Recursive Parameter Estimation: Convergence

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We propose a wide class of recursive estimation procedures for the general statistical model and study convergence.Comment: 25 pages with 1 postscript figur

Truncated Stochastic Approximation with Moving Bounds: Convergence

In this paper we propose a wide class of truncated stochastic approximation procedures with moving random bounds. While we believe that the proposed class of procedures will find its way to a wider range of applications, the main motivation is to accommodate applications to parametric statistical estimation theory. Our class of stochastic approximation procedures has three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and dynamically changing random regression function. We establish convergence and consider several examples to illustrate the results

The Leadership Stories of Students of Color at Predominantly White Christian Institutions

Leadership has been identified as an important component of higher education and the college student experience (Dugan, 2006; Komives, Dugan, & Owen, 2011; Shertzer & Schuh, 2004; St. John, Rowley, & Hu, 2009). Although there has been an in-crease in leadership initiatives across higher education, many institutions, specifically dominantly White Christian institutions have struggled to find ways to involve students of color in leadership. Utilizing a phenomenological approach, this study explored the leadership experiences of 11 students of color from 3 dominantly White Christian institutions (DWI). This article will provide a broad overview of the study while focusing on how the participants perceived, experienced, and made of meaning of the influence of race in shaping their leadership experiences. Furthermore, implications for fostering a campus environment that better supports and encourages students of color as they navigate the leadership journey will be discussed

On Recursive Parametric Estimation Theory

The classical non-recursive methods to estimate unknown parameters of the model, such as the maximum likelihood method, the method of least squares etc. eventually require maximization procedures. These methods are often difficult to implement, especially for non i.i.d. models. If for every sample size n, when new data are acquired, an estimator has to be computed afresh, and if a numerical method is needed to do so, it generally becomes very laborious. Therefore, it is important to consider recursive estimation procedures which are appealing from the computational point of view. Recursive procedures are those which at each step allow one to re-estimate values of unknown parameters based on the values already obtained at the previous step together with new information. We propose a wide class of recursive estimation procedures for the general statistical model and study convergence, the rate of convergence, and the local asymptotic linearity. Also, we demonstrate the use of the results on some examples

Rate of convergence of truncated stochastic approximation procedures with moving bounds

The paper is concerned with stochastic approximation procedures having three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. We study convergence and rate of convergence. Main results are supplemented with corollaries to establish various sets of sufficient conditions, with the main emphases on the parametric statistical estimation. The theory is illustrated by examples and special cases.Comment: 30 page

Flame retardants, hexabromocyclododecane (HCBD) and tetrabromobisphenol a (TBBPA), alter secretion of tumor necrosis factor alpha (TNFα) from human immune cells

Hexabromocyclododecane (HBCD) and tetrabromobisphenol A (TBBPA) are flame retardants, used in a variety of applications, which contaminate the environment and are found in human blood. HBCD and TBBPA have been shown to alter the tumor killing function of natural killer (NK) lymphocytes and the secretion of the inflammatory cytokines interferon gamma (IFNγ) and interleukin 1 beta (IL-1β). The current study examined the effects of HBCD and TBBPA on secretion of the critical pro-inflammatory cytokine tumor necrosis factor alpha (TNFα) from human immune cells. Preparations of human immune cells that ranged in complexity were studied to determine if the effects of the compounds were consistent as the composition of the cell preparation became more heterogeneous. Cell preparations studied were: NK cells, monocyte-depleted (MD) peripheral blood mononuclear cells (PBMCs), and PBMCs. Exposure of NK cells to higher concentrations of HBCD (5 and 2.5 µM) caused decreased secretion of TNFα. However, when the cell preparation contained T lymphocytes (MD-PBMCs and PBMCs) these same concentrations of HBCD increased TNFα secretion as did nearly all other concentrations. This suggests that HBCD’s ability to increase TNFα secretion from immune cells was dependent on the presence of T lymphocytes. In contrast, exposures to TBBPA decreased the secretion of TNFα from all immune cell preparations regardless of the composition of the cell preparation. Further, HBCD-induced increases in TNFα secretion utilized the p38 MARK pathway. Thus, both HBCD and TBBPA may have the capacity to disrupt the inflammatory response with HBCD having the potential to cause chronic inflammation

The Intersection of Christianity and Racial Justice Advocacy

Those working toward institutional social change and supporting students from diverse background are considered social justice allies (Edwards, 2006). Patton et al. (2007) describe these individuals as knowledgeable and aware of how their own racial identities influence their interactions with others, understanding of racism, as well as their decisions, policies, and interactions with students of diverse backgrounds. There are several studies that have examined the development of White college students as social justice allies, but the development of White administrators as social justice allies is under-studied (Broido, 2000; Eichstedt, 2001; Reason, Roosa Millar, & Scales, 2005). Additionally, there is limited research related to social justice advocacy and Christian higher education. Through examining the experiences of White administrators who are active in leading social justice efforts at their Christian institutions, our findings demonstrate the influence of the participants’ Christian beliefs in the development of becoming social justice advocates