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This paper is concerned with the problem of feature screening for multi-class linear discriminant analysis under ultrahigh dimensional setting. We allow the number of classes to be relatively large. As a result, the total number of relevant features is larger than usual. This makes the related classification problem much more challenging than the conventional one, where the number of classes is small (very often two). To solve the problem, we propose a novel pairwise sure…

回归设定下大型协方差矩阵的对角性检验AI 解读

In multivariate analysis, the covariance matrix associated with a set of variables of interest (namely response variables) commonly contains valuable information about the dataset. When the dimension of response variables is considerably larger than the sample size, it is a nontrivial task to assess whether there are linear relationships between the variables. It is even more challenging to determine whether a set of explanatory variables can explain those relationships. To…

时变朴素贝叶斯模型及其在中文文本分类中的应用AI 解读

Document classification is an area of great importance for which many classification methods have been developed. However, most of these methods cannot generate time-dependent classification rules. Thus, they are not the best choices for problems with time-varying structures. To address this problem, we propose a varying naïve Bayes model, which is a natural extension of the naïve Bayes model that allows for time-dependent classification rule. The method of kernel smoothing…

高斯过程混合模型的核平滑估计AI 解读

When the functional data are not homogeneous, e.g., there exist multiple classes of functional curves in the dataset, traditional estimation methods may fail. In this paper, we propose a new estimation procedure for the Mixture of Gaussian Processes, to incorporate both functional and inhomogeneous properties of the data. Our method can be viewed as a natural extension of high-dimensional normal mixtures. However, the key difference is that smoothed structures are imposed…

超高维分类数据的特征筛选及应用AI 解读

Ultrahigh dimensional data with both categorical responses and categorical covariates are frequently encountered in the analysis of big data, for which feature screening has become an indispensable statistical tool. We propose a Pearson chi-square based feature screening procedure for categorical response with ultrahigh dimensional categorical covariates. The proposed procedure can be directly applied for detection of important interaction effects. We further show that the…

高维影响度量AI 解读

Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high-dimensional data, it is particularly so, as the increased dimensionality and complexity may amplify both the chance of an observation being influential, and its potential impact on the analysis. In this article, we propose a novel high-dimensional influence measure for regressions with the number of predictors far exceeding the…

高斯随机场驱动空间点过程的充分降维AI 解读

Summary We develop a sufficient dimension reduction paradigm for inhomogeneous spatial point processes driven by Gaussian random fields. Specifically, we introduce the notion of the kth-order central intensity subspace. We show that a central subspace can be defined as the combination of all central intensity subspaces. For many commonly used spatial point process models, we find that the central subspace is equivalent to the first-order central intensity subspace. To…

基于轮廓投影的降维AI 解读

In regression analysis, we employ contour projection (CP) to develop a new dimension reduction theory. Accordingly, we introduce the notions of the central contour subspace and generalized contour subspace. We show that both of their structural dimensions are no larger than that of the central subspace Cook [Regression Graphics (1998b) Wiley]. Furthermore, we employ CP-sliced inverse regression, CP-sliced average variance estimation and CP-directional regression to estimate…

超高维变量筛选中的前向回归AI 解读

Motivated by the seminal theory of Sure Independence Screening (Fan and Lv 2008, SIS), we investigate here another popular and classical variable screening method, namely, forward regression (FR). Our theoretical analysis reveals that FR can identify all relevant predictors consistently, even if the predictor dimension is substantially larger than the sample size. In particular, if the dimension of the true model is finite, FR can discover all relevant predictors within a…

尾指数回归AI 解读

In extreme value statistics, the tail index is an important measure to gauge the heavy-tailed behavior of a distribution. Under Pareto-type distributions, we employ the logarithmic function to link the tail index to the linear predictor induced by covariates, which constitutes the tail index regression model. We then propose an approximate log-likelihood function to obtain regression parameter estimators, and subsequently show the asymptotic normality of those estimators.…

参数数量发散时的收缩调节参数选择AI 解读

Summary Contemporary statistical research frequently deals with problems involving a diverging number of parameters. For those problems, various shrinkage methods (e.g. the lasso and smoothly clipped absolute deviation) are found to be particularly useful for variable selection. Nevertheless, the desirable performances of those shrinkage methods heavily hinge on an appropriate selection of the tuning parameters. With a fixed predictor dimension, Wang and co-worker have…

变系数模型的收缩估计AI 解读

The varying coefficient model is a useful extension of the linear regression model. Nevertheless, how to conduct variable selection for the varying coefficient model in a computationally efficient manner is poorly understood. To solve the problem, we propose here a novel method, which combines the ideas of the local polynomial smoothing and the Least Absolute Shrinkage and Selection Operator (LASSO). The new method can do nonparametric estimation and variable selection…

用于降维的切片回归AI 解读

A new dimension-reduction method involving slicing the region of the response and applying local kernel regression to each slice is proposed. Compared with the traditional inverse regression methods [e.g., sliced inverse regression (SIR)], the new method is free of the linearity condition and has much better estimation accuracy. Compared with the direct estimation methods (e.g., MAVE), the new method is much more robust against extreme values and can capture the entire…

GARCH 模型估计：何时选择哪种方法？AI 解读

The class of generalized autoregressive conditional heteroscedastic (GARCH) models has proved particularly valuable in modelling time series with time varying volatility. These include financial data, which can be particularly heavy tailed. It is well understood now that the tail heaviness of the innovation distribution plays an important role in determining the relative performance of the two competing estimation methods, namely the maximum quasi-likelihood estimator based…

通过最小二乘近似统一 LASSO 估计AI 解读

We propose a method of least squares approximation (LSA) for unified yet simple LASSO estimation. Our general theoretical framework includes ordinary least squares, generalized linear models, quantile regression, and many others as special cases. Specifically, LSA can transfer many different types of LASSO objective functions into their asymptotically equivalent least squares problems. Thereafter, the standard asymptotic theory can be established and the LARS algorithm can…

通过 LAD-lasso 实现稳健回归收缩与一致变量选择AI 解读

The least absolute deviation (LAD) regression is a useful method for robust regression, and the least absolute shrinkage and selection operator (lasso) is a popular choice for shrinkage estimation and variable selection. In this article we combine these two classical ideas together to produce LAD-lasso. Compared with the LAD regression, LAD-lasso can do parameter estimation and variable selection simultaneously. Compared with the traditional lasso, LAD-lasso is resistant to…

利用 lasso 收缩与选择回归系数及自回归阶数AI 解读

Summary The least absolute shrinkage and selection operator (‘lasso’) has been widely used in regression shrinkage and selection. We extend its application to the regression model with autoregressive errors. Two types of lasso estimators are carefully studied. The first is similar to the traditional lasso estimator with only two tuning parameters (one for regression coefficients and the other for autoregression coefficients). These tuning parameters can be easily calculated…

回归插补下调查数据的样本相关系数AI 解读

Regression imputation is commonly used to compensate for item nonresponse when auxiliary data are available. It is common practice to compute survey estimators by treating imputed values as observed data and using the standard unbiased (or nearly unbiased) estimation formulas designed for the case of no nonresponse. Although the commonly used regression imputation method preserves unbiasedness for population marginal totals (i.e., survey estimators computed from imputed data…