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.     

A comparison of maximum likelihood and least squares for the estimation of a cumulative distribution

Monte Carlo methods are used to compare the methods of maximum likelihood and least squares to estimate a cumulative distribution function. When the probabilistic model used is correct or nearly correct, the two methods produce similar results with the MLE usually slightly superior When an incorrect model is used, or when the data is contaminated, the least squares technique often gives substantially superior results.     

Bias correction for parameter estimates of spatial point process models

When a spatial point process model is fitted to spatial point pattern data using standard software, the parameter estimates are typically biased. Contrary to folklore, the bias does not reflect weaknesses of the underlying mathematical methods, but is mainly due to the effects of discretization of the spatial domain. We investigate two approaches to correcting the bias: a Newton–Raphson-type correction and Richardson extrapolation. In simulation experiments, Richardson extrapolation performs best.     

Percentage points of the statistics for testing hypotheses on mean vectors of multivariate normal distributions with missing observations

A problem of testing of hypotheses on the mean vector of a multivariate normal distribution with unknown and positive definite covariance matrix is considered when a sample with a special, though not unusual, pattern of missing observations from that population is available. The approximate percentage points of the test statistic are obtained and their accuracy has been checked by comparing them with some exact percentage points which are calculated for complete samples and some special incomplete samples. The approximate percentage points are in good agreement with exact percentage points. The above work is extended to the problem of testing the hypothesis of equality of two mean vectors of two multivariate normal distributions with the same, unknown covariance matrix     

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.     

Modified likelihood ratio tests in heteroskedastic multivariate regression models with measurement error

In this paper, we develop modified versions of the likelihood ratio test for multivariate heteroskedastic errors-in-variables regression models. The error terms are allowed to follow a multivariate distribution in the elliptical class of distributions, which has the normal distribution as a special case. We derive the Skovgaard-adjusted likelihood ratio statistics, which follow a chi-squared distribution with a high degree of accuracy. We conduct a simulation study and show that the proposed tests display superior finite sample behaviour as compared to the standard likelihood ratio test. We illustrate the usefulness of our results in applied settings using a data set from the WHO MONICA Project on cardiovascular disease.     

A pool-adjacent-violators-algorithm approach to detect infinite parameter estimates in one-regressor dose–response models with asymptotes

Binary response models are often applied in dose–response settings where the number of dose levels is limited. Commonly, one can find cases where the maximum likelihood estimation process for these models produces infinite values for at least one of the parameters, often corresponding to the ‘separated data’ issue. Algorithms for detecting such data have been proposed, but are usually incorporated directly into in the parameter estimation. Additionally, they do not consider the use of asymptotes in the model formulation. In order to study this phenomenon in greater detail, we define the class of specifiably degenerate functions where this can occur (including the popular logistic and Weibull models) that allows for asymptotes in the dose–response specification. We demonstrate for this class that the well-known pool-adjacent-violators algorithm can efficiently pre-screen for non-estimable data. A simulation study demonstrates the frequency with which this problem can occur for various response models and conditions.     

男女性别比失衡问题的思考

目前,我国男女性别比例严重失衡,由此带来性犯罪现象增加、婚姻挤压、拜金主义思想等各种社会问题,究其原因,除了传统的重男轻女观念的影响和妇女地位的不平等外,还有科技手段的滥用。应该树立先进的社会性别意识,禁止非法的胎儿性别鉴定,提高女性的社会地位,这样,才能切实解决出生人口性别比例失调问题。