Choosing summary statistics by least angle regression for approximate Bayesian computation

Bayesian statistical inference relies on the posterior distribution. Depending on the model, the posterior can be more or less difficult to derive. In recent years, there has been a lot of interest in complex settings where the likelihood is analytically intractable. In such situations, approximate Bayesian computation (ABC) provides an attractive way of carrying out Bayesian inference. For obtaining reliable posterior estimates however, it is important to keep the approximation errors small in ABC. The choice of an appropriate set of summary statistics plays a crucial role in this effort. Here, we report the development of a new algorithm that is based on least angle regression for choosing summary statistics. In two population genetic examples, the performance of the new algorithm is better than a previously proposed approach that uses partial least squares.     

An exploratory data analysis in scale-space for interval-valued data

We propose an exploratory data analysis approach when data are observed as intervals in a nonparametric regression setting. The interval-valued data contain richer information than single-valued data in the sense that they provide both center and range information of the underlying structure. Conventionally, these two attributes have been studied separately as traditional tools can be readily used for single-valued data analysis. We propose a unified data analysis tool that attempts to capture the relationship between response and covariate by simultaneously accounting for variability present in the data. It utilizes a kernel smoothing approach, which is conducted in scale-space so that it considers a wide range of smoothing parameters rather than selecting an optimal value. It also visually summarizes the significance of trends in the data as a color map across multiple locations and scales. We demonstrate its effectiveness as an exploratory data analysis tool for interval-valued data using simulated and real examples.     

Some maximum-indifference estimators for the slope of a univariate linear model

As known, the least-squares estimator of the slope of a univariate linear model sets to zero the covariance between the regression residuals and the values of the explanatory variable. To prevent the estimation process from being influenced by outliers, which can be theoretically modelled by a heavy-tailed distribution for the error term, one can substitute covariance with some robust measures of association, for example Kendall's tau in the popular Theil–Sen estimator. In a scarcely known Italian paper, Cifarelli [(1978), ‘La Stima del Coefficiente di Regressione Mediante l'Indice di Cograduazione di Gini’, Rivista di matematica per le scienze economiche e sociali, 1, 7–38. A translation into English is available at http://arxiv.org/abs/1411.4809 and will appear in Decisions in Economics and Finance] shows that a gain of efficiency can be obtained by using Gini's cograduation index instead of Kendall's tau. This paper introduces a new estimator, derived from another association measure recently proposed. Such a measure is strongly related to Gini's cograduation index, as they are both built to vanish in the general framework of indifference. The newly proposed estimator is shown to be unbiased and asymptotically normally distributed. Moreover, all considered estimators are compared via their asymptotic relative efficiency and a small simulation study. Finally, some indications about the performance of the considered estimators in the presence of contaminated normal data are provided.     

基于主成分logistic回归模型的餐饮商务信息意识研究

数据挖掘技术日趋成熟,广泛应用于金融、地产、投资、评估等各个领域。数据挖掘技术亦可应用于餐饮业,为其经营决策做出分析。其他领域的数据挖掘的成功案例也可以引用到餐饮行业中。本文对餐饮人士在餐饮商务中是否具备信息意识、对信息意识的重视程度进行调查,利用数据挖掘中主成分分析和 logistic 回归处理和分析收集来的数据,从而说明数据挖掘在餐饮业管理中的重要意义,反映餐饮人士信息意识状况。利用数据挖掘技术对餐饮商务资讯进行管理势必提高企业效率和盈利水平,促进餐饮业健康稳定的发展。     

Variance estimation based on blocked 3×2 cross-validation in high-dimensional linear regression

In high-dimensional linear regression, the dimension of variables is always greater than the sample size. In this situation, the traditional variance estimation technique based on ordinary least squares constantly exhibits a high bias even under sparsity assumption. One of the major reasons is the high spurious correlation between unobserved realized noise and several predictors. To alleviate this problem, a refitted cross-validation (RCV) method has been proposed in the literature. However, for a complicated model, the RCV exhibits a lower probability that the selected model includes the true model in case of finite samples. This phenomenon may easily result in a large bias of variance estimation. Thus, a model selection method based on the ranks of the frequency of occurrences in six votes from a blocked 3×2 cross-validation is proposed in this study. The proposed method has a considerably larger probability of including the true model in practice than the RCV method. The variance estimation obtained using the model selected by the proposed method also shows a lower bias and a smaller variance. Furthermore, theoretical analysis proves the asymptotic normality property of the proposed variance estimation.     

A new regression model for bimodal data and applications in agriculture

We define the odd log-logistic exponential Gaussian regression with two systematic components, which extends the heteroscedastic Gaussian regression and it is suitable for bimodal data quite common in the agriculture area. We estimate the parameters by the method of maximum likelihood. Some simulations indicate that the maximum-likelihood estimators are accurate. The model assumptions are checked through case deletion and quantile residuals. The usefulness of the new regression model is illustrated by means of three real data sets in different areas of agriculture, where the data present bimodality.     

Modified maximum likelihood estimator under the Jones and Faddy's skew t-error distribution for censored regression model

It is well-known that classical Tobit estimator of the parameters of the censored regression (CR) model is inefficient in case of non-normal error terms. In this paper, we propose to use the modified maximum likelihood (MML) estimator under the Jones and Faddy''s skew t-error distribution, which covers a wide range of skew and symmetric distributions, for the CR model. The MML estimators, providing an alternative to the Tobit estimator, are explicitly expressed and they are asymptotically equivalent to the maximum likelihood estimator. A simulation study is conducted to compare the efficiencies of the MML estimators with the classical estimators such as the ordinary least squares, Tobit, censored least absolute deviations and symmetrically trimmed least squares estimators. The results of the simulation study show that the MML estimators work well among the others with respect to the root mean square error criterion for the CR model. A real life example is also provided to show the suitability of the MML methodology.     

An elastic-net penalized expectile regression with applications

To perform variable selection in expectile regression, we introduce the elastic-net penalty into expectile regression and propose an elastic-net penalized expectile regression (ER-EN) model. We then adopt the semismooth Newton coordinate descent (SNCD) algorithm to solve the proposed ER-EN model in high-dimensional settings. The advantages of ER-EN model are illustrated via extensive Monte Carlo simulations. The numerical results show that the ER-EN model outperforms the elastic-net penalized least squares regression (LSR-EN), the elastic-net penalized Huber regression (HR-EN), the elastic-net penalized quantile regression (QR-EN) and conventional expectile regression (ER) in terms of variable selection and predictive ability, especially for asymmetric distributions. We also apply the ER-EN model to two real-world applications: relative location of CT slices on the axial axis and metabolism of tacrolimus (Tac) drug. Empirical results also demonstrate the superiority of the ER-EN model.     

Outlier detection and robust variable selection via the penalized weighted LAD-LASSO method

This paper studies the outlier detection and robust variable selection problem in the linear regression model. The penalized weighted least absolute deviation (PWLAD) regression estimation method and the adaptive least absolute shrinkage and selection operator (LASSO) are combined to simultaneously achieve outlier detection, and robust variable selection. An iterative algorithm is proposed to solve the proposed optimization problem. Monte Carlo studies are evaluated the finite-sample performance of the proposed methods. The results indicate that the finite sample performance of the proposed methods performs better than that of the existing methods when there are leverage points or outliers in the response variable or explanatory variables. Finally, we apply the proposed methodology to analyze two real datasets.