regression analysis is a statistical process for estimating the relationships among variables based on probability. Because not all the imprecise quantities can be described by random variables, it is necessary to inv...
详细信息
regression analysis is a statistical process for estimating the relationships among variables based on probability. Because not all the imprecise quantities can be described by random variables, it is necessary to investigate relationships between an uncertain variable and some other variables. In this paper, an uncertain linear regression model is established based on uncertainty theory. Then, the estimators of parameters are obtained in the proposed model by the empirical uncertainty distribution coming from experts' experimental data. Finally, the uncertain linear regression model is applied to solve an estimate problem.
This article first defines a hidden Markov linear regression model for the purpose of further studying the mutual transformation between different states in the linear regression model, and the regression relationship...
详细信息
This article first defines a hidden Markov linear regression model for the purpose of further studying the mutual transformation between different states in the linear regression model, and the regression relationship between the dependent variable and the independent variable in each state. And then, K-means clustering analysis methods are used to identify the hidden states of observed data, and the maximum likelihood estimation of the hidden state transition probability matrix elements is obtained by using the maximum likelihood estimation method, and parameter estimation of unknown parameters in linear regression model is also presented by using the least squares method. Finally, the observation vector set is generated according to the defined model, and the empirical simulation demonstrates that the parameter estimation method shown in this work is reliable.
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 sta...
详细信息
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.
In this article, empirical likelihood is applied to the linear regression model with inequality constraints. We prove that asymptotic distribution of the adjusted empirical likelihood ratio test statistic is a weighte...
详细信息
In this article, empirical likelihood is applied to the linear regression model with inequality constraints. We prove that asymptotic distribution of the adjusted empirical likelihood ratio test statistic is a weighted mixture of chi-square distribution.
The consistency of various estimators under the semi-parametric linear regression model and the standard right censorship model (SPLRRC model) has been studied under various assumptions since the 1970s. These assumpti...
详细信息
The consistency of various estimators under the semi-parametric linear regression model and the standard right censorship model (SPLRRC model) has been studied under various assumptions since the 1970s. These assumptions are somewhat sufficient conditions for the identifiability of the parameters under the SPLRRC model. Since then, it has been a difficult open problem in survival analysis to find the necessary and sufficient condition for the identifiability of the parameters under the SPLRRC model. The open problem is solved in this paper. It is of interest to investigate whether the common estimators under this model are consistent under the identifiability condition. Under the latter condition, we show that the Buckley-James estimator and quantile regression estimator can be inconsistent and present partial results on the consistency of the semi-parametric maximum likelihood estimator.
The consistency of the semi-parametric maximum likelihood estimator (SMLE) under the semi-parametric linear regression model with right-censoring data (SPLRRC model) has not been studied under the necessary and suffic...
详细信息
The consistency of the semi-parametric maximum likelihood estimator (SMLE) under the semi-parametric linear regression model with right-censoring data (SPLRRC model) has not been studied under the necessary and sufficient condition for the identifiability of the parameters. In this paper, we discuss the necessary and sufficient condition for the consistency of SMLE under type I right censoring.
If the errors in the linear regression model are assumed to be independent with nonvanishing third and finite fourth moments, then it is possible to improve all linear estimators by so-called linear plus quadratic (LP...
详细信息
If the errors in the linear regression model are assumed to be independent with nonvanishing third and finite fourth moments, then it is possible to improve all linear estimators by so-called linear plus quadratic (LPQ) estimators. These consist of linear and quadratic terms in the endogeneous variable and depend on the unknown moments of the errors which, in general, have to be estimated from the data. In this paper, we will use LPQ estimators for quasiminimax estimation and some related problems.
In precision beekeeping, bee colony weight is an important indicator to monitor the behaviours such as foraging and swarming. However, ambient temperature variations can greatly affect the measured values. In this pap...
详细信息
In precision beekeeping, bee colony weight is an important indicator to monitor the behaviours such as foraging and swarming. However, ambient temperature variations can greatly affect the measured values. In this paper, a combined method with linear regression model and Kalman filter is proposed to reduce the influence of ambient temperature. Monitoring data is collected to validate the effectiveness of the proposed method. Moreover, methods that solely rely on the statistic model or Kalman filter are investigated as a comparison with the proposed method. The compensation results indicate that the proposed method outperforms the two others, and is feasible and effective in temperature drift removal. The mean absolute errors can be decreased over 40% from that before removal during periods of no honeycombs, the coefficient of variations can also be reduced by over 40% and 5% respectively during the periods of no bees and bees in the beehives. As the proposed method can improve the reading accuracy of bee colony weight, it has potential to benefit the precision beekeeping and basic research on bee activities.& COPY;2023 IAgrE. Published by Elsevier Ltd. All rights reserved.
When the observed data are imprecise, the uncertain regressionmodel is more suitable for the linearregression analysis. Least squares estimation can fully consider the given data and minimize the sum of squares of r...
详细信息
When the observed data are imprecise, the uncertain regressionmodel is more suitable for the linearregression analysis. Least squares estimation can fully consider the given data and minimize the sum of squares of residual error and can effectively solve the linearregression equation of imprecisely observed data. On the basis of uncertainty theory, this paper presents an equation deformation method for solving unknown parameters in uncertain linearregression equations. We first establish the equation deformation method of one-dimensional linear regression model and then extend it to the case of multiple linear regression model. We also combine the equation deformation method with Cramer's rule and matrix and propose the Cramer's rule and matrix elementary transformation method to solve the unknown parameters of the uncertain linearregression equation. Numerical example show that the equation deformation method can effectively solve the unknown parameters of the uncertain linearregression equation.
We consider LS-, LAD-, R-, M-, S-, LMS-, LTS-, MM-, and HBR-estimates for the parameters of a linear regression model with unknown noise distribution. With computer modeling for medium sized samples, we compare the ac...
详细信息
We consider LS-, LAD-, R-, M-, S-, LMS-, LTS-, MM-, and HBR-estimates for the parameters of a linear regression model with unknown noise distribution. With computer modeling for medium sized samples, we compare the accuracy of the considered estimates for the most popular probability distributions of noise in a regressionmodel. For different noise distributions, we analytically compute asymptotic efficiencies of LS-, LAD-, R-, M-, S-, and LTS- estimates. We give recommendations for practical applications of these methods for different noise distributions in the model. We show examples on real datasets that support the advantages of robust estimates.
暂无评论