Accounting for Uncertainty in Heteroscedasticity in Nonlinear Regression

Toxicologists and pharmacologists often describe toxicity of a chemical using parameters of a nonlinear regression model. Thus estimation of parameters of a nonlinear regression model is an important problem. The estimates of the parameters and their uncertainty estimates depend upon the underlying error variance structure in the model. Typically, a priori the researcher would not know if the error variances are homoscedastic (i.e., constant across dose) or if they are heteroscedastic (i.e., the variance is a function of dose). Motivated by this concern, in this paper we introduce an estimation procedure based on preliminary test which selects an appropriate estimation procedure accounting for the underlying error variance structure. Since outliers and influential observations are common in toxicological data, the proposed methodology uses M-estimators. The asymptotic properties of the preliminary test estimator are investigated; in particular its asymptotic covariance matrix is derived. The performance of the proposed estimator is compared with several standard estimators using simulation studies. The proposed methodology is also illustrated using a data set obtained from the National Toxicology Program.     

Support for a Fluid-Continuum Model of Sexual Orientation: A Large-Scale Internet Study

In a study with 17,785 subjects obtained over the Internet from the United States and 47 other countries, Kinsey's hypothesis that sexual orientation lies on a continuum was supported. Self-identifications of subjects as gay, straight, bisexual, and other corresponded to broad, skewed distributions, suggesting that such terms are misleading for many people. Sexual orientation range—roughly, how much flexibility someone has in expressing sexual orientation—was also measured. The results support a fluid-continuum model of sexual orientation, according to which genetic and environmental factors determine both the size of the sexual orientation range and the point at which an individual's sexual orientation is centered on the continuum.     

On an asymptotic relative efficiency concept based on expected volumes of confidence regions

ABSTRACT

The paper deals with an asymptotic relative efficiency concept for confidence regions of multidimensional parameters that is based on the expected volumes of the confidence regions. Under standard conditions the asymptotic relative efficiencies of confidence regions are seen to be certain powers of the ratio of the limits of the expected volumes. These limits are explicitly derived for confidence regions associated with certain plugin estimators, likelihood ratio tests and Wald tests. Under regularity conditions, the asymptotic relative efficiency of each of these procedures with respect to each one of its competitors is equal to 1. The results are applied to multivariate normal distributions and multinomial distributions in a fairly general setting.     

超声波提取胡椒中有效成分条件优化

试验研究温度、时间、超声波频率对超声波-食用乙醇提取胡椒有效成分的影响,以胡椒粗提取物的提取率为指标,正交实验确定较适宜提取条件为,温度55℃、时间55 min,超声波频率60 KHz,胡椒粗提取物的提取率为4.29%.     

Testing dominance of biometric functions

The hazard rate (HR) and mean residual lifetime are two of the most practical and best-known functions in biometry, reliability, statistics and life testing. Recently, the reversed HR function is found to have interesting properties useful in additional areas such as censored data and forensic science. For these three biometric functions, we propose testing methods that they take on a known functional form against that they dominate or are dominated by this known form. This goodness-of-fit-type testing is wider in applications and more interesting than the long-standing testing procedures for exponentiality against the monotonicity of these functions or even the change point problems. This is so since we can test against any choice of the survival distribution and not just exponentiality. For this general testing, we present easy to implement tests and generalize them into classes of statistics that could lead to more powerful and efficient testing.     

Rank invariant tests with left truncated and interval censored data

Peto and Peto (1972) have studied rank invariant tests to compare two survival curves for right censored data. We apply their tests, including the logrank test and the generalized Wilcoxon test, to left truncated and interval censored data. The significance levels of the tests are approximated by Monte Carlo permutation tests. Simulation studies are conducted to show their size and power under different distributional differences. In particular, the logrank test works well under the Cox proportional hazards alternatives, as for the usual right censored data. The methods are illustrated by the analysis of the Massachusetts Health Care Panel Study dataset.     

Exact monte carlo tests using several statistics

Concepts of ranking and boundary of multivariate statistics are discussed and applied to the simultaneous use of several test statistics calculated for data and simulated replicates. An example of residual analysis in regression is given using layer ranks and supplementary simulation with a stopping rule.     

An improved two-stage procedure to compare hazard curves

Qiu and Sheng has proposed a powerful and robust two-stage procedure to compare two hazard rate functions. In this paper we improve their method by using the Fisher test to combine the asymptotically independent p-values obtained from the two stages of their procedure. In addition, we extend the procedure to situations with multiple hazard rate functions. Our comprehensive simulation study shows that the proposed method has a good performance in terms of controlling the type I error rate and of detecting power. Three real data applications are considered for illustrating the use of the new method.     

Monte Carlo comparison of five exponentiality tests using different entropy estimates

The paper studies five entropy tests of exponentiality using five statistics based on different entropy estimates. Critical values for various sample sizes determined by means of Monte Carlo simulations are presented for each of the test statistics. By simulation, we compare the power of these five tests for various alternatives and sample sizes.     

An adaptive two-sample location-scale test of lepage type for symmetric distributions

For the two-sample location and scale problem we propose an adaptive test which is based on so called Lepage type tests. The well known test of Lepage (1971) is a combination of the Wilcoxon test for location alternatives and the Ansari-Bradley test for scale alternatives and it behaves well for symmetric and medium-tailed distributions. For the cae of short-, medium- and long-tailed distributions we replace the Wilcoxon test and the .Ansari-Bradley test by suitable other two-sample tests for location and scale, respectively, in oder to get higher power than the classical Lepage test for such distribotions. These tests here are called Lepage type tests. in practice, however, we generally have no clear idea about the distribution having generated our data. Thus, an adaptive test should be applied which takes the the given data set inio consideration. The proposed adaptive test is based on the concept of Hogg (1974), i.e., first, to classify the unknown symmetric distribution function with respect to a measure for tailweight and second, to apply an appropriate Lepage type test for this classified type of distribution. We compare the adaptive test with the three Lepage type tests in the adaptive scheme and with the classical Lepage test as well as with other parametric and nonparametric tests. The power comparison is carried out via Monte Carlo simulation. It is shown that the adaptive test is the best one for the broad class of distributions considered.