With drastic increases in electricity prices throughout 2021, the public’s en- gagement in the discourse about the cost of electricity has reached new heights. With this in mind, this project was set in motion to try to make sense of factors that affect electricity prices in Sweden and thus identify areas of interest that further research could focus on.The variables chosen to be investigated were: Temperature, Exchange rate be- tween SEK and EUR, Export of electricity, Import of electricity, Inflation, Price of coal, Price of natural gas, and Price of crude oil. The data was gathered from various sources and was used to create a linear regression model.Exchange rate between SEK and EUR, Export of electricity, Inflation, Price of coal and Price of natural gas were found to be significant predictors of elec- tricity prices in Sweden and the source of electricity, economic policy, and energy trade were the areas of interest for further research.

Estimation of nonlinear models finds applications in every field of engineering and the sciences. Much work has been done to build solid statistical theories for its use and interpretation. However, there has been little analysis of the tolerance of nonlinear model estimators to deviations from assumptions and normality. We focus on analyzing the robustness properties of M-estimators of nonlinear models by studying the effects of deviations from assumptions and normality on these estimators. We discuss St. Laurent and Cook's Jacobian Leverage and identify the relationship of the technique to the robustness concept of influence. We derive influence functions for M-estimators of nonlinear models and show that influence of position becomes, more generally, influence of model. The result shows that, for M-estimators, we must bound not only influence of residual but also influence of model. Several examples highlight the unique problems of nonlinear model estimation and demonstrate the utility of the influence function. / Master of Science

Recently, variable selection in high-dimensional data has attracted much research interest. Classical stepwise subset selection methods are widely used in practice, but when the number of predictors is large these methods are difficult to implement. In these cases, modern regularization methods have become a popular choice as they perform variable selection and parameter estimation simultaneously. However, the estimation procedure becomes more difficult and challenging when the data suffer from outliers or when the assumption of normality is violated such as in the case of heavy-tailed errors. In these cases, quantile regression is the most appropriate method to use. In this thesis we combine these two classical approaches together to produce regularized quantile regression methods. Chapter 2 shows a comparative simulation study of regularized and robust regression methods when the response variable is continuous. In chapter 3, we develop a quantile regression model with a group lasso penalty for binary response data when the predictors have a grouped structure and when the data suffer from outliers. In chapter 4, we extend this method to the case of censored response variables. Numerical examples on simulated and real data are used to evaluate the performance of the proposed methods in comparisons with other existing methods.

published_or_final_version / abstract / Statistics and Actuarial Science / Master / Master of Philosophy

The integration of remote sensing satellite data in air quality monitoring system at a regional scale is an important method to provide high spatial / temporal resolution information. This work focuses on estimating high spatial / temporal resolution ground-level information about particulate matter with aerodynamic diameters less than 2.5 um (PM2.5), with the utilization of MODIS aerosol optical thickness (AOT) data and meteorological data. Several missing data reconstruction techniques including Bayesian inversion, regularization and prediction-error filter are employed to estimate PM2.5 from satellite data. The results show that several direct missing data interpolation methods have the capability to estimate some distinctive features on the basis of available ground-based measurements, while the PEF method tends to generate more information with the aid of satellite AOT information. In addition to interpolation methods, general linear regression methods are used to predict ground-level PM2.5 with the consideration of other factors that have been shown to play an important role in predictions. Ordinary Least Square (OLS) method, when natural log taken on dependent and independent variables, is able to reduce the violation of homoscedasticity. The scatterplot of predicted and measured PM2.5 shows a strong correlation over the validation region, indicating the ability of the regression model to predict PM2.5. Weighted Least Square (WLS) method also has advantage in improving homoscedasticity. The predicted and measured PM2.5 has a relatively high correlation. / text

The problem considered relates to estimating an arbitrary regression function m(x) from sample pairs (Xᵢ,Yᵢ) 1 ≤ i ≤ n. A model is assumed of the form Y = m(x) + ε(x) where ε(x) is a random variable with expectation 0. One well known method for estimating m(x) is by using one of a class of kernel regression estimators say m(n)(x). Schuster (1972) has shown conditions under which the limiting distribution of the kernel estimator m(n)(x) is the normal distribution. It might also be of interest to use the data to estimate the distribution of m(n)(x). One could, given this estimate, construct approximate confidence bounds for the function m(x). Three estimators are proposed for the density of m(n)(x). They share a basis in non-parametric kernel regression and utilize bootstrap techniques to obtain the density estimate. The order of convergence of one of the estimators is examined and conditions are given under which the order is higher then when estimation is by the normal approximation. Finally the performance of each estimator for constructing confidence bounds is compared for moderate sample sizes using computer studies.

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