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This paper focuses on estimating the Self-Exciting Threshold Autoregressive (SETAR) type time-series model under right-censored data. As is known, the SETAR model is used when the underlying function of the relation-ship between the time-series itself (Yt), and its p delays (Yt−j)j=1p$$({Y_{t - j}})_{j = 1}^p$$ violates the lin-earity assumption and this function is formed by multiple behaviors that called regime. This paper addresses the right-censored dependent time-series problem which has a serious negative effect on the estimation performance. Right-censored time series cause biased coefficient estimates and unqualified predictions. The main contribution of this paper is solving the censorship problem for the SETAR by three different techniques that are kNN imputation which represents the imputation techniques, Kaplan-Meier weights that is applied based on the weighted least squares, synthetic data transformation which adds the effect of censorship to the modeling process by manipulating dataset. Then, these solutions are combined by the SETAR-type model estimation process. To observe the behavior of the nonlinear estimators in practice, a simulation study and a real data example are carried out. The Covid-19 dataset collected in China is used as real data. Results prove that although the three estimators show satisfying performance, the quality of the estimate SETAR model based on the kNN imputation technique dominates the other two estimators.

This paper considers a partially linear regression model relating a right-censored response variable to predictors and an extra covariate with measured error. The main problem here is that censorship and measurement error problems need to be solved to estimate the model correctly. In this sense, we propose three modified semiparametric estimators obtained from local polynomial regression, kernel smoothing, and B-spline smoothing methods based on kernel deconvolution approach and synthetic data transformation. Here, kernel deconvolution technique is used to solve the measurement error problem in the model and synthetic data transformation is considered to add the effect of censorship to the estimation procedure, which is a very common method in the literature. The performances of the introduced estimators are compared in the detailed Monte-Carlo simulation study. In addition, Carotid endarterectomy data is used as real-world data example and results are presented. According to the results, it is seen that the deconvoluted local polynomial method gives more qualified estimates than other two methods. [ABSTRACT FROM AUTHOR]

PURPOSEWe aimed to evaluate Vieussens’ arterial ring (VAR) variants by consecutive coronary computed tomography (CT) angiography examinations.METHODSWe retrospectively evaluated the presence of VAR in a total of 3443 consecutive coronary CT angiography examinations performed between November 2010 and January 2015. CT examinations were performed with a 64-row multidetector computed tomography (MDCT) scanner. All CT angiography images were evaluated for the presence and morphologic features of VAR subtypes. VAR variants were classified into four subgroups.RESULTSEleven VAR variations (3.19‰) were identified. Type 1A was the most common VAR type (n=8), followed by Type 2 (n=2) and Type 3 (n=1). Type 1B was not detected.CONCLUSIONAlthough VAR variation is less frequently detected with coronary CT angiography than in previously reported anatomic series, coronary CT angiography is quite effective to reveal VAR subtypes and other relevant cardiocoronary anomalies.

This paper introduces a modified local linear estimator (LLR) for partially linear additive models (PLAM) when the response variable is subject to random right-censoring. In the case of modeling right-censored data, PLAM offers a more flexible and realistic approach to the estimation procedure by involving multiple parametric and nonparametric components. This differs from the widely used partially linear models that feature a univariate nonparametric function. The LLR method is employed to estimate unknown smooth functions using a modified backfitting algorithm, delivering a non-iterative solution for the right-censored PLAM. To address the censorship issue, three approaches are employed: synthetic data transformation (ST), Kaplan–Meier weights (KMW), and the kNN imputation technique (kNNI). Asymptotic properties of the modified backfitting estimators are detailed for both ST and KMW solutions. The advantages and disadvantages of these methods are discussed both theoretically and practically. Comprehensive simulation studies and real-world data examples are conducted to assess the performance of the introduced estimators. The results indicate that LLR performs well with both KMW and kNNI in the majority of scenarios, along with a real data example. [ABSTRACT FROM AUTHOR]

This paper aims to present an overview of Semiparametric additive models. An estimation of the finite‐parameters of semiparametric regression models that involve additive nonparametric components is explained, including their historical background. In addition, three different smoothing techniques are considered in order to show the working procedures of the estimators and to explore their statistical properties: smoothing splines, kernel smoothing and local linear regression. These methods are compared with respect to both their theoretical and practical behaviors. A simulation study and a real data example are carried out to reveal the performances of the three methods. Accordingly, the advantages and disadvantages of each method regarding semiparametric additive models are presented based on their comparative scores using determined evaluation metrics for loss of information. This article is categorized under:Statistical Learning and Exploratory Methods of the Data Sciences > Modeling MethodsStatistical and Graphical Methods of Data Analysis > Multivariate AnalysisStatistical Models > Semiparametric Models [ABSTRACT FROM AUTHOR]

