On Second Order Neighbourhood Analysis of Mapped Point Patterns

Getis and Franklin (1987), introduced a technique based on second order methods, called second order neighbourhood method, which is used to quantify clustering at various spatial scales. Variants of this method are introduced for testing whether a spatial point pattern is consistent with the hypothesis of a Poisson process. These variants are applied to point location data for a sample of Ponderosa pine (Pinus ponderosa) trees.     

Nonparametric association analysis of bivariate left‐truncated competing risks data

We develop time‐varying association analyses for onset ages of two lung infections to address the statistical challenges in utilizing registry data where onset ages are left‐truncated by ages of entry and competing‐risk censored by deaths. Two types of association estimators are proposed based on conditional cause‐specific hazard function and cumulative incidence function that are adapted from unconditional quantities to handle left truncation. Asymptotic properties of the estimators are established by using the empirical process techniques. Our simulation study shows that the estimators perform well with moderate sample sizes. We apply our methods to the Cystic Fibrosis Foundation Registry data to study the relationship between onset ages of Pseudomonas aeruginosa and Staphylococcus aureus infections.     

A Semiparametric Estimator of the Crossing Point in the Two‐Sample Linear Shift Function: Application to Crossing Lifetime Distributions

Let X and Y be two random variables with continuous distribution functions F and G. Consider two independent observations X₁, … , X_m from F and Y₁, … , Y_n from G. Moreover, suppose there exists a unique x* such that F(x) > G(x) for x < x* and F(x) < G(x) for x > x* or vice versa. A semiparametric model with a linear shift function (Doksum, 1974) that is equivalent to a location‐scale model (Hsieh, 1995) will be assumed and an empirical process approach (Hsieh, 1995) is used to estimate the parameters of the shift function. Then, the estimated shift function is set to zero, and the solution is defined to be an estimate of the crossing‐point x*. An approximate confidence band of the linear shift function at the crossing‐point x* is also presented, which is inverted to yield an approximate confidence interval for the crossing‐point. Finally, the lifetime of guinea pigs in days observed in a treatment‐control experiment in Bjerkedal (1960) is used to demonstrate our procedure for estimating the crossing‐point. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Self‐Organization of Polymer Additive,Poly(2‐vinylpyridine) via One‐Step Solution Processing to Enhance the Efficiency and Stability of Polymer Solar Cells

Interfaces between the photoactive layers and electrodes play critical roles in controlling the performance of optoelectronic devices. Herein, a novel nonconjugated polymer additive (nPA), poly(2‐vinylpyridine) (P2VP), is reported for modifying the interfaces between the bulk‐heterojunction (BHJ) and cathode/metal oxide (MO) layers. The P2VP nPA enables remarkably enhanced power conversion efficiencies (PCEs) and ambient stability in different types of polymer solar cells (PSCs). Importantly, interfacial engineering can be achieved during deposition of the P2VP nPA‐containing BHJ active layer via simple, one‐step solution processing. The P2VP nPA has much higher surface energy than the BHJ active components and stronger interaction with the surface of MO, which affords spontaneous vertical phase separation from the BHJ layer on the MO surface by one‐step solution processing. The self‐assembled P2VP layer substantially reduces the work function and surface defect density of MO, thereby minimizing the charge‐extraction barrier and increasing the PCEs of the PSCs significantly, i.e., PTB7‐Th:PC₇₁BM (10.53%→11.14%), PTB7:PC₇₁BM (7.37%→8.67%), and PTB7‐Th:P(NDI2HD‐T) all‐PSCs (5.52%→6.14%). In addition, the lifetimes of the PSCs are greatly improved by the use of the P2VP nPA.     

Avoiding misinterpretation of biotic interactions with the intertype K12‐function: population independence vs. random labelling hypotheses

Abstract. The interactions between plants of different species, age or size play an important role in the dynamics of an ecosystem and can induce specific structures. These interactions can be studied by analysing the spatial structure of the corresponding bivariate patterns. The intertype L₁₂‐function has recently been successfully used in many papers for that purpose. However, when interpreting the results obtained with ecological data, at least two different null hypotheses – independence or random labelling – can be appropriate, depending on the context of the study and the nature of the data. As these two hypotheses correspond to different confidence intervals, an inappropriate choice of the null hypothesis can lead to misinterpretations of biotic interactions when studying ecological data. This problem has rarely been mentioned in the literature. In this paper we clarify the differences between these two null hypotheses, and illustrate the risk of misinterpretation when using an inappropriate null hypothesis. We review the main characteristics of these two hypotheses, and analyse the spatial structure of both real data from forest stands and simulated virtual stands of different structures. We demonstrate that the risk of misinterpretation is quite high, and that extreme misinterpretations, i.e. cases leading to opposite conclusions in terms of spatial interaction, can occur in a significant number of cases. We therefore propose some guidelines to help ecologists avoid such misinterpretations.