In many fields of statistical application the fundamental task is to quantify the association between some explanatory variables or covariates and a response or outcome variable through a suitable regression model. The accuracy of such quantification depends on how precisely we measure the relevant covariates. In many instances, we can not measure some of the covariates accurately, rather we can measure noisy versions of them. In statistical terminology this is known as measurement errors or errors in variables. Regression analyses based on noisy covariate measurements lead to biased and inaccurate inference about the true underlying response-covariate associations. In this thesis we investigate some aspects of measurement error modelling in the case of binary logistic regression models. We suggest a flexible parametric approach for adjusting the measurement error bias while estimating the response-covariate relationship through logistic regression model. We investigate the performance of the proposed flexible parametric approach in comparison with the other flexible parametric and nonparametric approaches through extensive simulation studies. We also compare the proposed method with the other competitive methods with respect to a real-life data set. Though emphasis is put on the logistic regression model the proposed method is applicable to the other members of the generalized linear models, and other types of non-linear regression models too. Finally, we develop a new computational technique to approximate the large sample bias that my arise due to exposure model misspecification in the estimation of the regression parameters in a measurement error scenario. / Science, Faculty of / Statistics, Department of / Graduate

In some applications, we require a monotone estimate of a regression function. In others, we want to test whether the regression function is monotone. For solving the first problem, Ramsay's, Kelly and Rice's, as well as point-wise monotone regression functions in a spline space are discussed and their properties developed. Three monotone estimates are defined: least-square regression splines, smoothing splines and binomial regression splines. The three estimates depend upon a "smoothing parameter": the number and location of knots in regression splines and the usual [formula omitted] in smoothing splines. Two standard techniques for choosing the smoothing parameter, GCV and AIC, are modified for monotone estimation, for the normal errors case. For answering the second question, a test statistic is proposed and its null distribution conjectured. Simulations are carried out to check the conjecture. These techniques are applied to two data sets. / Science, Faculty of / Statistics, Department of / Graduate

The motivation for this thesis came from the provision of a large data set from Saudi Arabia giving anthropometric measurements of children and adolescents from birth to eighteen years of age, with a requirement to construct growth charts. The construction of these growth charts revealed a number of issues particularly in the respect to statistical inference relating to quantile regression. To investigate a range of different statistical inference procedures in parametric quantile regression in particular the estimation of the confidence limits of the ?th (?? [0, 1]) quantile, a number of sets of simulated data in which various error structures are imposed including homoscedastic and heteroscedastic structures were developed. Methods from the statistical literature were then compared with a method proposed within this thesis based on the idea of Silverman's (1986) kernel smoothing. This proposed bootstrapping method requires the estimation of the conditional variance function of the fitted quantile. The performance of a variety of variance estimation methods combined within the proposed bootstrapping procedure are assessed under various data structures in order to examine the performance of the proposed bootstrapping approach. The validity of the proposed bootstrapping method is then illustrated using the Saudi Arabian anthropometric data.

abstract: Lifespan psychological perspectives have long suggested the context in which individuals live having the potential to shape the course of development across the adult lifespan. Thus, it is imperative to examine the role of both the objective and subjective neighborhood context in mitigating the consequences of lifetime adversity on mental and physical health. To address the research questions, data was used from a sample of 362 individuals in midlife who were assessed on lifetime adversity, multiple outcomes of mental and physical health and aspects of the objective and subjective neighborhood. Results showed that reporting more lifetime adversity was associated with poorer mental and physical health. Aspects of the objective and subjective neighborhood, such as green spaces moderated these relationships. The discussion focuses on potential mechanisms underlying why objective and subjective indicators of the neighborhood are protective against lifetime adversity. / Dissertation/Thesis / Masters Thesis Psychology 2019

Energy Consumption is a topic of great interest, especially since a surge in prices in late 2021 has caused a considerable increase in discussion around the topic. Data from the Swedish Central Bureau of statistics (SCB) and the Swedish Meteorological Institute (SMHI) were provided for macroscopic regressors. These regressors are temperature, population, GDP, day length, electricity price, electricity production, production of variable renewable energy and average income in order to predict electricity consumption. Four models were created, a full multiple linear regression model using all regressors. A reduced multiple linear regression model using a subset of the regressors determined by cross validation. A ridge model and a LASSO model. These were then used to attempt to predict the power consumption of 20% of the data set that were left out when creating the models. The LASSO model was most successful in this as it had the smallest cumulative residual and the ridge model was the worst. Since the reduced and the full model both had very high multicollinearity the conclusion was that the LASSO model is the best model out of the four.

Ordinary Least Squares (OLS) models are popular tools among field scientists, because they are easy to understand and use. Although OLS estimators are unbiased, it is often advantageous to introduce some bias in order to lower the overall variance in a model. This study focuses on comparing ridge regression and the LASSO methods which both introduce bias to the regression problem. Both approaches are modeled after the OLS but also implement a tuning parameter. Additionally, this study will compare the use of two different functions in R, one of which will be used for ridge regression and the LASSO while the other will be used strictly for the LASSO. The techniques discussed are applied to a real set of data involving some physiochemical properties of wine and how they affect the overall quality of the wine.

No description available.

No description available.

No description available.

Note: