodate the missing response and apply the popular empirical likelihood (EL) to obtain an unbiased estimator, we construct bias-corrected and smoothed estimating equations based on the inverse probability weighting approach. The asymptotic properties of the maximum EL estimator for the parametric component and the convergence rate of the estimator for the nonparametric function are derived. In addition, the variable selection in the linear component based on the penalized EL is also proposed. The finite-sample performance of the proposed estimators is studied through simulations, and an application to HIV-CD4 data set is also presented. PubDate: 2022-06-01
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Abstract: Abstract Spatial dynamic panel data (SDPD) models have received great attention in economics in recent 10 years. Existing approaches for the estimation and test of SDPD models are quasi-maximum likelihood (QML) approach and generalized method of moments (GMM). In this article, we introduce the empirical likelihood (EL) method to the statistical inference for SDPD models. The EL ratio statistics are constructed for the parameters of spatial dynamic panel data models. It is shown that the limiting distributions of the empirical likelihood ratio statistics are chi-squared distributions, which are used to construct confidence regions for the parameters of the models. Simulation results show that the EL based confidence regions outperform the normal approximation based confidence regions. PubDate: 2022-06-01
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Abstract: Abstract For right-censored survival data, censored quantile regression is emerging as an attractive alternative to the Cox’s proportional hazards and the accelerated failure time models. Censored quantile regression has been considered as a robust and flexible alternative in the sense that it can capture a variety of treatment effects at different quantile levels of survival function. In this paper, we present a novel regularized estimation and variable selection procedure for censored quantile regression model. Statistical inference on censored quantile regression is often based on a martingale-based estimating function that may require a strict linearity assumption and a grid-search procedure. Instead, we employ a local kernel-based Kaplan–Meier estimator and modify the quantile loss function to facilitate censored observations. This approach allows us to assume the linearity condition only at the particular quantile level of interest. Our proposed method is then regularized by using LASSO and adaptive LASSO, along with sufficient dimension reduction, to select a subset of informative covariates in a high-dimension setting. The asymptotic properties of the proposed estimators are rigorously studied. Their finite-sample properties and practical utility are explored via simulation studies and application to PBC data. PubDate: 2022-06-01
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Abstract: Abstract This paper deals with one-way classification analysis when the response variable follows the one-parameter Fréchet distribution and the factor effects are random. The stochastic properties of the response variable are studied in detail. Maximum likelihood estimations of the model parameters are also given in explicit expressions. Under the square error loss function, the best predictions for the random-effects are derived. Three procedures for testing the hypothesis of population homogeneity are proposed and misspecification problem is investigated in a special case. Several illustrative examples are also given to assess the performances of the proposed model. Findings of this paper may be used in engineering, survival and, longitudinal studies. PubDate: 2022-06-01
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Abstract: Abstract In this study, we have developed one new approximate method to obtain a probability density function of a solution of a given stochastic differential equation (SDE) at a fixed time. The mentioned method is based on the estimation SDE fitting to given statistical data and approximate methods solving SDE. For this purpose, by approximate methods solving SDE trajectories of this equation are constructed. For example, it is possible to use the Euler–Maruyama (EM) method. By using trajectories at a fixed time are obtained reasonable random variables of the solution of SDE. The probability density function of the mentioned random variables is obtained. It is possible to use different statistical methods. These results are acquired by using the theorem. In our investigation, it is used Generalized Entropy Optimization Methods (GEOM). The reason using GEOM’s is explained oneself by the fact that these methods represent distributions that are more flexible distributions. We illustrated the use of this new method to apply the SDE model fitting on S&P 500 stock data. PubDate: 2022-06-01
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Abstract: Abstract In this paper, we introduce a bivariate extension of three-parameter generalized crack distribution for modelling loss data. Some basic properties such as the conditional distribution and the measures of association are discussed, and a method of parameter estimation is offered. A simulation-based approach to compute bivariate value-at-risk under the model is also discussed. The proposed model and estimation method are illustrated with a model fitting exercise on a real catastrophic loss data set. PubDate: 2022-06-01
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Abstract: Abstract In this study, we consider the problem of detecting a change point in the conditional quantile of GARCH models. The task is essential in risk management as the conditional quantile is utilized to calculate the value-at-risk (VaR) of asset prices. We propose the cumulative sum (CUSUM) tests based on the residuals and derive their limiting distributions under mild conditions. We also demonstrate the validity of the tests by conducting Monte Carlo simulations, followed by a real data analysis of the exchange rate between the US Dollar and Korean Won and the Korea composite stock price index. PubDate: 2022-06-01
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Abstract: Abstract In this paper, we propose a new scalar-transformation-invariant test for linear hypothesis on mean vectors of normal population with unequal covariance matrices in high-dimensional data. The asymptotic null and non-null distributions of our new test are obtained under some regularity conditions. The performance of the proposed test is conducted by numerical simulation and a real data example, which illustrates our new test outperforms competitors in the considered cases. Moreover, numerical studies show that our new test can also be applied to non-normal data. PubDate: 2022-06-01
