On the accuracy of empirical likelihood confidence regions for linear regression model

1993 ◽  
Vol 45 (4) ◽  
pp. 621-637 ◽  
Author(s):  
Song Xi Chen
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Empirical Likelihood ◽  
Linear Regression Model ◽  
Confidence Regions

scholarly journals A Literature Review of Semi-functional Partial Linear Regression Models

2021 ◽  
Author(s):  
Mohammad Fayaz
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Missing Values ◽  
Electricity Consumption ◽  
Confidence Regions ◽  
Mixed Data ◽  
Linear Regression Models ◽  
Partial Linear ◽  
Functional Linear Regression

Background: In the functional data analysis (FDA), the hybrid or mixed data are scalar and functional datasets. The semi-functional partial linear regression model (SFPLR) is one of the first semiparametric models for the scalar response with hybrid covariates. Various extensions of this model are explored and summarized. Methods: Two first research articles, including “semi-functional partial linear regression model”, and “Partial functional linear regression” have more than 300 citations in Google Scholar. Finally, only 106 articles remained according to the inclusion and exclusion criteria such as 1) including the published articles in the ISI journals and excluding 2) non-English and 3) preprints, slides, and conference papers. We use the PRISMA standard for systematic review. Results: The articles are categorized into the following main topics: estimation procedures, confidence regions, time series, and panel data, Bayesian, spatial, robust, testing, quantile regression, varying Coefficient Models, Variable Selection, Single-index model, Measurement error, Multiple Functions, Missing values, Rank Method and Others. There are different applications and datasets such as the Tecator dataset, air quality, electricity consumption, and Neuroimaging, among others. Conclusions: SFPLR is one of the most famous regression modeling methods for hybrid data that has a lot of extensions among other models.

scholarly journals Localization and Change Point Detection using GPS Data

2021 ◽  
Author(s):  
◽  
Xiaoyu Zhai
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Low Cost ◽  
Bootstrap Method ◽  
Confidence Regions ◽  
Change Point Detection ◽  
Gps Data ◽  
Distance Method ◽  
Data Set

<p>The Global Positioning System (GPS) has become widely used in modern life and most people use GPS to find locations, therefore the accuracy of these locations is very important.  In this thesis, we will use Longitude and Latitude from raw GPS data to estimate the location of a GPS receiver. To improve accuracy of the estimation, we will use two methods to delete outliers in Longitude and Latitude: the Euclidean distance method and the Mahalanobis distance method. We will then use two methods to estimate the location: Maximum Likelihood and Bootstrap method.  The confidence ellipse and the simultaneous confidence intervals are used to construct confidence regions for bivariate data, and we compared the two methods. In this thesis, we also did some simulations to understand the effect of sample size and variance in the linear regression model for AIC and BIC, and use these two criteria to find a best model to fit the multivariate linear regression model with response variables Latitude and Longitude. This thesis forms part of a larger project to detect land movement, such as that seen in landslides using low cost GPS devices. We therefore consider methods for detecting changes in location over time.  In this thesis, we used converted Longitude, Latitude and Altitude (in meters) from the same GPS data set after deleting outliers as our variables and applied two methods (Hotelling’s T2 chart method and Multivariate exponentially weighted moving average method) to detect changes in location in our data.</p>

scholarly journals Localization and Change Point Detection using GPS Data

2021 ◽  
Author(s):  
◽  
Xiaoyu Zhai
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Low Cost ◽  
Bootstrap Method ◽  
Confidence Regions ◽  
Change Point Detection ◽  
Gps Data ◽  
Distance Method ◽  
Data Set

<p>The Global Positioning System (GPS) has become widely used in modern life and most people use GPS to find locations, therefore the accuracy of these locations is very important.  In this thesis, we will use Longitude and Latitude from raw GPS data to estimate the location of a GPS receiver. To improve accuracy of the estimation, we will use two methods to delete outliers in Longitude and Latitude: the Euclidean distance method and the Mahalanobis distance method. We will then use two methods to estimate the location: Maximum Likelihood and Bootstrap method.  The confidence ellipse and the simultaneous confidence intervals are used to construct confidence regions for bivariate data, and we compared the two methods. In this thesis, we also did some simulations to understand the effect of sample size and variance in the linear regression model for AIC and BIC, and use these two criteria to find a best model to fit the multivariate linear regression model with response variables Latitude and Longitude. This thesis forms part of a larger project to detect land movement, such as that seen in landslides using low cost GPS devices. We therefore consider methods for detecting changes in location over time.  In this thesis, we used converted Longitude, Latitude and Altitude (in meters) from the same GPS data set after deleting outliers as our variables and applied two methods (Hotelling’s T2 chart method and Multivariate exponentially weighted moving average method) to detect changes in location in our data.</p>

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