A monotonicity property of weighted log-rank tests

Log-supermodularity of weight functions and the loading monotonicity of weighted insurance premiums

The paper is motivated by a problem concerning the monotonicity of insurance premiums with respect to their loading parameter: the larger the parameter, the larger the insurance premium is expected to be. This property, usually called loading monotonicity, is satisfied by premiums that appear in the literature. The increased interest in constructing new insurance premiums has raised a question as to what weight functions would produce loading-monotonic premiums. In this paper we demonstrate a decisive role of log-supermodularity in answering this question. As a consequence, we establish - at a…

Instrumental Variable Estimation When Compliance is not Deterministic: The Stochastic Monotonicity Assumption

The instrumental variables (IV) method is a method for making causal inferences about the effect of a treatment based on an observational study in which there are unmeasured confounding variables. The method requires a valid IV, a variable that is independent of the unmeasured confounding variables and is associated with the treatment but which has no effect on the outcome beyond its effect on the treatment. An additional assumption that is often made for the IV method is deterministic monotonicity, which is an assumption that for each subject, the level of the treatment that a subject would t…

Iterative algorithms for weighted and unweighted finite-rank time-series approximations

The problem of time series approximation by series of finite rank is considered from the viewpoint of signal extraction. For signal estimation, a weighted least-squares method is applied to the trajectory matrix of the considered time series. Matrix weights are chosen to obtain equal or approximately equal weights in the equivalent problem of time-series least-squares approximation. Several new methods are suggested and examined together with the Cadzow's iterative method. The questions of convergence, computational complexity, and accuracy are considered for the proposed methods. The methods …

稳健的适度加权 log-rank 检验

Robust modestly weighted log-rank tests

针对免疫肿瘤学中生存曲线非比例风险导致传统log-rank检验效能降低的问题，提出一种结合标准与适度加权log-rank统计量最大值的新检验，在延迟效应下保持效能并最小化最坏情况效能损失。

Estimation of the relative risk following group sequential procedure based upon the weighted log-rank statistic

In this paper we consider a group sequentially monitored trial on a survival endpoint, monitored using a weighted log-rank (WLR) statistic with deterministic weight function. We introduce a summary statistic in the form of a weighted average logged relative risk and show that if there is no sign change in the instantaneous logged relative risk, there always exists a bijection between the WLR statistic and the weighted average logged relative risk. We show that this bijection can be consistently estimated at each analysis under a suitable shape assumption, for which we have listed two possibili…

加权低秩矩阵逼近：加速与应用

Weighted Low-Rank Matrix Approximation: Acceleration and Applications

研究加权低秩矩阵逼近问题，在统一框架构建相关问题，开发基于Nesterov动量和Anderson加速的算法及正则化方案，提出大稀疏数据矩阵实现和有效秩准则，通过模拟研究和数据集应用证明算法优势与框架作用。