This study aims to propose modified semiparametric estimators based on six different penalty and shrinkage strategies for the estimation of a right-censored semiparametric regression model. In this context, the methods used to obtain the estimators are ridge, lasso, adaptive lasso, SCAD, MCP, and elasticnet penalty functions. The most important contribution that distinguishes this article from its peers is that it uses the local polynomial method as a smoothing method. The theoretical estimation procedures for the obtained estimators are explained. In addition, a simulation study is performed to see the behavior of the estimators and make a detailed comparison, and hepatocellular carcinoma data are estimated as a real data example. As a result of the study, the estimators based on adaptive lasso and SCAD were more resistant to censorship and outperformed the other four estimators. [ABSTRACT FROM AUTHOR]

In this study, parametric and semi-parametric regression models are examined for random right censorship. The components of the aforementioned regression models are estimated with weights based on Cox and Kaplan–Meier estimates, which are semi-parametric and nonparametric methods used in survival analysis, respectively. The Tobit based on weights obtained from a Cox regression is handled as a parametric model instead of other parametric models requiring distribution assumptions such as exponential, Weibull, and gamma distributions. Also, the semi-parametric smoothing spline and the semi-parametric smoothing kernel estimators based on Kaplan–Meier weights are used. Therefore, estimates are obtained from two models with flexible approaches. To show the flexible shape of the models depending on the weights, Monte Carlo simulations are conducted, and all results are presented and discussed. Two empirical datasets are used to show the performance of the aforementioned estimators. Although three approaches gave similar results to each other, the semi-parametric approach was slightly superior to the parametric approach. The parametric approach method, on the other hand, yields good results in medium and large sample sizes and at a high censorship level. All other findings have been shared and interpreted. [ABSTRACT FROM AUTHOR]

This paper proposes a new smoothing technique based on rational function approximation using truncated total least squares ( P − T T L S) and compares it with the widely used smoothing spline method, which has become a very powerful smoothing technique in the semiparametric regression setting. Due to the nature of rational approximation, it generates a system of linear equations with multi-collinearities and errors in all its variables. The proposed method is mainly designed to deal with these problems, especially for solving error-contaminated systems and ill-conditioned issues. To indicate the ability of the proposed method, we perform simulation experiments under different conditions and employ a real-world data application. The outcomes from the studies show that the model parameters estimated by P − T T L S have lower variances than benchmarked the smoothing spline ( B − S S) technique. [ABSTRACT FROM AUTHOR]

Objective: This paper aims to introduce a modified kernel-type ridge estimator for partially linear models under randomly-right censored data. Such models include two main issues that need to be solved: multi-collinearity and censorship. To address these issues, we improved the kernel estimator based on synthetic data transformation and kNN imputation techniques. The key idea of this paper is to obtain a satisfactory estimate of the partially linear model with multi-collinear and right-censored using a modified ridge estimator. Results: To determine the performance of the method, a detailed simulation study is carried out and a kernel-type ridge estimator for PLM is investigated for two censorship solution techniques. The results are compared and presented with tables and figures. Necessary derivations for the modified semiparametric estimator are given in appendices. [ABSTRACT FROM AUTHOR]

This paper presents different ridge type estimators based on maximum likelihood ( M L) for parameters of a Tobit model. In this context, an algorithm is introduced to get the estimators based on M L. The most important issue in implementing these estimators is the selection of the optimum shrinkage parameter. Here attention is focused on the way in which the shrinkage parameter can be selected by six selection methods, including improved Akaike information criterion ( A I C c ), Bayesian information criterion ( B I C), generalized cross-validation ( G C V), risk estimation using classical pilots ( R E C P), Mallows' ( C p ) and k ^ G M proposed by Kibria [Performance of some new ridge regression estimators. Commun Stat Simul Comput. 2003;32:419–435]. Monte Carlo simulation experiments are performed and a real data example is presented to illustrate the ideas in the paper. Hence, an appropriate selection criterion or criteria are provided for optimum shrinkage parameter. [ABSTRACT FROM AUTHOR]

