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Articles 1 - 4 of 4
Full-Text Articles in Statistical Models
Nonparametric Derivative Estimation Using Penalized Splines: Theory And Application, Bright Antwi Boasiako
Nonparametric Derivative Estimation Using Penalized Splines: Theory And Application, Bright Antwi Boasiako
Doctoral Dissertations
This dissertation is in the field of Nonparametric Derivative Estimation using
Penalized Splines. It is conducted in two parts. In the first part, we study the L2
convergence rates of estimating derivatives of mean regression functions using penalized splines. In 1982, Stone provided the optimal rates of convergence for estimating derivatives of mean regression functions using nonparametric methods. Using these rates, Zhou et. al. in their 2000 paper showed that the MSE of derivative estimators based on regression splines approach zero at the optimal rate of convergence. Also, in 2019, Xiao showed that, under some general conditions, penalized spline estimators …
Model-Free Descriptive Modeling For Multivariate Categorical Data With An Ordinal Dependent Variable, Li Wang
Model-Free Descriptive Modeling For Multivariate Categorical Data With An Ordinal Dependent Variable, Li Wang
Doctoral Dissertations
In the process of statistical modeling, the descriptive modeling plays an essential role in accelerating the formulation of plausible hypotheses in the subsequent explanatory modeling and facilitating the selection of potential variables in the subsequent predictive modeling. Especially, for multivariate categorical data analysis, it is desirable to use the descriptive modeling methods for uncovering and summarizing the potential association structure among multiple categorical variables in a compact manner. However, many classical methods in this case either rely on strong assumptions for parametric models or become infeasible when the data dimension is higher. To this end, we propose a model-free method …
Inference From Network Data In Hard-To-Reach Populations, Isabelle Beaudry
Inference From Network Data In Hard-To-Reach Populations, Isabelle Beaudry
Doctoral Dissertations
The objective of this thesis is to develop methods to make inference about the prevalence of an outcome of interest in hard-to-reach populations. The proposed methods address issues specific to the survey strategies employed to access those populations. One of the common sampling methodology used in this context is respondent-driven sampling (RDS). Under RDS, the network connecting members of the target population is used to uncover the hidden members. Specialized techniques are then used to make inference from the data collected in this fashion. Our first objective is to correct traditional RDS prevalence estimators and their associated uncertainty estimators for …
Mixture Of Factor Analyzers With Information Criteria And The Genetic Algorithm, Esra Turan
Mixture Of Factor Analyzers With Information Criteria And The Genetic Algorithm, Esra Turan
Doctoral Dissertations
In this dissertation, we have developed and combined several statistical techniques in Bayesian factor analysis (BAYFA) and mixture of factor analyzers (MFA) to overcome the shortcoming of these existing methods. Information Criteria are brought into the context of the BAYFA model as a decision rule for choosing the number of factors m along with the Press and Shigemasu method, Gibbs Sampling and Iterated Conditional Modes deterministic optimization. Because of sensitivity of BAYFA on the prior information of the factor pattern structure, the prior factor pattern structure is learned directly from the given sample observations data adaptively using Sparse Root algorithm. …