Multiple Linear Regression

Some Modifications to Calculate Regression Coefficients in Multiple Linear Regression

In a multiple linear regression model, there are instances where one has to update the regression parameters. In such models as new data become available, by adding one row to the design matrix, the least-squares estimates for the parameters must be updated to reflect the impact of the new data. We will modify two existing methods of calculating regression coefficients in multiple linear regres...

Linear Regression Under Multiple

This dissertation studies the least squares estimator of a trend parameter in a simple linear regression model with multiple changepoints when the changepoint times are known. The error component in the model is allowed to be autocorrelated. The least squares estimator of the trend and the variance of the trend estimator are derived. Consistency and asymptotic normality of the trend estimator a...

Part II Multiple Linear Regression

Multiple Linear Regression Models in Outlier Detection

Identifying anomalous values in the realworld database is important both for improving the quality of original data and for reducing the impact of anomalous values in the process of knowledge discovery in databases. Such anomalous values give useful information to the data analyst in discovering useful patterns. Through isolation, these data may be separated and analyzed. The analysis of outlie...

Mixed Linear Regression with Multiple Components

In this paper, we study the mixed linear regression (MLR) problem, where the goal is to recover multiple underlying linear models from their unlabeled linear measurements. We propose a non-convex objective function which we show is locally strongly convex in the neighborhood of the ground truth. We use a tensor method for initialization so that the initial models are in the local strong convexi...