Chemical and forensic analysis of JFK assassination bullet lots: Is a second shooter possible?

The assassination of President John Fitzgerald Kennedy (JFK) traumatized the nation. In this paper we show that evidence used to rule out a second assassin is fundamentally flawed. This paper discusses new compositional analyses of bullets reportedly to have been derived from the same batch as those used in the assassination. The new analyses show that the bullet fragments involved in the assassination are not nearly as rare as previously reported. In particular, the new test results are compared to key bullet composition testimony presented before the House Select Committee on Assassinations (HSCA). Matches of bullets within the same box of bullets are shown to be much more likely than indicated in the House Select Committee on Assassinations' testimony. Additionally, we show that one of the ten test bullets is considered a match to one or more assassination fragments. This finding means that the bullet fragments from the assassination that match could have come from three or more separate bullets. Finally, this paper presents a case for reanalyzing the assassination bullet fragments and conducting the necessary supporting scientific studies. These analyses will shed light on whether the five bullet fragments constitute three or more separate bullets. If the assassination fragments are derived from three or more separate bullets, then a second assassin is likely, as the additional bullet would not easily be attributable to the main suspect, Mr. Oswald, under widely accepted shooting scenarios [see Posner (1993), Case Closed, Bantam, New York].Comment: Published in at http://dx.doi.org/10.1214/07-AOAS119 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A finite sample estimate of the variance of the sample median

A finite sample estimate of the variance of the sample median is proposed. This estimate is shown to have smaller bias than the related estimate of Maritz and Jarrett (1978) and Efron (1979).median variance estimate

On optimal data-based bandwidth selection in kernel density estimation

A bandwidth selection method is proposed for kernel density estimation. This is based on the straightforward idea of plugging estimates into the usual asymptotic representation for the optimal bandwidth, but with two important modifications. The result is a bandwidth selector with the, by nonparametric standards, extremely fast asymptotic rate of convergence of n−½ where n → ∞ denotes sample size. Comparison is given to other bandwidth selection methods, and small sample impact is investigated

A comparison of testing and confidence interval methods for the median

There are only relatively few confidence coefficients and levels available for distribution-free confidence intervals and test for the median based on the sign statistic. This problem can be overcome by interpolating confidence intervals or by studentizing the median by an estimate of its standard error. Such methods are discussed and then compared via simulation.median standard error estimate studentization interpolation

Confidence intervals based on interpolated order statistics

Confidence intervals for the population median based on interpolating adjacent order statistics are presented. They are shown to depend only slightly on the underlying distribution. A simple, nonlinear interpolation formula is given which works well for a broad collection of underlying distributions.nonparametric sign test

Indirect Cross-Validation for Density Estimation

A new method of bandwidth selection for kernel density estimators is proposed. The method, termed indirect cross-validation, or ICV, makes use of so-called selection kernels. Least squares cross-validation (LSCV) is used to select the bandwidth of a selection-kernel estimator, and this bandwidth is appropriately rescaled for use in a Gaussian kernel estimator. The proposed selection kernels are linear combinations of two Gaussian kernels, and need not be unimodal or positive. Theory is developed showing that the relative error of ICV bandwidths can converge to 0 at a rate of n−1/4, which is substantially better than the n−1/10 rate of LSCV. Interestingly, the selection kernels that are best for purposes of bandwidth selection are very poor if used to actually estimate the density function. This property appears to be part of the larger and well-documented paradox to the effect that “the harder the estimation problem, the better cross-validation performs. ” The ICV method uniformly outperforms LSCV in a simulation study, a real data example, and a simulated example in which bandwidths are chosen locally