On the small sample properties of norm-restricted maximum likelihood estimators for logistic regression models

This paper develops alternatives to maximum likelihood estimators (MLE) for logistic regression models and compares the mean squared error (MSE) of the estimators. The MLE for the vector of underlying success probabilities has low MSE only when the true probabilities are extreme (i.e., near 0 or 1). Extreme probabilities correspond to logistic regression parameter vectors which are large in norm. A competing “restricted” MLE and an empirical version of it are suggested as estimators with better performance than the MLE for central probabilities. An approximate EM-algorithm for estimating the restriction is described. As in the case of normal theory ridge estimators, the proposed estimators are shown to be formally derivable by Bayes and empirical Bayes arguments. The small sample operating characteristics of the proposed estimators are compared to the MLE via a simulation study; both the estimation of individual probabilities and of logistic parameters are considered.     

To meet or not to meet? Measuring motivations and risks as predictors of outcomes in the use of mobile dating applications in China

Mobile dating applications (MDAs), such as Momo and Tinder, allow mobile phone owners to meet potential mates through social media, thus contributing to the radicalization of Chinese attitudes toward sex. Although these applications may gratify the needs of users for love and sex, the potential of risk is often overlooked. However, it should be considered in their decision regarding whether to meet a stranger or not. This study investigated the motivations and risks involved in the use of MDAs to meet strangers and the outcomes of using this technology. The results showed that sexuality was the only predictor of the reasons that people use MDAs to meet people offline for dates and casual sex. Among the perceived risks of mobile dating, only the fear of self-exposure to friends, professional networks, and the community significantly explained why users would not meet people offline for casual sex.     

Mean Squared Error Matrix Comparisons of Some Restricted Almost Unbiased Estimators

In this article, we introduce two almost unbiased estimators for the vector of unknown parameters in a linear regression model when additional linear restrictions on the parameter vector are assumed to hold. Superiority of the two estimators under the mean squared error matrix (MSEM) is discussed. Furthermore, a numerical example and simulation study are given to illustrate some of the theoretical results.     

Ridge estimation in logistic regression

The variance of the Maximum Likelihood Estimator (MLE) of the slope parameter in a logistic regression model becomes large as the degree of collinearity among the explanatory variables increases. In a Monte Carlo study, we observed that a ridge type estimator is at least as good as, and often much better than, the MLE in terms of Total and Prediction Mean Squared Error criteria. Using a set of medical data it is illustrated that the ridge trace of the estimator considered here is a useful diagnostic tool in logistic regression analysis.     

Ridge regression versus ols by pitman's closeness under quadratic and fisher's loss

The existence of values of the ridge parameter such that ridge regression is preferable to OLS by the Pitman nearness criterion under both the quadratic and the Fisher's loss is shown. Preference regions of the two estimators under the above loss functions are found. An upper bound for the value of the Pitman's measure of closeness, independent of a deterministic or stochastic choice of the ridge parameter, is given.     

On the restricted almost unbiased estimators in linear regression

In this paper, the restricted almost unbiased ridge regression estimator and restricted almost unbiased Liu estimator are introduced for the vector of parameters in a multiple linear regression model with linear restrictions. The bias, variance matrices and mean square error (MSE) of the proposed estimators are derived and compared. It is shown that the proposed estimators will have smaller quadratic bias but larger variance than the corresponding competitors in literatures. However, they will respectively outperform the latter according to the MSE criterion under certain conditions. Finally, a simulation study and a numerical example are given to illustrate some of the theoretical results.     

Cross validation of ridge regression estimator in autocorrelated linear regression models

ABSTRACT

In this paper, we investigated the cross validation measures, namely OCV, GCV and Cp under the linear regression models when the error structure is autocorrelated and regressor data are correlated. The best performed ridge regression estimator is obtained by getting the optimal ridge parameter so as to minimize these measures. A Monte Carlo simulation study is given to see how the optimal ridge parameter is affected by autocorrelation and the strength of multicollinearity.     

A review of some adaptive statistical techniques

We present several methods for full, partial, and practical adaptation. Selector statistics that are measures of skewness, peakedness, and tailweight are used, primarily in estimating loca-tion in some single-sample situations. We note several practical adaptive techniques in current use, including illustrations in-volving stepwise regression, analysis of variance, ridge regres-sion, and splines. We suggest some areas in which future develop-ment of adaptive methods is needed:density estimation; M, R, and L estimation in regression; and dependent data. There is also a need to develop better selector statistics.     

On the Stochastic Restricted Almost Unbiased Estimators in Linear Regression Model

In this article, the stochastic restricted almost unbiased ridge regression estimator and stochastic restricted almost unbiased Liu estimator are proposed to overcome the well-known multicollinearity problem in linear regression model. The quadratic bias and mean square error matrix of the proposed estimators are derived and compared. Furthermore, a numerical example and a Monte Carlo simulation are given to illustrate some of the theoretical results.