Overview: Recall that a point estimator for a parameter of interest is a statistic which is a function of the random variables from which our sampling method chooses values. The properties of such an estimator, such as having a small bias or a small mean square error, are usually dependent only upon certain features of the sampling distribution of the statistic, such as its mean or variance. Ho...

We derive the Edgeworth expansion for the studentized version of the kernel quantile estimator. Inverting the expansion allows us to get very accurate confidence intervals for the pth quantile under general conditions. The results are applicable in practice to improve inference for quantiles when sample sizes are moderate.

In non-parametric function estimation, providing a confidence interval with the right coverage is a challenging problem. This is especially the case when the underlying function has a wide range of unknown degrees of smoothness. Here we propose two methods of constructing an average coverage confidence interval built from block shrinkage estimation methods. One is based on the James-Stein shrin...

We propose a new method to compute prediction intervals. Especially for small data sets the width of a prediction interval does not only depend on the variance of the target distribution, but also on the accuracy of our estimator of the mean of the target, i.e., on the width of the confidence interval. The confidence interval follows from the variation in an ensemble of neural networks, each of...

notion the theoretical distribution on the random variable ) is not available. All we have ICOTS8 (2010) Invited Paper Engel International Association of Statistical Education (IASE) www.stat.auckland.ac.nz/~iase/ to rely on are the data at hand, i.e. the sample or recapture of size n. These data–if drawn by some random mechanism–may well be taken as a good representation of the total fish popu...

Fukuhara and Hori’s article [1] reported the possibility of calculating the incidence of spontaneous intracerebral hemorrhage (sICH) using publicly accessible data in Japan. If the method were valid and satisfied statistical assumptions, overcoming the limitation of the source of the data, known as Diagnosis Procedure Combination (DPC) data, this suggestion could be an innovative method. Becaus...

Extended Abstract. Let Xi1 ,..., Xini   ,i=1,2,3,....,k  be independent random samples from distribution $F^{alpha_i}$،  i=1,...,k, where F is an absolutely continuous distribution function and $alpha_i>0$ Also, suppose that these samples are independent. Let Mi,ni and  M'i,ni  respectively, denote the maximum and minimum of the ith sa...

If you have just two discrete hypotheses, then a hypothesis test is simply an application of Bayes’ Theorem. You check to see whether your data can reasonably be explained by that boring old null hypothesis (conventionally called H0), or not. To test H0, you need to compare it to one other model. One never tests a hypothesis in isolation; it is tested against an alternative (typically called H1...

probabilities, it can be determined that combining the probability values of 0.11 and 0.07 results in a probability value of 0.045. Therefore, these two nonsignificant findings taken together result in a significant finding. Although there is never a statistical basis for concluding that an effect is exactly zero, a statistical analysis can demonstrate that an effect is most likely small. This ...