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Abstract: Abstract We consider modeling of Fourier coefficients, known as a spectral density function to represent spatial dependence of a stationary spatial random field and use it for spatial regression under a Bayesian framework. Especially, we switch from the space domain to the frequency domain and introduce a Gaussian process prior to the log spectral density. As we do not impose any further assumption on log spectral density, resulting covariance function is not of a parametric form and/or isotropic assumption. Simulation study supports that our approach is robust over various parametric covariance models. Also, our approach gives comparable or better prediction results over conventional spatial prediction under most parametric covariance models that we considered. Even though we need to estimate spectral density at all Fourier frequencies during the Bayesian procedure, our approach does not lose much computational efficiency compared to estimating only a few parameters in the parametric covariance models. We also compare our approach with some other existing spatial prediction approaches using two datasets of Korean ozone concentration. Our approach performs reasonably good in terms of mean absolute error and root mean squared error. PubDate: 2022-06-01
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Abstract: In this paper, the Bayesian empirical likelihood (BEL) inference is considered for the generalized binomial AR(1) model. We establish a nonparametric likelihood using the empirical likelihood (EL) approach and consider a specific prior based on copulas. An efficient Markov chain Monte Carlo (MCMC) procedure is described for the required computation of the posterior distribution. In the simulation study, we analyze the accuracy and sensitivity of the MCMC algorithm. We also study the robustness of the new method. The results imply that our algorithm converges quickly and not strongly influenced by the model assumptions. Furthermore, the BEL method is robust. Finally, a real data example is analyzed to illustrate of our method. PubDate: 2022-05-09
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Abstract: Abstract The relative belief ratio becomes a widespread tool in many hypothesis testing problems. It measures the statistical evidence that a given statement is true based on a combination of data, model and prior. Additionally, a measure of the strength is used to calibrate its value. In this paper, robustness of the relative belief ratio and its strength to the choice of the prior is studied. Specifically, the Gâteaux derivative is used to measure their sensitivity when the geometric contaminated prior is used. Examples are presented to illustrate the results. PubDate: 2022-05-03
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Abstract: Abstract Meta-analysis, the statistical analysis of results from separate studies, is a fundamental building block of science. But the assumptions of classical meta-analysis models are not satisfied whenever publication bias is present, which causes inconsistent parameter estimates. Hedges’ selection function model takes publication bias into account, but estimating and inferring with this model is tough for some datasets. Using a generalized Gleser–Hwang theorem, we show there is no confidence set of guaranteed finite diameter for the parameters of Hedges’ selection model. This result provides a partial explanation for why inference with Hedges’ selection model is fraught with difficulties. PubDate: 2022-04-22
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Abstract: Abstract In this article, we develop a distance-based testing for assessing the adequacy of conditional variance function using pairwise distances. Under the null hypothesis, we state the limiting distribution of the proposed statistic, which is complicated. A resampling type statistic is proposed for approximating the null distribution, and we prove the validity of the resampling algorithm. The test could detect any local alternatives at a nearly optimal rate. Simulation studies are provided to examine the numerical performance of the proposed test, and a real data example is illustrated its application. PubDate: 2022-04-19
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Abstract: Abstract With the explosive growth of data, it is a challenge to infer the quantity of interest by combining the existing different research data about the same topic. In the case-cohort setting, our aim is to improve the efficiency of parameter estimation for Cox model by using subgroup information in the aggregate data. So we put forward the generalized moment method (GMM) to use the auxiliary survival information at some critical time points. However, the auxiliary information is likely obtained from other studies or populations, two extended GMM estimators are proposed to account for multiplicative and additive inconsistencies. We establish the consistency and asymptotic normality of the proposed estimators. In addition, the uniform consistency and asymptotic normality of Breslow estimator are also presented. From the asymptotic normality, we show that the proposed approaches are more efficient than the traditional weighted estimating equation method. In particular, if the number of subgroups is equal to one, the asymptotic variance-covariances of the GMM estimators are identical with the weighted score estimate. Some simulation studies and a real data study demonstrate the proposed methods and theories. In the numerical studies, our approaches are even better than the full cohort estimator and the extended GMM methods are robust. PubDate: 2022-03-28
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Abstract: Abstract We give strong large deviation results for some ratio distributions. Then we apply these results to two statistical examples: a ratio distribution with sums of gamma-distributed random variables and another one with sums of \(\chi ^2\) -distributed random variables. We eventually carry out numerical comparisons with a saddlepoint approximation using an indirect Edgeworth expansion and a Lugannani and Rice saddlepoint approximation. PubDate: 2022-03-22
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Abstract: Abstract In this study, we propose a multivariate-response regression by imposing structural conditions on the underlying regression coefficient matrix motivated by an analysis of Cancer Cell Line Encyclopedia (CCLE) data consisting of resistance responses to multiple drugs and gene expression of cancer cell lines. It is important to estimate the drug resistance response from gene information and identify those genes responsible for the sensitivity of the resistance response to each drug. We consider a penalized multiple-response regression estimator using both generalized \(\ell _1\) norm and nuclear norm regularizers based on the motivations that only a few genes are relevant to the effect of drug resistance responses and that some genes could have similar effects on multiple responses. For the statistical properties, we developed non-asymptotic error bounds of the proposed estimator. In our numerical analysis using simulated and CCLE data, the proposed method better predicts the drug responses than the other methods. PubDate: 2022-03-03
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