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Advances in Confidence distribution (CD): multivariate exact inference based on estimating equations and inference on model confidence set
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Sun, Xinyu. Advances in Confidence distribution (CD): multivariate exact inference based on estimating equations and inference on model confidence set. Retrieved from https://doi.org/doi:10.7282/t3-x9ke-fr72

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TitleAdvances in Confidence distribution (CD): multivariate exact inference based on estimating equations and inference on model confidence set
NameSun, Xinyu (author); Liu, Regina (chair); Cheng, Jerry (member); Hung, Ying (member); Xie, Minge (member); Liu, Regina (member); Rutgers University; School of Graduate Studies
Date Created2022
Other Date2022-10 (degree)
SubjectStatistics, Confidence intervals
Extent104 pages : illustrations
DescriptionAlthough the field of statistics has experienced tremendous growth in recent years, several fundamental statistical problems still remain unsolved, especially in the tasks of drawing valid inferences in the settings: i) with limited data set, and ii) in discrete model space. In this dissertation, we develop new methodologies to solve two specific research problems in these two areas. The first research problem is on making an exact statistical inference based on estimating equations under minimal model assumptions and with a finite sample size. Specifically, we develop a new statistical approach and Monte-Carlo algorithms to obtain simultaneous exact inference on multivariate parameters in a broad range of scenarios of real applications, including a number of complex quantile regression and rank regression settings. The key tool underlying our approach is the so-called “exact depth Confidence Distribution” (ed-CD). The ed-CD inherits the desirable nonparametric properties from data depth and is derived directly from multivariate estimating equations. Our approach is broadly applicable and particularly useful in finite sample settings where the underlying distribution of the estimating equations is asymmetric (e.g., non-normal distribution) and complex (e.g., non-smooth or non-differential), and/or the confidence region is of a non-standard form (e.g., non-ellipsoid). This development is shown to be valid and efficient both theoretically and empirically in simulation studies and real data examples. The second research problem is on constructing a confidence set of models to quantify the uncertainty of a model selection when the underlying model is unknown. The common approach in the literature is to select a single model from a set of candidate models, and then estimations and predictions are performed without accounting for the uncertainty incurred in the model selection phase. Consequently, the variability tends to be underestimated, which yields overly optimistic confidence and predictive intervals (or regions). To address the issue of model selection uncertainty, we propose a new approach to constructing a model confidence set for the unknown true model with a guaranteed coverage probability. In the case that the true model is not inside the candidate models set M, this approach yields a model confidence set for the candidate model that is the “closest” to the true model. Our approach is developed under the classical linear regression setting where M is discrete and fixed beforehand. There is no specific requirement on the M in general, and the models in M are not necessarily nested or linearly ordered. The development is shown to be valid and asymptotically efficient. Its performance is further demonstrated numerically in several simulated studies and a real data application.
NotePh.D.
NoteIncludes bibliographical references
Genretheses
Persistent URLhttps://doi.org/doi:10.7282/t3-x9ke-fr72
LanguageEnglish
CollectionSchool of Graduate Studies Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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