Quantile Regression and its Application to Spatial Data

Hegde, Disha (2022) Quantile Regression and its Application to Spatial Data. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Disha Hegde (17MS126)) 17MS126_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

Quantile Regression aims to estimate the conditional quantiles of the response variable, given the explanatory variable. We use the check loss function and define the quantile regression model. We then look at different optimization techniques to find the regression coefficients. We also explore various tests to compare regression coefficients for different models and different values of quantiles. We then explore a different approach, Bayesian Quantile Regression. We then incorporate a spatial structure in the Bayesian Quantile Regression using the asymmetric Laplace process. We exploit the mixture representation of the asymmetric Laplace process to include the spatial information of the data. We interpolate the model to find the estimates of quantiles of the response variable at new spatial locations. We use this technique on the rainfall and temperature data of South India. It is observed that the temperature has a small effect on the rainfall, and the impact of temperature increases with increasing quantiles. We also compare this method with the frequentist approach of Quantile Regression and Bayesian Quantile Regression without spatial reference using the check loss function. It is found that the Spatial Bayesian Quantile Regression performs well for some datasets and does not for some others. This could be attributed to the erroneous assumptions regarding the covariance function. We expect that better assumptions related to the covariance function will improve performance.

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