Digital Commons Network^™

Group-Lasso Estimation In High-Dimensional Factor Models With Structural Breaks, Yujie Song

Major Papers

In this major paper, we study the influence of structural breaks in the financial market model with high-dimensional data. We present a model which is capable of detecting changes in factor loadings, determining the number of factors and detecting the break date. We consider the case where the break date is both known and unknown and identify the type of instability. For the unknown break date case, we propose a group-LASSO estimator to determine the number of pre- and post-break factors, the break date and the existence of instability of factor loadings when the number of factor is constant. We …

Estimation In High-Dimensional Factor Models With Structural Instabilities, Wen Gao

Major Papers

In this major paper, we use high-dimensional models to analyze macroeconomic data which is in influenced by the break point. In particular, we consider to detect the break point and study the changes of the number of factors and the factor loadings with the structural instability.

Concretely, we propose two factor models which explain the processes of pre- and post- break periods. Then, we consider the break point as known or unknown. In both situations, we derive the shrinkage estimators by minimizing the penalized least square function and calculate the estimators of the numbers of pre- and post- break factors …

Topological Vector Spaces, Chunqing Li

Major Papers

This major paper is a report on author’s study of some topics on topological vector spaces. We prove a well-known Hahn-Banach theorem and some important consequences, including several separation and extension theorems. We study the weak topology on a topological vector space X and the weak-star topology on the dual space X* of X. We also prove the Banach-Alaoglu theorem. Consequently, we characterize the closed convex hull and the closed linear span for sets in X and X* , identify the dual of a subspace of X with the quotient of its annihilator, and obtain the Goldstine theorem as well …

Markushevich Bases And Auerbach Bases In Banach Spaces, Apala Mandal

Major Papers

This paper studies Markushevich bases and Auerbach bases in Banach spaces. Firstly, a countable 1-norming Markushevich basis is constructed for any infinite-dimensional separable Banach space. Secondly, an Auerbach basis is constructed for any finite-dimensional Banach space. Thirdly, a Markushevich basis is constructed for a class of non-separable Banach spaces by applying projectional generators and projectional resolution identities, and the transfinite induction on the density character of the space.

Multi-State Modeling Of Hospital Frequent Users, Yu Liang

Major Papers

The top 1% of frequent users account for 34% of public health system expenditures in Ontario, while the top 5% account for 66%. In this paper, we explore the efficacy of an intervention aimed at reducing hospital utilization for a group of patients defined as frequent users, by using Multi-state modeling. We employ time-homogeneous, time-inhomogeneous, parametric and semi-parametric Markov processes to study the transitions of the patients between hospital, ER and outside during a follow up period of one year. The results do not indicate any strong evidence that the intervention was beneficial.

Queues With Server Utilization Of One, Robert Aidoo

Major Papers

In most queueing systems of type GI/G/1, the stability condition requires that the server utilization be strictly less than 1. The standard exception is a D/D/1 system in which stability still holds for server utilization equal to 1. This paper presents other cases when server utilization can equal 1, and discusses their characteristics.

The Price Of Stocks, Geometric Brownian Motion, And Black Scholes Formula, Fatimah Fathalden Asiri

Major Papers

In this paper, we discuss the stock price model as Geometric Brownian motion.

After that, we obtain a closed form solution to the model using It^o's Lemma.

Moreover, we use this solution to derive the Black Scholes formula.

Exploring Quantitative Timed Up And Go Sensor Data With Statistical Learning Techniques, Anthony Wright

Major Papers

Injuries and hospitalizations due to accidental falls among seniors represent a major expense for the Canadian public health system. It is highly desirable to be able to predict risk of falls for senior individuals in order to place them in prevention programs. Recently, sensor technologies have been used to predict risk of falls and levels of frailty of individuals. A commonly used test for assessing risk of falls is known as QTUG (Quantitative `Timed Up and Go'). The QTUG data often consist of a small set of survey answers about the individuals' historic variables (e.g., number of falls in the …

Geometric Model Of Roots Of Stochastic Matrices, Yelyzaveta Chetina

Major Papers

In this paper we examine the conditions under which discrete-time homogenous Markov transition matrices have probability roots. A method based on geometric interpretation of 2x2 Markov matrices is used to find regions within the unit square corresponding to probability matrices with zero, single or multiple probability roots.