Semiparametric regression methods for temporal processes subject to multiple sources of censoring

Process regression methodology is underdeveloped relative to the frequency with which pertinent data arise. In this article, the response-190 is a binary indicator process representing the joint event of being alive and remaining in a specific state. The process is indexed by time (e.g., time since diagnosis) and observed continuously. Data of this sort occur frequently in the study of chronic disease. A general area of application involves a recurrent event with non-negligible duration (e.g., hospitalization and associated length of hospital stay) and subject to a terminating event (e.g., death). We propose a semiparametric multiplicative model for the process version of the probability of being alive and in the (transient) state of interest. Under the proposed methods, the regression parameter is estimated through a procedure that does not require estimating the baseline probability. Unlike the majority of process regression methods, the proposed methods accommodate multiple sources of censoring. In particular, we derive a computationally convenient variant of inverse probability of censoring weighting based on the additive hazards model. We show that the regression parameter estimator is asymptotically normal, and that the baseline probability function estimator converges to a Gaussian process. Simulations demonstrate that our estimators have good finite sample performance. We apply our method to national end-stage liver disease data. The Canadian Journal of Statistics 48: 222–237; 2020 © 2019 Statistical Society of Canada     

Affine LIBOR models driven by real-valued affine processes

The class of affine LIBOR models is appealing since it satisfies three central requirements of interest rate modeling. It is arbitrage-free, interest rates are nonnegative, and caplet and swaption prices can be calculated analytically. In order to guarantee nonnegative interest rates affine LIBOR models are driven by nonnegative affine processes, a restriction that makes it hard to produce volatility smiles. We modify the affine LIBOR models in such a way that real-valued affine processes can be used without destroying the nonnegativity of interest rates. Numerical examples show that in this class of models, pronounced volatility smiles are possible.     

Estimation of the joint survival function for successive duration times under double-truncation and right-censoring

ABSTRACT

In incident cohort studies, survival data often include subjects who have had an initiate event at recruitment and may potentially experience two successive events (first and second) during the follow-up period. When disease registries or surveillance systems collect data based on incidence occurring within a specific calendar time interval, the initial event is usually subject to double truncation. Furthermore, since the second duration process is observable only if the first event has occurred, double truncation and dependent censoring arise. In this article, under the two sampling biases with an unspecified distribution of truncation variables, we propose a nonparametric estimator of the joint survival function of two successive duration times using the inverse-probability-weighted (IPW) approach. The consistency of the proposed estimator is established. Based on the estimated marginal survival functions, we also propose a two-stage estimation procedure for estimating the parameters of copula model. The bootstrap method is used to construct confidence interval. Numerical studies demonstrate that the proposed estimation approaches perform well with moderate sample sizes.     

计算机网络技术应用下的外语词汇教学模式研究

鉴于词汇教学在整个外语教学中的重要性及目前外语词汇教学所面临的问题,创建系统性外语词汇教学模式,并与计算机网络技术的应用相结合,来促进教师的外语词汇教学,进而提高学生的词汇学习效率。系统性外语词汇教学模式涉及三个主要教学阶段：课前预习、课堂教学和课后复习,而这三个教学阶段将与一系列新设计的词汇认知过程进行有机的结合。同时,还将尝试通过计算机网络技术的应用来优化新创建的系统性外语词汇教学模式。教师可以利用计算机网络技术为学生提供丰富的学习资源,并帮助他们充分运用各种词汇学习策略,从而调动学生对重点词汇学习的兴趣,进而提升教学效果。     

Bayesian nonparametric modelling of the link function in the single-index model using a Bernstein–Dirichlet process prior

This paper proposes the use of the Bernstein–Dirichlet process prior for a new nonparametric approach to estimating the link function in the single-index model (SIM). The Bernstein–Dirichlet process prior has so far mainly been used for nonparametric density estimation. Here we modify this approach to allow for an approximation of the unknown link function. Instead of the usual Gaussian distribution, the error term is assumed to be asymmetric Laplace distributed which increases the flexibility and robustness of the SIM. To automatically identify truly active predictors, spike-and-slab priors are used for Bayesian variable selection. Posterior computations are performed via a Metropolis-Hastings-within-Gibbs sampler using a truncation-based algorithm for stick-breaking priors. We compare the efficiency of the proposed approach with well-established techniques in an extensive simulation study and illustrate its practical performance by an application to nonparametric modelling of the power consumption in a sewage treatment plant.     

A dimensionality reduction method of continuous dependent variables based supervised Laplacian eigenmaps

Dimensionality reduction is one of the important preprocessing steps in high-dimensional data analysis. In this paper we propose a supervised manifold learning method, it makes use of the information of continuous dependent variables to distinguish intrinsic neighbourhood and extrinsic neighbourhood of data samples, and construct two graphs according to these two kinds of neighbourhoods. Following the idea of Laplacian eigenmaps, we reveal that on the low-dimensional manifold the neighbourhood structure can be preserved or even improved. Our approach has two important characteristics: (i) it uses dependent variables to find an informative low-dimensional projection which is robust to noisy independent variables and (ii) the objective function simultaneously enlarges the distance between dissimilar samples and pushes similar samples close to each other according to the graph constructed with the help of continuous dependent variables. Our experiments demonstrate that the effectiveness of our method is over their traditional rivals.     

The nested joint clustering via Dirichlet process mixture model

This article focuses on the clustering problem based on Dirichlet process (DP) mixtures. To model both time invariant and temporal patterns, different from other existing clustering methods, the proposed semi-parametric model is flexible in that both the common and unique patterns are taken into account simultaneously. Furthermore, by jointly clustering subjects and the associated variables, the intrinsic complex shared patterns among subjects and among variables are expected to be captured. The number of clusters and cluster assignments are directly inferred with the use of DP. Simulation studies illustrate the effectiveness of the proposed method. An application to wheal size data is discussed with an aim of identifying novel temporal patterns among allergens within subject clusters.     

Time‐change models for asymmetric processes

Many records in environmental sciences exhibit asymmetric trajectories. The physical mechanisms behind these records may lead for example to sample paths with different characteristics at high and low levels (up–down asymmetries) or in the ascending and descending phases leading to time irreversibility (front–back asymmetries). Such features are important for many applications, and there is a need for simple and tractable models that can reproduce them. In this paper, we explore original time‐change models where the clock is a stochastic process that depends on the observed trajectory. The ergodicity of the proposed model is established under general conditions, and this result is used to develop nonparametric estimation procedures based on the joint distribution of the process and its derivative. The methodology is illustrated on meteorological and oceanographic data sets. We show that, combined with a marginal transformation, the proposed methodology is able to reproduce important characteristics of the data set such as marginal distributions, up‐crossing intensity, and up–down and front–back asymmetries.