Nonsmooth parameter

The jackknife has a number of advantages. First, the jackknife is a nonparametric approach to parameter inference that does not rely on asymptotic methods to be accurate. A major disadvantage is that a batch or script file will need to be needed to delete the ith observation, recompute the test statistic, compute the pseudovalues, and then calculate the jackknife statistics of course, this disadvantage applies to all other computer intensive methods as well, so it might not be a disadvantage after all. Also, if 9 is a nonsmooth parameter, where the sampling distribution may be discontinuous, e.g., the median, the jackknife estimate of the variance may be quite poor (Pigeot, 2001). For example, data were simulated from a normal distribution with mean 100 and... 

We prove an existence of solutions for the Prandtl-Reuss model of elastoplastic plates with cracks. The proof is based on a special combination of a parabolic regularization and the penalty method. With the appropriate a priori estimates, uniform with respect to the regularization and penalty parameters, a passage to the limit along the parameters is fulfilled. Both the smooth and nonsmooth domains are considered in the present section. The results obtained provide a fulfilment of all original boundary conditions. 

Nonsmoothness of the parameters usually leads to nonadiabatic corrections in transition amplitude of order p if the nonsmoothness is characterized by a discontinuous pth derivative. Nonsmooth pulse ends can be investigated [58] in the simplified model... 

For large data sets, the delete-1 jackknife may be impractical since it may require fitting hundreds of data sets. A modification of the delete-1 jackknife is the delete 10% jackknife, where 10 different jackknife data sets are created with each data set having a unique 10% of the data removed. Only 10 data sets are modeled using this jackknife modification. All other calculations are as before but n now becomes the number of data sets, not the number of subjects. The use of the jackknife has largely been supplanted by the bootstrap since the jackknife has been criticized as producing standard errors that have poor statistical behavior when the estimator is nonsmooth, e.g., the median, which may not be a valid criticism for pharmacokinetic parameters. But whether one is better than the other at estimating standard errors of continuous functions is debatable and a matter of preference. 

Note the limit (as well as the partial derivative) in the above equation may not exist as the normalized demand function Dj, z) may be nonsmooth with respect to both the design parameter vectory and the tmcertain variable vector z. In order to avoid this issue and still obtain a sensitivity measure of the first-excursion probability, approximate representations for the normalized demand function and the excursion probabihty are introduced. These approximations - which were proposed in Jensen et al. (2009) and Valdebenito and Schueller (2011) - are discussed in the following. The first approximation comprises an approximate representation of the normalized demand function, i.e.,... 

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