A Modification of Least Squares with High Efficiency and High Breakdown Point in Linear Regression

1994 ◽  
pp. 183-194
Author(s):  
Konrad Behnen
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
High Efficiency ◽  
Breakdown Point ◽  
High Breakdown Point

scholarly journals Regional Zenith Tropospheric Delay Modeling Based on Least Squares Support Vector Machine Using GNSS and ERA5 Data

2021 ◽  
Vol 13 (5) ◽  
pp. 1004
Author(s):  
Song Li ◽  
Tianhe Xu ◽  
Nan Jiang ◽  
Honglei Yang ◽  
Shuaimin Wang ◽  
...  
Keyword(s):  
Support Vector Machine ◽  
Least Squares ◽  
High Efficiency ◽  
Rapid Development ◽  
Support Vector ◽  
Tropospheric Delay ◽  
Improvement Rate ◽  
Zenith Tropospheric Delay ◽  
Background Data ◽  
Mean Square Errors

The meteorological reanalysis data has been widely applied to derive zenith tropospheric delay (ZTD) with a high spatial and temporal resolution. With the rapid development of artificial intelligence, machine learning also begins as a high-efficiency tool to be employed in modeling and predicting ZTD. In this paper, we develop three new regional ZTD models based on the least squares support vector machine (LSSVM), using both the International GNSS Service (IGS)-ZTD products and European Centre for Medium-Range Weather Forecasts Reanalysis 5 (ERA5) data over Europe throughout 2018. Among them, the ERA5 data is extended to ERA5S-ZTD and ERA5P-ZTD as the background data by the model method and integral method, respectively. Depending on different background data, three schemes are designed to construct ZTD models based on the LSSVM algorithm, including the without background data, with the ERA5S-ZTD, and with the ERA5P-ZTD. To investigate the advantage and feasibility of the proposed ZTD models, we evaluate the accuracy of two background data and three schemes by segmental comparison with the IGS-ZTD of 85 IGS stations in Europe. The results show that the overall average Root Mean Square Errors (RMSE) value of all sites is 30.1 mm for the ERA5S-ZTD, and 10.7 mm for the ERA5P-ZTD. The overall average RMSE is 25.8 mm, 22.9 mm, and 9 mm for the three schemes, respectively. Moreover, the overall improvement rate is 19.1% and 1.6% for the ZTD model with ERA5S-ZTD and ERA5P-ZTD, respectively. In order to explore the reason of the lower improvement for the ZTD model with ERA5P-ZTD, the loop verification is performed by estimating the ZTD values of each available IGS station. In actuality, the monthly improvement rate of estimated ZTD is positive for most stations, and the biggest improvement rate can even reach about 40%. The negative rate mainly comes from specific stations, these stations are located on the edge of the region, near the coast, as well as the lower similarity between the individual verified station and training stations.

Fuzzy C-Regression Models

2013 ◽  
Vol 278-280 ◽  
pp. 1323-1326
Author(s):  
Yan Hua Yu ◽  
Li Xia Song ◽  
Kun Lun Zhang
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Methods ◽  
Statistical Regression ◽  
Fuzzy Linear Regression ◽  
Fuzzy Degree

Fuzzy linear regression has been extensively studied since its inception symbolized by the work of Tanaka et al. in 1982. As one of the main estimation methods, fuzzy least squares approach is appealing because it corresponds, to some extent, to the well known statistical regression analysis. In this article, a restricted least squares method is proposed to fit fuzzy linear models with crisp inputs and symmetric fuzzy output. The paper puts forward a kind of fuzzy linear regression model based on structured element, This model has precise input data and fuzzy output data, Gives the regression coefficient and the fuzzy degree function determination method by using the least square method, studies the imitation degree question between the observed value and the forecast value.

Functional Linear Regression

2018 ◽  
Author(s):  
Hervé Cardot ◽  
Pascal Sarda
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Estimation Error ◽  
Asymptotic Properties ◽  
Principal Component Regression ◽  
Principal Component ◽  
Penalized Least Squares ◽  
Open Problems ◽  
Functional Linear Regression

This article presents a selected bibliography on functional linear regression (FLR) and highlights the key contributions from both applied and theoretical points of view. It first defines FLR in the case of a scalar response and shows how its modelization can also be extended to the case of a functional response. It then considers two kinds of estimation procedures for this slope parameter: projection-based estimators in which regularization is performed through dimension reduction, such as functional principal component regression, and penalized least squares estimators that take into account a penalized least squares minimization problem. The article proceeds by discussing the main asymptotic properties separating results on mean square prediction error and results on L2 estimation error. It also describes some related models, including generalized functional linear models and FLR on quantiles, and concludes with a complementary bibliography and some open problems.

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