The Hazards of Predicting Divorce Without Crossvalidation

Divorce prediction studies (e.g., Gottman, Coan, Carrere, & Swanson, 1998) suggest that couples' eventual divorce can be very accurately predicted from a number of different variables. Recent attention to these studies has failed to consider the need to crossvalidate prediction equations and to consider the prevalence of divorce in the population. We analyze archival data to demonstrate that accuracy and predictive value drops precipitously during crossvalidation. We conclude that results of studies without crossvalidation analyses should be interpreted with extreme caution, no matter how impressive the initial results appear to be.     

Discrete regularized discriminant analysis

A method of regularized discriminant analysis for discrete data, denoted DRDA, is proposed. This method is related to the regularized discriminant analysis conceived by Friedman (1989) in a Gaussian framework for continuous data. Here, we are concerned with discrete data and consider the classification problem using the multionomial distribution. DRDA has been conceived in the small-sample, high-dimensional setting. This method has a median position between multinomial discrimination, the first-order independence model and kernel discrimination. DRDA is characterized by two parameters, the values of which are calculated by minimizing a sample-based estimate of future misclassification risk by cross-validation. The first parameter is acomplexity parameter which provides class-conditional probabilities as a convex combination of those derived from the full multinomial model and the first-order independence model. The second parameter is asmoothing parameter associated with the discrete kernel of Aitchison and Aitken (1976). The optimal complexity parameter is calculated first, then, holding this parameter fixed, the optimal smoothing parameter is determined. A modified approach, in which the smoothing parameter is chosen first, is discussed. The efficiency of the method is examined with other classical methods through application to data.     

经济周期波动的函数型时序分解方法——基于CPI的实证分析

建立一个函数型时序分解模型,根据交叉验证方法将数据分为趋势项、周期项和随机项,因而提取出的趋势项具有较好的泛化能力;提出的基于调节粗惩系数的转折点选取法,通过优化粗惩系数较好地分割了CPI的扩张期和收缩期,可判断经济指数的转折点。另外利用傅里叶变换(FFT)提取数据主频,改进了周期型基函数,相比于传统的傅里叶基函数,新的周期基函数对周期项的拟合精度较高。通过对近十年和近两年的CPI数据进行分析,结果表明季节影响较为明显,而且最后的组合模型预测精度较高。     

A comparative study of smoothing procedures for ordered categorical data

Methods for estimating probabilities on sample spaces for ordered-categorical variables are surveyed. The methods all involve smoothing the relative frequencies in manners which recognise the ordering among categories. Approaches of this type include convex smoothing, weighting-function and kernel-based methods, near neighbour methods, Bayes-based methods and penalized minimum-distance methods. The relationships among the methods are brought out, application is made to a medical example and a simulation study is reported which compares the methods on univariate and bivariate examples. Links with smoothing procedures in other contexts are indicated.     

Smoothing spline growth curves with covariates

We adapt the interactive spline model of Wahba. to growth curves o with covariates. The smoothing spline formulation permits a nonpara-metric representation of the growth curves. In the limit when the discretization error is small relative to the estimation error, the resulting growth curve estimates often depend only weakly on the number and locations of the knots. The smoothness parameter is determined from the data by minimizing an empirical estimate of the expected error. We show that the risk estimate of Craven and Wahba is a weighted goodness of fit estimate, A modified loss estimate is given, where a2 is replaced by its unbiased estimate.