In the presence of multicollinearity in logistic regression, the variance of the Maximum Likelihood Estimator (MLE) becomes inflated. Siray et al. (2015) [1] proposed a restricted Liu estimator in logistic regression ...In the presence of multicollinearity in logistic regression, the variance of the Maximum Likelihood Estimator (MLE) becomes inflated. Siray et al. (2015) [1] proposed a restricted Liu estimator in logistic regression model with exact linear restrictions. However, there are some situations, where the linear restrictions are stochastic. In this paper, we propose a Stochastic Restricted Maximum Likelihood Estimator (SRMLE) for the logistic regression model with stochastic linear restrictions to overcome this issue. Moreover, a Monte Carlo simulation is conducted for comparing the performances of the MLE, Restricted Maximum Likelihood Estimator (RMLE), Ridge Type Logistic Estimator(LRE), Liu Type Logistic Estimator(LLE), and SRMLE for the logistic regression model by using Scalar Mean Squared Error (SMSE).展开更多
The following heteroscedastic regression model Yi = g（xi） ＋σiei （1 ≤i ≤ n） is 2 considered, where it is assumed that σi^2 = f（ui）, the design points （xi,ui） are known and nonrandom, g and f are unknown f...The following heteroscedastic regression model Yi = g（xi） ＋σiei （1 ≤i ≤ n） is 2 considered, where it is assumed that σi^2 = f（ui）, the design points （xi,ui） are known and nonrandom, g and f are unknown functions. Under the unobservable disturbance ei form martingale differences, the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.展开更多
Estimation of the unknown mean, μ and variance, σ2 of a univariate Gaussian distribution given a single study variable x is considered. We propose an approach that does not require initialization of the sufficient u...Estimation of the unknown mean, μ and variance, σ2 of a univariate Gaussian distribution given a single study variable x is considered. We propose an approach that does not require initialization of the sufficient unknown distribution parameters. The approach is motivated by linearizing the Gaussian distribution through differential techniques, and estimating, μ and σ2 as regression coefficients using the ordinary least squares method. Two simulated datasets on hereditary traits and morphometric analysis of housefly strains are used to evaluate the proposed method (PM), the maximum likelihood estimation (MLE), and the method of moments (MM). The methods are evaluated by re-estimating the required Gaussian parameters on both large and small samples. The root mean squared error (RMSE), mean error (ME), and the standard deviation (SD) are used to assess the accuracy of the PM and MLE;confidence intervals (CIs) are also constructed for the ME estimate. The PM compares well with both the MLE and MM approaches as they all produce estimates whose errors have good asymptotic properties, also small CIs are observed for the ME using the PM and MLE. The PM can be used symbiotically with the MLE to provide initial approximations at the expectation maximization step.展开更多
By exponentiating each of the components of a finite mixture of two exponential components model by a positive parameter, several shapes of hazard rate functions are obtained. Maximum likelihood and Bayes methods, bas...By exponentiating each of the components of a finite mixture of two exponential components model by a positive parameter, several shapes of hazard rate functions are obtained. Maximum likelihood and Bayes methods, based on square error loss function and objective prior, are used to obtain estimators based on balanced square error loss function for the parameters, survival and hazard rate functions of a mixture of two exponentiated exponential components model. Approximate interval estimators of the parameters of the model are obtained.展开更多
The problem of predicting continuous scalar outcomes from functional predictors has received high levels of interest in recent years in many fields,especially in the food industry.The k-nearest neighbor(k-NN)method of...The problem of predicting continuous scalar outcomes from functional predictors has received high levels of interest in recent years in many fields,especially in the food industry.The k-nearest neighbor(k-NN)method of Near-Infrared Reflectance(NIR)analysis is practical,relatively easy to implement,and becoming one of the most popular methods for conducting food quality based on NIR data.The k-NN is often named k nearest neighbor classifier when it is used for classifying categorical variables,while it is called k-nearest neighbor regression when it is applied for predicting noncategorical variables.The objective of this paper is to use the functional Near-Infrared Reflectance(NIR)spectroscopy approach to predict some chemical components with some modern statistical models based on the kernel and k-Nearest Neighbour procedures.In this paper,three NIR spectroscopy datasets are used as examples,namely Cookie dough,sugar,and tecator data.Specifically,we propose three models for this kind of data which are Functional Nonparametric Regression,Functional Robust Regression,and Functional Relative Error Regression,with both kernel and k-NN approaches to compare between them.The experimental result shows the higher efficiency of k-NN predictor over the kernel predictor.The predictive power of the k-NN method was compared with that of the kernel method,and several real data sets were used to determine the predictive power of both methods.展开更多
We revisit a comparison of two discriminant analysis procedures, namely the linear combination classifier of Chung and Han (2000) and the maximum likelihood estimation substitution classifier for the problem of classi...We revisit a comparison of two discriminant analysis procedures, namely the linear combination classifier of Chung and Han (2000) and the maximum likelihood estimation substitution classifier for the problem of classifying unlabeled multivariate normal observations with equal covariance matrices into one of two classes. Both classes have matching block monotone missing training data. Here, we demonstrate that for intra-class covariance structures with at least small correlation among the variables with missing data and the variables without block missing data, the maximum likelihood estimation substitution classifier outperforms the Chung and Han (2000) classifier regardless of the percent of missing observations. Specifically, we examine the differences in the estimated expected error rates for these classifiers using a Monte Carlo simulation, and we compare the two classifiers using two real data sets with monotone missing data via parametric bootstrap simulations. Our results contradict the conclusions of Chung and Han (2000) that their linear combination classifier is superior to the MLE classifier for block monotone missing multivariate normal data.展开更多
目的在特定脑网络中对赌博障碍(GD)患者任务态和静息态功能连接(FC)研究结果进行荟萃分析,旨在探索GD的神经机制。方法检索PubMed、Cochrane、Web of Science、EMBASE、CNKI、万方、维普,检索时限均为从建库至2022年5月,使用激活似然估...目的在特定脑网络中对赌博障碍(GD)患者任务态和静息态功能连接(FC)研究结果进行荟萃分析,旨在探索GD的神经机制。方法检索PubMed、Cochrane、Web of Science、EMBASE、CNKI、万方、维普,检索时限均为从建库至2022年5月,使用激活似然估计(ALE)的方法进行Meta分析。结果纳入9篇文献,包括166例GD和170例健康对照(HC)。Meta分析结果与HC相比,GD患者存在边缘网络(LN)和默认网络(DMN)网络内连接增强。DMN与背侧注意网络(DAN)、执行控制网络(ECN)、感知皮层系统以及LN与DMN、DAN、右侧额顶网络(FPN)的网络间功能连接增强。结论GD患者表现出的功能网络连接改变可能与自我控制减弱、奖赏敏感性增加、注意力分配障碍、自我相关心理活动障碍等行为异常有关。为未来进一步研究非物质成瘾障碍的神经机制及GD的治疗提供了参考。展开更多
文摘In the presence of multicollinearity in logistic regression, the variance of the Maximum Likelihood Estimator (MLE) becomes inflated. Siray et al. (2015) [1] proposed a restricted Liu estimator in logistic regression model with exact linear restrictions. However, there are some situations, where the linear restrictions are stochastic. In this paper, we propose a Stochastic Restricted Maximum Likelihood Estimator (SRMLE) for the logistic regression model with stochastic linear restrictions to overcome this issue. Moreover, a Monte Carlo simulation is conducted for comparing the performances of the MLE, Restricted Maximum Likelihood Estimator (RMLE), Ridge Type Logistic Estimator(LRE), Liu Type Logistic Estimator(LLE), and SRMLE for the logistic regression model by using Scalar Mean Squared Error (SMSE).
基金Partially supported by the National Natural Science Foundation of China(10571136)
文摘The following heteroscedastic regression model Yi = g（xi） ＋σiei （1 ≤i ≤ n） is 2 considered, where it is assumed that σi^2 = f（ui）, the design points （xi,ui） are known and nonrandom, g and f are unknown functions. Under the unobservable disturbance ei form martingale differences, the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.
文摘Estimation of the unknown mean, μ and variance, σ2 of a univariate Gaussian distribution given a single study variable x is considered. We propose an approach that does not require initialization of the sufficient unknown distribution parameters. The approach is motivated by linearizing the Gaussian distribution through differential techniques, and estimating, μ and σ2 as regression coefficients using the ordinary least squares method. Two simulated datasets on hereditary traits and morphometric analysis of housefly strains are used to evaluate the proposed method (PM), the maximum likelihood estimation (MLE), and the method of moments (MM). The methods are evaluated by re-estimating the required Gaussian parameters on both large and small samples. The root mean squared error (RMSE), mean error (ME), and the standard deviation (SD) are used to assess the accuracy of the PM and MLE;confidence intervals (CIs) are also constructed for the ME estimate. The PM compares well with both the MLE and MM approaches as they all produce estimates whose errors have good asymptotic properties, also small CIs are observed for the ME using the PM and MLE. The PM can be used symbiotically with the MLE to provide initial approximations at the expectation maximization step.
文摘By exponentiating each of the components of a finite mixture of two exponential components model by a positive parameter, several shapes of hazard rate functions are obtained. Maximum likelihood and Bayes methods, based on square error loss function and objective prior, are used to obtain estimators based on balanced square error loss function for the parameters, survival and hazard rate functions of a mixture of two exponentiated exponential components model. Approximate interval estimators of the parameters of the model are obtained.
基金funding this work through the Research Groups Program under Grant Number R.G.P.1/189/41.I.M.A.and M.K.A.received the grant.
文摘The problem of predicting continuous scalar outcomes from functional predictors has received high levels of interest in recent years in many fields,especially in the food industry.The k-nearest neighbor(k-NN)method of Near-Infrared Reflectance(NIR)analysis is practical,relatively easy to implement,and becoming one of the most popular methods for conducting food quality based on NIR data.The k-NN is often named k nearest neighbor classifier when it is used for classifying categorical variables,while it is called k-nearest neighbor regression when it is applied for predicting noncategorical variables.The objective of this paper is to use the functional Near-Infrared Reflectance(NIR)spectroscopy approach to predict some chemical components with some modern statistical models based on the kernel and k-Nearest Neighbour procedures.In this paper,three NIR spectroscopy datasets are used as examples,namely Cookie dough,sugar,and tecator data.Specifically,we propose three models for this kind of data which are Functional Nonparametric Regression,Functional Robust Regression,and Functional Relative Error Regression,with both kernel and k-NN approaches to compare between them.The experimental result shows the higher efficiency of k-NN predictor over the kernel predictor.The predictive power of the k-NN method was compared with that of the kernel method,and several real data sets were used to determine the predictive power of both methods.
文摘We revisit a comparison of two discriminant analysis procedures, namely the linear combination classifier of Chung and Han (2000) and the maximum likelihood estimation substitution classifier for the problem of classifying unlabeled multivariate normal observations with equal covariance matrices into one of two classes. Both classes have matching block monotone missing training data. Here, we demonstrate that for intra-class covariance structures with at least small correlation among the variables with missing data and the variables without block missing data, the maximum likelihood estimation substitution classifier outperforms the Chung and Han (2000) classifier regardless of the percent of missing observations. Specifically, we examine the differences in the estimated expected error rates for these classifiers using a Monte Carlo simulation, and we compare the two classifiers using two real data sets with monotone missing data via parametric bootstrap simulations. Our results contradict the conclusions of Chung and Han (2000) that their linear combination classifier is superior to the MLE classifier for block monotone missing multivariate normal data.
文摘目的在特定脑网络中对赌博障碍(GD)患者任务态和静息态功能连接(FC)研究结果进行荟萃分析,旨在探索GD的神经机制。方法检索PubMed、Cochrane、Web of Science、EMBASE、CNKI、万方、维普,检索时限均为从建库至2022年5月,使用激活似然估计(ALE)的方法进行Meta分析。结果纳入9篇文献,包括166例GD和170例健康对照(HC)。Meta分析结果与HC相比,GD患者存在边缘网络(LN)和默认网络(DMN)网络内连接增强。DMN与背侧注意网络(DAN)、执行控制网络(ECN)、感知皮层系统以及LN与DMN、DAN、右侧额顶网络(FPN)的网络间功能连接增强。结论GD患者表现出的功能网络连接改变可能与自我控制减弱、奖赏敏感性增加、注意力分配障碍、自我相关心理活动障碍等行为异常有关。为未来进一步研究非物质成瘾障碍的神经机制及GD的治疗提供了参考。
