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Full-Text Articles in Physical Sciences and Mathematics
Joint Asymptotics For Smoothing Spline Semiparametric Nonlinear Models, Jiahui Yu
Joint Asymptotics For Smoothing Spline Semiparametric Nonlinear Models, Jiahui Yu
Doctoral Dissertations
We study the joint asymptotics of general smoothing spline semiparametric models in the settings of density estimation and regression. We provide a systematic framework which incorporates many existing models as special cases, and further allows for nonlinear relationships between the finite-dimensional Euclidean parameter and the infinite-dimensional functional parameter. For both density estimation and regression, we establish the local existence and uniqueness of the penalized likelihood estimators for our proposed models. In the density estimation setting, we prove joint consistency and obtain the rates of convergence of the joint estimator in an appropriate norm. The convergence rate of the parametric component …
Asymptotic Behavior Of The Random Logistic Model And Of Parallel Bayesian Logspline Density Estimators, Konstandinos Kotsiopoulos
Asymptotic Behavior Of The Random Logistic Model And Of Parallel Bayesian Logspline Density Estimators, Konstandinos Kotsiopoulos
Doctoral Dissertations
This dissertation is comprised of two separate projects. The first concerns a Markov chain called the Random Logistic Model. For r in (0,4] and x in [0,1] the logistic map fr(x) = rx(1 - x) defines, for positive integer t, the dynamical system xr(t + 1) = f(xr(t)) on [0,1], where xr(1) = x. The interplay between this dynamical system and the Markov chain xr,N(t) defined by perturbing the logistic map by truncated Gaussian noise scaled by N-1/2, where N -> infinity, is studied. A natural question is …