A connection between two nonparametric tests for perfect ranking in balanced ranked set sampling

In this note, we show that an extension of a test for perfect ranking in a balanced ranked set sample given by Li and Balakrishnan (2008) to the multi-cycle case turns out to be equivalent to the test statistic proposed by Frey et al. (2007). This provides an alternative interpretation and motivation for their test statistic.

A Parametric Test of Perfect Ranking in Balanced Ranked Set Sampling

Many techniques based on data which are drawn by Ranked Set Sampling (RSS) scheme assume that the ranking of observations is perfect. Therefore it is essential to develop some methods for testing this assumption. In this article, we propose a parametric location-scale free test for assessing the assumption of perfect ranking. The results of a simulation study in two special cases of normal and exponential distributions indicate that the proposed test performs well in comparison with its leading competitors.

Variance estimation in ranked set sampling using a concomitant variable

We propose a nonparametric variance estimator when ranked set sampling (RSS) and judgment post stratification (JPS) are applied by measuring a concomitant variable. Our proposed estimator is obtained by conditioning on observed concomitant values and using nonparametric kernel regression.

(Tables 1,2) Tracking records and space use statistics of polar bears (Ursus maritimus) in Storfjorden, Svalbard

Arctic sea ice is declining rapidly, making it vital to understand the importance of different types of sea ice for ice-dependent species such as polar bears Ursus maritimus. In this study we used GPS telemetry (25 polar bear tracks obtained in Svalbard, Norway, during spring) and high-resolution synthetic aperture radar (SAR) sea-ice data to investigate fine-scale space use by female polar bears. Space use patterns differed according to reproductive state; females with cubs of the year (COYs) had smaller home ranges and used fast-ice areas more frequently than lone females. First-passage time (FPT) analysis revealed that females with COYs displayed significantly longer FPTs near (<10 km) glacier fronts than in other fast-ice areas; lone females also increased their FPTs in such areas, but they also frequently used drifting pack ice. These results clearly demonstrate the importance of fast-ice areas, in particular close to glacier fronts, especially for females with COYs. Access to abundant and predictable prey (ringed seal pups), energy conservation and reluctance to cross large open water areas are possible reasons for the observed patterns. However, glacier fronts are retracting in Svalbard, and declines in land-fast ice have been notable over the past decade. The eventual disappearance of these important habitats might become critical for the survival of polar bear cubs in Svalbard and other regions with similar habitat characteristics. Given the relatively small size of many fast-ice areas in Svalbard, the results observed in this study would not have been revealed using less accurate location data or lower-resolution sea-ice data.

(Table 1) Summary statistics of in situ sea-ice characteristics of Ice Station Belgica sites Fabra, Patria/Liège and Brussels in October 2007

Three ice type regimes at Ice Station Belgica (ISB), during the 2007 International Polar Year SIMBA (Sea Ice Mass Balance in Antarctica) expedition, were characterized and assessed for elevation, snow depth, ice freeboard and thickness. Analyses of the probability distribution functions showed great potential for satellite-based altimetry for estimating ice thickness. In question is the required altimeter sampling density for reasonably accurate estimation of snow surface elevation given inherent spatial averaging. This study assesses an effort to determine the number of laser altimeter 'hits' of the ISB floe, as a representative Antarctic floe of mixed first- and multi-year ice types, for the purpose of statistically recreating the in situ-determined ice-thickness and snow depth distribution based on the fractional coverage of each ice type. Estimates of the fractional coverage and spatial distribution of the ice types, referred to as ice 'towns', for the 5 km**2 floe were assessed by in situ mapping and photo-visual documentation. Simulated ICESat altimeter tracks, with spot size ~70 m and spacing ~170 m, sampled the floe's towns, generating a buoyancy-derived ice thickness distribution. 115 altimeter hits were required to statistically recreate the regional thickness mean and distribution for a three-town assemblage of mixed first- and multi-year ice, and 85 hits for a two-town assemblage of first-year ice only: equivalent to 19.5 and 14.5 km respectively of continuous altimeter track over a floe region of similar structure. Results have significant implications toward model development of sea-ice sampling performance of the ICESat laser altimeter record as well as maximizing sampling characteristics of satellite/airborne laser and radar altimetry missions for sea-ice thickness.

Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss

Sequential estimation of the success probability $p$ in inverse binomial sampling is considered in this paper. For any estimator $\hatvap$, its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters $a$ and $b$ for $\hatvap < p$ and $\hatvap > p$ respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as $p \rightarrow 0$, and which guarantee that, for any $p \in (0,1)$, the risk is lower than its asymptotic value. This allows selecting the required number of successes, $\nnum$, to meet a prescribed quality irrespective of the unknown $p$. In addition, the proposed estimators are shown to be approximately minimax when $a/b$ does not deviate too much from $1$, and asymptotically minimax as $\nnum \rightarrow \infty$ when $a=b$.

Reducing the dimensionality effect in importance sampling simulations

The dimensionality effect is avoided by the use of sufficient statistics in event probability estimators realised by importance sampling. If the system function is not a sufficient statistic, an approach is proposed to reduce the dimensionality effect in the estimators. Simulation results of false-alarm probability estimations, applied to radar detection, confirm a clear concordance with the theoretical results

Measurement of genetic structure within populations using Moran's spatial autocorrelation statistics.

Spatial structure of genetic variation within populations, an important interacting influence on evolutionary and ecological processes, can be analyzed in detail by using spatial autocorrelation statistics. This paper characterizes the statistical properties of spatial autocorrelation statistics in this context and develops estimators of gene dispersal based on data on standing patterns of genetic variation. Large numbers of Monte Carlo simulations and a wide variety of sampling strategies are utilized. The results show that spatial autocorrelation statistics are highly predictable and informative. Thus, strong hypothesis tests for neutral theory can be formulated. Most strikingly, robust estimators of gene dispersal can be obtained with practical sample sizes. Details about optimal sampling strategies are also described.

(Table 1) Summary statistics of taxa in samples of ODP Hole 181-1123B

Planktonic foraminifera are used to identify late Pliocene-Quaternary near surface water masses on the northeastern flank of Chatham Rise by comparison with faunas in core-tops east of New Zealand. In an overview study, distance measures, ordinations, and discriminant analysis are applied to 32 faunas from Site 1123B to identify similar faunas among 35 core-tops between 35 and 61°S east of New Zealand. Many Site 1123B faunas in the 2.72 myr interval sampled compare with those in core-tops on the northern side of Chatham Rise from a similar latitude, and are identified as transitional zone assemblages now associated with the subtropical gyre. This result is consistent with studies of late Quaternary planktonic foraminifera from this region and suggests that, typically, the Subtropical Front was locked to Chatham Rise through glacial and interglacial periods, at least back to the late Pliocene. However, a fauna at ca. 1.17 Ma compares with subpolar assemblages in core-tops between 44 and 48°S and identifies cooler surface water. Expectedly, closer sampling may reveal additional periods when southern water moved over the northeastern flank of Chatham Rise. Although the dominance of Globorotalia inflata, a species typical of the southern margin of subtropical gyres, is a principal feature of Site 1123B faunas, in a minority it is replaced as the most abundant species by dextral populations of Neogloboquadrina pachyderma, particularly about the time of the middle Pleistocene transition. Close analogues of these variant transitional assemblages are not present in core-tops about Chatham Rise but sediment trap and coretop data from other regions suggest that they identify high fertility in the mixed layer associated with upwelling or mixing of water masses. The proportion of sinistrally coiled Neogloboquadrina pachyderma rises to ca. 0.6 between ca. 2.45 and 2.57 Ma, soon after the intensification of Northern Hemisphere glaciation. Although the coiling data indicate subantarctic near surface water, the species remains rare. As the faunas retain their transitional zone character, only minor entrainment of subantarctic water may have occurred.

National Accident Sampling System. Report of a meeting.

Mode of access: Internet.