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Abstract–Data sharpening in kernel regression has been shown to be an effective method of reducing bias while having minimal effects on variance. Earlier efforts to iterate the data sharpening procedure have been less effective, due to the employment of an inappropriate sharpening transformation. In the present paper, an iterated data sharpening algorithm is proposed which reduces the asymptotic bias at each iteration, while having modest effects on the variance. The efficacy of the iterative approach is demonstrated theoretically and via a simulation study. Boundary effects persist and the affected region successively grows when the iteration is applied to local constant regression. By contrast, boundary bias successively decreases for each iteration step when applied to local linear regression. This study also shows that after iteration, the resulting estimates are less sensitive to bandwidth choice, and a further simulation study demonstrates that iterated data sharpening with data-driven bandwidth selection via cross-validation can lead to more accurate regression function estimation. Examples with real data are used to illustrate the scope of change made possible by using iterated data sharpening and to also identify its limitations. [ABSTRACT FROM AUTHOR]

Real-world phenomena simulation models, which can be used to engage middle-school students with probability, are described. Links to R instructional material and easy-to-use code are provided to facilitate implementation in the classroom.

Local polynomial regression is a convenient method for smoothing scatterplots with readily available software. However, it is well known that variable amounts of bias are induced by the smoothing operation. This article proposes a simple visualization tool based on approximate confidence intervals which can alert the data analyst to regions of the regression function domain which might be susceptible to unacceptably large levels of bias, and possibly indicating a need for a less automatic smoothing approach. A simulation study verifies the accuracy of the confidence bands, and the method is illustrated with several real datasets. [ABSTRACT FROM AUTHOR]

The Analysis of Variance is often taught in introductory statistics courses, but it is not clear that students really understand the method. This is because the derivation of the test statistic and p-value requires a relatively sophisticated mathematical background which may not be well-remembered or understood. Thus, the essential concept behind the Analysis of Variance can be obscured. On the other hand, it is possible to provide students with a graphical technique that makes the essential concept transparent. The technique discussed in this article can be understood by students with little or no background in probability or statistics. In fact, only the ability to add, subtract, compute averages, and interpret histograms is required. (Contains 7 tables and 3 figures.)

The increasing popularity of R is leading to an increase in its use in undergraduate courses at universities (R Development Core Team 2008). One of the strengths of R is the flexible graphics provided in its "base" package. However, students often run up against its limitations, or they find the amount of effort to create an interesting plot may be excessive. The "grid" package (Murrell 2005) has a wealth of graphical tools which are more accessible to such R users than many people may realize. The purpose of this paper is to highlight the main features of this package and to provide some examples to illustrate how students can have fun with this different form of plotting and to see that it can be used directly in the visualization of data. (Contains 22 figures.)

Protecting human life and property from wildfires is a primary concern to wildland fire management agencies. Under certain environmental conditions and wildfire situations, burning embers can be lofted across a natural or man-made barrier devoid of fuel, such as a river or road, resulting in new ignitions downwind of the main advancing fire front. This phenomenon, referred to as a "spot fire" or "spotting," can put a considerable strain on firefighting operations and pose a grave risk to wildland-urban interface communities. In this article, we formulate the process of spot fire development, and derive the distribution of the time to the first spot fire occurring beyond a barrier to fire spread. A simulator is developed in the framework of generating burning embers from an active wildfire that may result in a spot fire. With the generated data, we demonstrate how to estimate the rate of developing spot fires and identify significant covariates based on data in two practical formats. [ABSTRACT FROM AUTHOR]

A method is proposed for shape-constrained density estimation under a variety of constraints, including but not limited to unimodality, monotonicity, symmetry, and constraints on the number of inflection points of the density or its derivative. The method involves computing an adjustment curve that is used to bring a pre-existing pilot estimate into conformance with the specified shape restrictions. The pilot estimate may be obtained using any preferred estimator, and the optimal adjustment can be computed using fast, readily-available quadratic programming routines. This makes the proposed procedure generic and easy to implement. [ABSTRACT FROM AUTHOR]