We show by example that empirical likelihood and other commonly used tests for moment restrictions are unable to control the (exponential) rate at which the probability of a Type I error tends to zero. It follows that the optimality of empirical likelihood asserted in Kitamura (2001) does not hold without additional assumptions. Under stronger assumptions than those in Kitamura (2001), we estab...

In this paper we make two contributions. First, we show by example that empirical likelihood and other commonly used tests for parametric moment restrictions, including the GMM-based J-test of Hansen (1982), are unable to control the rate at which the probability of a Type I error tends to zero. From this it follows that, for the optimality claim for empirical likelihood in Kitamura (2001) to h...

We show by example that empirical likelihood and other commonly used tests for moment restrictions are unable to control the (exponential) rate at which the probability of a Type I error tends to zero unless the possible distributions for the observed data are restricted appropriately. From this, it follows that for the optimality claim for empirical likelihood in Kitamura (2001) to hold, addit...

Experimental design requires estimation of the sample size required to produce a meaningful conclusion. Often, experimental results are performed with sample sizes which are inappropriate to adequately support the conclusions made. In this paper, two factors which are involved in sample size estimation are detailed--namely type I (alpha) and type II (beta) error. Type I error can be considered ...

variations in lighting are a problem for visual systems. in the current research, a new thresholding method using a 3d euclidian elliptical surface was defined and applied for plant detection purposes. the results showed that this method had lower type i error, type ii error, total error and mean square error compared with those of conventional segmentation methods. the method was evaluated for...

Introductory statistics students learn that hypothesis tests in­ volve two types of error. If we reject a true null hypothesis, a Type I error occurs. If we fail to reject a false null hypothesis, a Type II error occurs. Students become adept at using tables to find critical values that control the probability of a Type I error. However, the calculations needed to control the probabil­ ity of a...