Local partial likelihood estimation in proportional hazards regression

Fan, Gijbels and King [Ann. Statist. 25 (1997) 1661--1690] considered the estimation of the risk function $\psi (x)$ in the proportional hazards model. Their proposed estimator is based on integrating the estimated derivative function obtained through a local version of the partial likelihood. They proved the large sample properties of the derivative function, but the large sample properties of the estimator for the risk function itself were not established. In this paper, we consider direct estimation of the relative risk function $\psi (x_2)-\psi (x_1)$ for any location normalization point $x_1$. The main novelty in our approach is that we select observations in shrinking neighborhoods of both $x_1$ and $x_2$ when constructing a local version of the partial likelihood, whereas Fan, Gijbels and King [Ann. Statist. 25 (1997) 1661--1690] only concentrated on a single neighborhood, resulting in the cancellation of the risk function in the local likelihood function. The asymptotic properties of our estimator are rigorously established and the variance of the estimator is easily estimated. The idea behind our approach is extended to estimate the differences between groups. A simulation study is carried out.Comment: Published at http://dx.doi.org/10.1214/009053606000001299 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Problems in Setting Teaching Objectives and Countermeasures to Work out Teaching Objectives in College English Class

The professional competence of college English teachers in setting teaching goal has a direct impact on their teaching design level. Enhancing college teachers’ ability in setting classroom teaching goal facilitates the improvement of their design level. By combining with the teaching design scheme of normal class, this paper defines the meaning of College English classroom teaching objectives, analyzes the problems that the college English teachers have in setting teaching objectives, and puts forward corresponding countermeasures to develop the college English teachers’ capability of setting teaching objectives, which are expected to promote college English teachers’ ability to design the activities for their class

An alternative approach to the σ\sigma-meson-exchange in nucleon-nucleon interaction

Through a quantitative comparative study of the properties of deuteron and nucleon-nucleon interaction with chiral quark model and quark delocalization color screening model. We show that the $\sigma$-meson exchange used in the chiral quark model can be replaced by quark delocalization and color screening mechanism.Comment: 4 pages, 4 figure

Making Sense of Noisy Data: Theory and Applications

This thesis introduces a novel and interpretable index of increase which is mathematically defined based on the distance between a given function and a set of non-increasing functions. Unlike the widely used traditional statistical methods for analyzing relationships between variables, the index does not rely on assumptions such as linearity, normality, and monotonicity, which may not be satisfied. Hence, it has the flexibility to be applied directly on pairs of data points to measure and compare non-linear, asymmetric, and non-monotonic relationships between two variables. We begin with a review of the literature and background knowledge in Chapter 2. In Chapter 3, we propose a distance-based index of increase, describe its properties in detail, and show its benefits through applying it to an educational dataset. In this way, we see the interpretability of the index of increase and how it can be applied. We also propose several modifications for different scenarios, such as subgroup analysis. Lastly, we provide a step-by-step implementation guideline for non-statistical researchers or practitioners. In Chapter 4, we investigate two extensions of the index of increase, which quantify the interchangeability between variables. We discuss the usage of them in the context of developing curricula, accompanied with extensive graphical and numerical illustrations. In Chapter 5, we introduce and explore an empirical index of increase that works in both deterministic and random environments, thus allowing to assess monotonicity of functions that are prone to random measurement-errors. We prove consistency of the empirical index and show how its rate of convergence is influenced by deterministic and random parts of the data. In particular, the obtained results suggest a frequency at which observations should be taken in order to reach any pre-specified level of estimation precision. We illustrate the index using data arising from purely deterministic and error-contaminated functions, which may or may not be monotonic. Finally, in Chapter 6, we summarize our main results and give an outline of potential future works

Low Temperature Oxidation Experiments and Kinetics Model of Heavy Oil

Air injection is an effective technique for improved oil recovery. For a typical heavy oil sample, the effects of temperature on the oxidation characteristics were studied by low temperature oxidation (LTO) experiments. Kinetic parameters such as activation energy, frequency factor (pre-exponential factor) and reaction order are determined by using Arrhenius Equation. These parameters provide a theoretical basis for numerical simulation of LTO taking place during air injection in heavy oil reservoirs. The results of LTO experiments show that heavy oil has good low temperature oxidation properties and LTO reaction rate is mainly related to temperature, oxygen partial pressure and properties of crude oil. In the experimental temperature range, the oxidation reaction can effectively consume oxygen and at the same time produce large amount of CO2.Key words: Air injection; Low temperature oxidation; Kinetics model (70-150 oC

Controlling Lethal Browning of \u3cem\u3eHemarthria compressa\u3c/em\u3e Tissue Cultures

Hemarthria compressa is an important warm-season forage grass for use in Southwest China. However, due to poor seed set, it is propagated by vegetative cuttings of stolons, rhizomes, and nodal sections. The in vitro propagation of H. compressa is still faced with difficulties including blackening or browning of tissues prior to culturing due to the oxidation of phenolic compounds by polyphenolic oxidase enzyme present in excised tissue (Yang et al. 2008). The objectives of the study were to investigate possible means of successful initiation of cultures through elimination of phenolic browning

Influence of tensor interactions on masses and decay widths of dibaryons

The influence of gluon and Goldstone boson induced tensor interactions on the dibaryon masses and D-wave decay widths has been studied in the quark delocalization, color screening model. The effective S-D wave transition interactions induced by gluon and Goldstone boson exchanges decrease rapidly with increasing strangeness of the channel. The tensor contribution of K and $\eta$ mesons is negligible in this model. There is no six-quark state in the light flavor world studied so far that can become bound by means of these tensor interactions besides the deuteron. The partial D-wave decay widths of the $IJ^p={1/2}2^+$ N$\Omega$ state to spin 0 and 1 $\Lambda\Xi$ final states are 12.0 keV and 21.9 keV respectively. This is a very narrow dibaryon resonance that might be detectable in relativistic heavy ion reactions by existing RHIC detectors through the reconstruction of the vertex mass of the decay product $\Lambda\Xi$ and by the COMPAS detector at CERN or at JHF in Japan and the FAIR project in Germany in the future.Comment: 19 pages, 5 figure