Parametric bootstrap approximation to the distribution of EBLUP and related prediction intervals in linear mixed models

Empirical best linear unbiased prediction (EBLUP) method uses a linear mixed model in combining information from different sources of information. This method is particularly useful in small area problems. The variability of an EBLUP is traditionally measured by the mean squared prediction error (MSPE), and interval estimates are generally constructed using estimates of the MSPE. Such methods have shortcomings like under-coverage or over-coverage, excessive length and lack of interpretability. We propose a parametric bootstrap approach to estimate the entire distribution of a suitably centered and scaled EBLUP. The bootstrap histogram is highly accurate, and differs from the true EBLUP distribution by only $O(d^3n^{-3/2})$, where $d$ is the number of parameters and $n$ the number of observations. This result is used to obtain highly accurate prediction intervals. Simulation results demonstrate the superiority of this method over existing techniques of constructing prediction intervals in linear mixed models.Comment: Published in at http://dx.doi.org/10.1214/07-AOS512 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

PREDICTION OF A FUNCTION OF MISCLASSIFIED BINARY DATA

We consider the problem of predicting a function of misclassified binary variables. We make an interesting observation that the naive predictor, which ignores the misclassification errors, is unbiased even if the total misclassification error is high as long as the probabilities of false positives and false negatives are identical. Other than this case, the bias of the naive predictor depends on the misclassification distribution and the magnitude of the bias can be high in certain cases. We correct the bias of the naive predictor using a double sampling idea where both inaccurate and accurate measurements are taken on the binary variable for all the units of a sample drawn from the original data using a probability sampling scheme. Using this additional information and design-based sample survey theory, we derive a biascorrected predictor. We examine the cases where the new bias-corrected predictors can also improve over the naive predictor in terms of mean square error (MSE)

Hindrance in heavy-ion fusion for lighter systems of astrophysical interest

The hindrance in fusion of heavy-ion reactions crops up in the region of extreme sub-barrier energies. This phenomenon can be effectively analyzed using a simple diffused barrier formula derived assuming a Gaussian distribution of fusion barrier heights. Folding the Gaussian barrier distribution with the classical expression for the fusion cross section for a fixed barrier, the fusion cross section is obtained. The energy dependence of the fusion cross section provides good description to the existing data on sub-barrier heavy-ion fusion for lighter systems of astrophysical interest. Using this simple formula, an analysis has been presented from $^{16}$O + $^{18}$O to $^{12}$C + $^{198}$Pt, all of which were measured down to $<$ 10 $\mu$b. The agreement of the present analysis with the measured values is better than those calculated even from the sophisticated coupled channels calculations. The relatively smooth variation of the three parameters of this formula implies that it may be exploited to estimate the excitation function or to extrapolate cross sections for pairs of interacting nuclei which are yet to be measured. Possible extensions of the present methodology and its limitations have also been discussed.Comment: 6 pages including 7 figures and 1 table. arXiv admin note: substantial text overlap with arXiv:1402.533