In this paper, we consider the estimation problem for the semiparametric regression model with censored data in which the number of explanatory variables p in the linear part is much larger than sample size n, often denoted as p n. The purpose of this paper is to study the effects of covariates on a response variable censored on the right by a random censoring variable with an unknown probability distribution. It should be noted that high variance and over-fitting are a major concern in such problems. Ordinary statistical methods for estimation cannot be applied directly to censored and high-dimensional data, and therefore a transformation is required. In the context of this paper, a synthetic data transformation is used for solving the censoring problem. We then apply the LASSO-type double-penalized least squares (DPLS) to achieve sparsity in the parametric component and use smoothing splines to estimate the nonparametric component. A Monte Carlo simulation study is performed to show the performance of the estimators and to analyse the effects of the different censoring levels. A real high-dimensional censored data example is used to illustrate the ideas discussed herein. [ABSTRACT FROM AUTHOR]

This paper introduces the operating of the selection criteria for right-censored nonparametric regression using smoothing spline. In order to transform the response variable into a variable that contains the right-censorship, we used the Kaplan- Meier weights proposed by [1], and [2]. The major problem in smoothing spline method is to determine a smoothing parameter to obtain nonparametric estimates of the regression function. In this study, the mentioned parameter is chosen based on censored data by means of the criteria such as improved Akaike information criterion (AICc), Bayesian (or Schwarz) information criterion (BIC) and generalized crossvalidation (GCV). For this purpose, a Monte-Carlo simulation study is carried out to illustrate which selection criterion gives the best estimation for censored data. [ABSTRACT FROM AUTHOR]

The focus in this paper embraces the hybrid models whose components are nonparametric regression and artificial neural networks. Smoothing spline, regression spline and additive regression models are considered as the nonparametric regression components. Furthermore, various multilayer perceptron algorithms and radial basis function network model are regarded as the artificial neural networks components. The performances of these models are compared by forecasting three real Turkish data sets: Domestic product per capita (GDP), the number of cars produced and the number of tourist arrivals. The results obtained by experimental evaluations show that hybrid models proposed in this paper have performed much better in comparison to hybrid models discussed in literature. [ABSTRACT FROM AUTHOR]

This paper presents a comparative study of different estimations of the partially linear models based on the smoothing spline technique. Performance of this technique greatly depends on the selection of smoothing parameters. Many methods of selecting smoothing parameters such as an improved version of Akaike information criterion (AICc), generalized cross-validation (GCV), cross-validation (CV), Mallows' Cp criterion, risk estimation using classical pilots (REC) and local risk estimation (LRS) are developed in literature. The smoothing parameter selection has been discussed in respect to a smoothing spline implementation in predicting the partially linear model (PLM). To this end, a simulation study has been conducted to evaluate and compare the performance of six selection methods. In this connection, 1000 replications have been performed in simulation for sample sets with different sizes. The AICc method is recommended since it is stable and works well in all simulations. It performs better than other methods especially when the sample sizes are not large. [ABSTRACT FROM AUTHOR]

In this article, we discuss the penalized least squares problem which has many advantageous computational properties. This method based on penalized spline (P-spline) smoothing can be formulated to fit into a linear mixed effects model framework. The most important issue in the implementation of this method is to specify the amount of smoothing. In an attempt to address the strategy of optimum amount of smoothing, this article provides a comparative study for different methods (or criteria) of choosing the optimum smoothing parameter: an improved version of the Akaike information criterion (AICc); generalized cross-validation (GCV); cross-validation (CV); Mallows’ C p criterion; risk estimation using classical pilots (RECP) and restricted maximum likelihood (REML). In order to explore and compare the performance of these methods, a simulation study is performed for data sets with different sample sizes. As a result of simulation, the appropriate selection criteria are provided for a suitable smoothing parameter selection. [ABSTRACT FROM PUBLISHER]

This paper focuses on the adaptive spline (A-spline) fitting of the semiparametric regression model to time series data with right-censored observations. Typically, there are two main problems that need to be solved in such a case: dealing with censored data and obtaining a proper A-spline estimator for the components of the semiparametric model. The first problem is traditionally solved by the synthetic data approach based on the Kaplan–Meier estimator. In practice, although the synthetic data technique is one of the most widely used solutions for right-censored observations, the transformed data's structure is distorted, especially for heavily censored datasets, due to the nature of the approach. In this paper, we introduced a modified semiparametric estimator based on the A-spline approach to overcome data irregularity with minimum information loss and to resolve the second problem described above. In addition, the semiparametric B-spline estimator was used as a benchmark method to gauge the success of the A-spline estimator. To this end, a detailed Monte Carlo simulation study and a real data sample were carried out to evaluate the performance of the proposed estimator and to make a practical comparison. [ABSTRACT FROM AUTHOR]