Variables X (variable + x)

Distribution by Scientific Domains

Selected Abstracts

Models with Errors due to Misreported Measurements

Brent Henderson
Summary Measurement error and misclassification models feature prominently in the literature. This paper describes misreporting error, which can be considered to fall somewhere between these two broad types of model. Misreporting is concerned with situations where a continuous random variable X is measured with error and only reported as the discrete random variable Z. Data grouping or rounding are the simplest examples of this, but more generally X may be reported as a value z of Z which refers to a different interval from the one in which X lies. The paper discusses a method for handling misreported data and draws links with measurement error and misclassification models. A motivating example is considered from a prenatal Down's syndrome screening, where the gestational age at which mothers present for screening is a true continuous variable but is misreported because it is only ever observed as a discrete whole number of weeks which may in fact be in error. The implications this misreporting might have for the screening are investigated. [source]

Closed-form approximations to the error and complementary error functions and their applications in atmospheric science

C. Ren
Abstract The error function, as well as related functions, occurs in theoretical aspects of many parts of atmospheric science. This note presents a closed-form approximation for the error, complementary error, and scaled complementary error functions, with maximum relative errors within 0.8%. Unlike other approximate solutions, this single equation gives answers within the stated accuracy for real variable x , [0,). The approximation is very useful in solving atmospheric science problems by providing analytical solutions. Examples of the utility of the approximation are: the computation of cirrus cloud physics inside a general circulation model, the cumulative distribution functions of normal and log-normal distributions, and the recurrence period for risk assessment. Copyright 2007 Royal Meteorological Society [source]

Selection correction and sensitivity analysis for ordered treatment effect on count response

Myoung-Jae Lee
In estimating the effect of an ordered treatment , on a count response y with an observational data where , is self-selected (not randomized), observed variables x and unobserved variables , can be unbalanced across the control group (, = 0) and the treatment groups (, = 1, ,, J). While the imbalance in x causes ,overt bias' which can be removed by controlling for x, the imbalance in , causes ,covert (hidden or selection) bias' which cannot be easily removed. This paper makes three contributions. First, a proper counter-factual causal framework for ordered treatment effect on count response is set up. Second, with no plausible instrument available for ,, a selection correction approach is proposed for the hidden bias. Third, a nonparametric sensitivity analysis is proposed where the treatment effect is nonparametrically estimated under no hidden bias first, and then a sensitivity analysis is conducted to see how sensitive the nonparametric estimate is to the assumption of no hidden bias. The analytic framework is applied to data from the Health and Retirement Study: the treatment is ordered exercise levels in five categories and the response is doctor office visits per year. The selection correction approach yields very large effects, which are however ruled out by the nonparametric sensitivity analysis. This finding suggests a good deal of caution in using selection correction approaches. Copyright 2004 John Wiley & Sons, Ltd. [source]

Fragmentation and pre-existing species turnover determine land-snail assemblages of tropical rain forest

Dinarzarde C. Raheem
Abstract Aim, The main aims of the study were: (1) to investigate the effect of fragment age in relation to other patch- and landscape-scale measures of forest fragmentation, and (2) to assess the relative importance of fragmentation, habitat degradation (i.e. degradation caused by selective logging and past shifting cultivation) and putative pre-existing species turnover in structuring current land-snail assemblages. Location, South-western Sri Lanka. Methods, The land-snail fauna was sampled using standardized belt transects. Fifty-seven transects were sampled in 21 lowland rain forest fragments (c. 1,33,000 ha). The spatial arrangement of fragments in the study area was explicitly considered in an effort to take into account the non-random nature of fragmentation and degradation and the possibility that current species composition may reflect patterns of species turnover that existed prior to fragmentation. The data set of 57 land-snail species and 28 environmental and spatial variables was analysed using canonical correspondence analysis and partial canonical correspondence analysis. Results, Fragment age, mean shape complexity (i.e. a landscape-scale measure of shape complexity), altitude, and the spatial variables x (longitude), y (latitude) and y2 explained significant variation in land-snail species composition. None of the three nominal variables quantifying habitat degradation was significantly correlated with variation in species composition. The independent effects of fragment age and mean shape complexity were similar. The combined effect of the spatial variables alone was larger than the independent effects of fragment age, mean shape complexity or altitude, but was of the same order of magnitude. The total variation explained by the spatial variables was comparable to the total non-spatial variation accounted for by fragment age, mean shape complexity and altitude. Main conclusions, Fragment age was found to be one of only two key determinants (the other was shape complexity at the landscape scale) driving fragmentation-related changes in community composition. The influence of pre-fragmentation patterns of species turnover on assemblage structure can be stronger than the effects of fragmentation measures, such as age, and may override the effects of forest degradation. Thus, strong patterns of pre-existing turnover may potentially confound interpretation of the effects of forest fragmentation and degradation. [source]

Pseudodifferential operators with compound non-regular symbols

Yu. I. Karlovich
Abstract Let V (,) denote the Banach algebra of absolutely continuous functions of bounded total variation on ,. We study an algebra ,, of pseudodifferential operators of zero order with compound slowly oscillating V (,)-valued symbols (x, y) , a (x, y, ) that satisfy a Lipschitz condition with respect to the spatial variables x, y , ,. Sufficient conditions for the boundedness and compactness of pseudodifferential operators with compound symbols on the Lebesgue spaces Lp(,), for p = 2 and 1 < p < ,, are obtained. A Fredholm criterion and an index formula for pseudodifferential operators A , ,, are presented. ( 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]