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通过自适应核范数惩罚进行降秩回归AI 解读

We propose an adaptive nuclear norm penalization approach for low-rank matrix approximation, and use it to develop a new reduced rank estimation method for high-dimensional multivariate regression. The adaptive nuclear norm is defined as the weighted sum of the singular values of the matrix, and it is generally non-convex under the natural restriction that the weight decreases with the singular value. However, we show that the proposed non-convex penalized regression method…

广义阈值随机回归模型的最大似然估计AI 解读

There is hardly any literature on modelling nonlinear dynamic relations involving nonnormal time series data. This is a serious lacuna because nonnormal data are far more abundant than normal ones, for example, time series of counts and positive time series. While there are various forms of nonlinearities, the class of piecewise-linear models is particularly appealing for its relative ease of tractability and interpretation. We propose to study the generalized threshold…

分析非正态非线性时间序列的广义阈值混合模型：哈萨克斯坦鼠疫应用AI 解读

We introduce the generalized threshold mixed model for piecewise-linear stochastic regression with possibly nonnormal time-series data. It is assumed that the conditional probability distribution of the response variable belongs to the exponential family, and the conditional mean response is linked to some piecewise-linear stochastic regression function. We study the particular case where the response variable equals zero in the lower regime. Some large-sample properties of…