Confidence Intervals for a Binomial Parameter after Observing No Successes

The easily computed, one-sided confidence interval for the binomial parameter provides the basis for an interesting classroom example of scientific thinking and its relationship to confidence intervals. The upper limit can be represented as the sample proportion from a number of “successes” in a future experiment of the same sample size. The upper limit reported by most people corresponds closely to that producing a 95 percent classical confidence interval and has a Bayesian interpretation.     

Use of the Correlation Coefficient with Normal Probability Plots

The use of the correlation coefficient is suggested as a technique for summarizing and objectively evaluating the information contained in probability plots. Goodness-of-fit tests are constructed using this technique for several commonly used plotting positions for the normal distribution. Empirical sampling methods are used to construct the null distribution for these tests, which are then compared on the basis of power against certain nonnormal alternatives. Commonly used regression tests of fit are also included in the comparisons. The results indicate that use of the plotting position p_i = (i - .375)/(n + .25) yields a competitive regression test of fit for normality.     

An Adaptive Test for the Two-Sample Location Problem Based on U-Statistics

For the two-sample location problem with continuous data we consider a general class of tests, all members of it are based on U-statistics. The asymptotic efficacies are investigated in detail. We construct an adaptive test where all statistics involved are suitably chosen U-statistics. It is shown that the proposed adaptive test has good asymptotic and finite sample power properties.     

Parameter estimation by minimizing a probability generating function-based power divergence

Abstract

Generating function-based statistical inference is an attractive approach if the probability (density) function is complicated when compared with the generating function. Here, we propose a parameter estimation method that minimizes a probability generating function (pgf)-based power divergence with a tuning parameter to mitigate the impact of data contamination. The proposed estimator is linked to the M-estimators and hence possesses the properties of consistency and asymptotic normality. In terms of parameter biases and mean squared errors from simulations, the proposed estimation method performs better for smaller value of the tuning parameter as data contamination percentage increases.     

A comparison of some conditional and unconditional exact tests for 2x2 contingency tables

In 1935, R.A. Fisher published his well-known “exact” test for 2x2 contingency tables. This test is based on the conditional distribution of a cell entry when the rows and columns marginal totals are held fixed. Tocher (1950) and Lehmann (1959) showed that Fisher s test, when supplemented by randomization, is uniformly most powerful among all the unbiased tests UMPU). However, since all the practical tests for 2x2 tables are nonrandomized - and therefore biased the UMPU test is not necessarily more powerful than other tests of the same or lower size. Inthis work, the two-sided Fisher exact test and the UMPU test are compared with six nonrandomized unconditional exact tests with respect to their power. In both the two-binomial and double dichotomy models, the UMPU test is often less powerful than some of the unconditional tests of the same (or even lower) size. Thus, the assertion that the Tocher-Lehmann modification of Fisher's conditional test is the optimal test for 2x2 tables is unjustified.     

Locally best invariant test for outliers in a gamma type distribution

It is shown that the locally best invariant test for the existence of outliers for scale parameters of the gamma distribution is given by Bartholomew's test for exponentiality which is the ratio of the sum of squares of the data to the square of the sample mean. The optimality robustness, including null and nonnull robustness of the test is shown. A small simulation study to compare the power among the other eight competitive tests for testing exponentiality is performed. It is seen that the locally best invariant test is not always best but is reasonably good. It is slightly better than Cochran's test and suffers less from the limiting masking effect.     

Optimal testing in a three way anova model

We consider likelihood ratio, score and Wald tests for a three-way random effects ANOVA model. Competitor tests are compared using criteria such as small sample power, asymptotic relative efficiency, and convenient null distribution. The final choice is between a new test and two tests long used in practice.     

On the one-sample location hypothesis for mixed bivariate data

We study a hypothesis testing problem involving the location model suggested by Olkin and Tate (1961). Specifically, we derive a likelihood ratio lest of the associated location hypothesis as an alternative to the conventional method of carrying out separate tests for each of the parameters. A small sample Monte Carlo comparison indicates the general superiority of the former in terms of statistical power. We also comment briefly on the properties of the test.     

Testing of Suspected Observations in an Exponential Sample With Unknown Origin

The problem of multiple upper outliers in two-parameter exponential sample is considered. A test statistic is proposed to identify the outliers at the upper end of the sample. The null distribution of the test statistic is obtained and the critical values are found. The performance of the test is also compared with the earlier work.     

An Application of Matrix Power Series to Linear Models

In the system of two seemingly unrelated regressions, employing a matrix power series, we show that the two-stage estimator is better than the ordinary least square estimator (OLSE) in terms of the mean square error matrix (MSEM) criterion. The result enriches the existing literature and can be applied to many fields of applications related to economics and statistics.