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Full-Text Articles in Statistical Models
Advances In Measurement Error Modeling, Linh Nghiem
Advances In Measurement Error Modeling, Linh Nghiem
Statistical Science Theses and Dissertations
Measurement error in observations is widely known to cause bias and a loss of power when fitting statistical models, particularly when studying distribution shape or the relationship between an outcome and a variable of interest. Most existing correction methods in the literature require strong assumptions about the distribution of the measurement error, or rely on ancillary data which is not always available. This limits the applicability of these methods in many situations. Furthermore, new correction approaches are also needed for high-dimensional settings, where the presence of measurement error in the covariates adds another level of complexity to the desirable structure …
Estimation And Variable Selection In High-Dimensional Settings With Mismeasured Observations, Michael Byrd
Estimation And Variable Selection In High-Dimensional Settings With Mismeasured Observations, Michael Byrd
Statistical Science Theses and Dissertations
Understanding high-dimensional data has become essential for practitioners across many disciplines. The general increase in ability to collect large amounts of data has prompted statistical methods to adapt for the rising number of possible relationships to be uncovered. The key to this adaptation has been the notion of sparse models, or, rather, models where most relationships between variables are assumed to be negligible at best. Driving these sparse models have been constraints on the solution set, yielding regularization penalties imposed on the optimization procedure. While these penalties have found great success, they are typically formulated with strong assumptions on the …
Modeling Stochastically Intransitive Relationships In Paired Comparison Data, Ryan Patrick Alexander Mcshane
Modeling Stochastically Intransitive Relationships In Paired Comparison Data, Ryan Patrick Alexander Mcshane
Statistical Science Theses and Dissertations
If the Warriors beat the Rockets and the Rockets beat the Spurs, does that mean that the Warriors are better than the Spurs? Sophisticated fans would argue that the Warriors are better by the transitive property, but could Spurs fans make a legitimate argument that their team is better despite this chain of evidence?
We first explore the nature of intransitive (rock-scissors-paper) relationships with a graph theoretic approach to the method of paired comparisons framework popularized by Kendall and Smith (1940). Then, we focus on the setting where all pairs of items, teams, players, or objects have been compared to …