This paper transforms fuzzy number into clear number using the centroid method, thus we can research the traditional linear regression model which is transformed from the fuzzy linear regression model. The model’s in...This paper transforms fuzzy number into clear number using the centroid method, thus we can research the traditional linear regression model which is transformed from the fuzzy linear regression model. The model’s input and output are fuzzy numbers, and the regression coefficients are clear numbers. This paper considers the parameter estimation and impact analysis based on data deletion. Through the study of example and comparison with other models, it can be concluded that the model in this paper is applied easily and better.展开更多
The purpose of this paper is two fold.First,the authors investigate quantile regression(QR)estimation for single-index QR models when the response is subject to random left truncation.The random weights are introduced...The purpose of this paper is two fold.First,the authors investigate quantile regression(QR)estimation for single-index QR models when the response is subject to random left truncation.The random weights are introduced to deal with left truncated data and the associated iteration estimation method is proposed.The asymptotic properties for the proposed QR estimates of the index parameter and unknown link function are both obtained.Further,by combining the QR loss function and the adaptive LASSO penalization,a variable selection procedure for the index parameter is introduced and its oracle property is established.Second,a weighted empirical log-likelihood ratio of the index parameter based on the QR method is introduced and is proved to be asymptotic standard chi-square distribution.Furthermore,confidence regions of the index parameter can be constructed.The finite sample performance of the proposed methods are demonstrated.A real data analysis is also conducted to show the usefulness of the proposed approaches.展开更多
文摘This paper transforms fuzzy number into clear number using the centroid method, thus we can research the traditional linear regression model which is transformed from the fuzzy linear regression model. The model’s input and output are fuzzy numbers, and the regression coefficients are clear numbers. This paper considers the parameter estimation and impact analysis based on data deletion. Through the study of example and comparison with other models, it can be concluded that the model in this paper is applied easily and better.
基金supported by the National Social Science Foundation of China under Grant No.21BTJ038。
文摘The purpose of this paper is two fold.First,the authors investigate quantile regression(QR)estimation for single-index QR models when the response is subject to random left truncation.The random weights are introduced to deal with left truncated data and the associated iteration estimation method is proposed.The asymptotic properties for the proposed QR estimates of the index parameter and unknown link function are both obtained.Further,by combining the QR loss function and the adaptive LASSO penalization,a variable selection procedure for the index parameter is introduced and its oracle property is established.Second,a weighted empirical log-likelihood ratio of the index parameter based on the QR method is introduced and is proved to be asymptotic standard chi-square distribution.Furthermore,confidence regions of the index parameter can be constructed.The finite sample performance of the proposed methods are demonstrated.A real data analysis is also conducted to show the usefulness of the proposed approaches.
基金The Natural Science Foundation of Beijing City of China(1042002)Science and Technology Development Foundation of Education Committee of Beijing City.
