Quantile Regression for Functional Data
Specialeforsvar ved Elisabeth Olsen
Titel: Quantile Regression for Functional Data
Abstract: This thesis studies quantile regression, which opposite the usual mean regression Where the conditional expectation is estimated, estimates the conditional quantiles. This enables inference to be made on the entire conditional distribution. Therefore is quantile regression extended to estimation when the response variable is scalar and the covariate is a function, for which the functional covariate is discretely observed. The two different regression methods was demonstrated with a simulation study, and theory for the quantile regression estimation method and the asymptotic behaviour of the quantile and the estimator was established.
Basis expansion was used to estimate the weight function for generated data. The co-variate function was estimated with a smoothing method, where it was represented by a known basis function. With the estimated covariate function were the "scores" estimated, for which the scalar response variable was regressed on as in standard quantile regression. Hereof were the estimated coeffcients obtained which constitutes the weight function. The comparative simulation study illustrated the differences in two regression methods and highlighted the similarities in the estimates obtained. As such did the use of basis function perform well as reasonable estimates was obtained. However, as the basis func-tion chosen was used to generate data, made things a lot easier. As different components of the framework was altered, were these components emphasized as possible challenges. One of these challenges was the choice of truncation K, as a to small or to large K can affect the estimates.
Vejleder: Anders Tolver
Censor: Birger Stjernholm Madsen