Linear Rank Regression
نویسنده
چکیده
The errors ei in (1.1) are assumed to be independent and identically distributed, but are not necessarily normal and may be heavy-tailed. Assume for convenience that β is one dimensional. Then (1.1) is a simple linear regression. However, most of the following extends more-or-less easily to higher-dimensional β, in which case (1.1) is a multiple regression. Given β, define Ri(β) as the rank (or midrank) of Yi − βXi among {Yj − βXj }. Thus 1 ≤ Ri(β) ≤ n. The rank-regression estimator β̂ is any value of β that minimizes the sum
منابع مشابه
Reduced rank ridge regression and its kernel extensions
In multivariate linear regression, it is often assumed that the response matrix is intrinsically of lower rank. This could be because of the correlation structure among the prediction variables or the coefficient matrix being lower rank. To accommodate both, we propose a reduced rank ridge regression for multivariate linear regression. Specifically, we combine the ridge penalty with the reduced...
متن کاملAsymptotic properties of a rank estimate in heteroscedastic linear regression
In this paper a simple linear regression model with independent and symmetric, but nonidentically distributed errors is considered. Asymptotic properties of the rank regression estimate defined in Jaeckel (1972) are studied. We show that the studied estimator is consistent and asymptotically normally distributed. The cases of bounded and unbounded score functions are examined separately.
متن کاملA Closed Form Solution to Multi-View Low-Rank Regression
Real life data often includes information from different channels. For example, in computer vision, we can describe an image using different image features, such as pixel intensity, color, HOG, GIST feature, SIFT features, etc.. These different aspects of the same objects are often called multi-view (or multi-modal) data. Lowrank regression model has been proved to be an effective learning mech...
متن کاملEfficient Rank Regression with Wavelet Estimated Scores
We provide an estimate of the score function for rank regression using compactly supported wavelets. This estimate is then used to find a rank-based asymptotically efficient estimator for the slope parameter of a linear model. We also provide a consistent estimator of the asymptotic variance of the rank estimator. For related mixed models, the asymptotic relative efficiency is also discussed
متن کاملStatistical approach for selection of regression model during validation of bioanalytical method
The selection of an adequate regression model is the basis for obtaining accurate and reproducible results during the bionalytical method validation. Given the wide concentration range, frequently present in bioanalytical assays, heteroscedasticity of the data may be expected. Several weighted linear and quadratic regression models were evaluated during the selection of the adequate curve fit u...
متن کامل