Physical Sciences and Mathematics Commons^™

The Periglacial Landscape Of Mars: Insight Into The 'Decameter-Scale Rimmed Depressions' In Utopia Planitia, Arya Bina

Electronic Thesis and Dissertation Repository

Currently, Mars appears to be in a ‘frozen’ and ‘dry’ state, with the clear majority of the planet’s surface maintaining year-round sub-zero temperatures. However, the discovery of features consistent with landforms found in periglacial environments on Earth, suggests a climate history for Mars that may have involved freeze and thaw cycles. Such landforms include hummocky, polygonised, scalloped, and pitted terrains, as well as ice-rich deposits and gullies, along the mid- to high-latitude bands, typically with no lower than 20o N/S. The detection of near-surface and surface ice via the Phoenix lander, excavation of ice via recent impact cratering activity as …

Analysis Challenges For High Dimensional Data, Bangxin Zhao

Electronic Thesis and Dissertation Repository

In this thesis, we propose new methodologies targeting the areas of high-dimensional variable screening, influence measure and post-selection inference. We propose a new estimator for the correlation between the response and high-dimensional predictor variables, and based on the estimator we develop a new screening technique termed Dynamic Tilted Current Correlation Screening (DTCCS) for high dimensional variables screening. DTCCS is capable of picking up the relevant predictor variables within a finite number of steps. The DTCCS method takes the popular used sure independent screening (SIS) method and the high-dimensional ordinary least squares projection (HOLP) approach as its special cases.

Two methods …

Advances In Semi-Nonparametric Density Estimation And Shrinkage Regression, Hossein Zareamoghaddam

Electronic Thesis and Dissertation Repository

This thesis advocates the use of shrinkage and penalty techniques for estimating the parameters of a regression model that comprises both parametric and nonparametric components and develops semi-nonparametric density estimation methodologies that are applicable in a regression context.

First, a moment-based approach whereby a univariate or bivariate density function is approximated by means of a suitable initial density function that is adjusted by a linear combination of orthogonal polynomials is introduced. Such adjustments are shown to be mathematically equivalent to making use of standard polynomials in one or two variables. Once extended to apply to density estimation, in which case …

Modelling The Common Risk Among Equities Using A New Time Series Model, Jingjia Chu

Electronic Thesis and Dissertation Repository

A new additive structure of multivariate GARCH model is proposed where the dynamic changes of the conditional correlation between the stocks are aggregated by the common risk term. The observable sequence is divided into two parts, a common risk term and an individual risk term, both following a GARCH type structure. The conditional volatility of each stock will be the sum of these two conditional variance terms. All the conditional volatility of the stock can shoot up together because a sudden peak of the common volatility is a sign of the system shock.

We provide sufficient conditions for strict stationarity …