Multiply robust estimators of the longitudinal g‐formula have recently been proposed to protect against model misspecification better than the standard augmented inverse probability weighted ...estimator (Rotnitzky et al., 2017; Luedtke et al., 2018). These multiply robust estimators ensure consistency if one of the models for the treatment process or outcome process is correctly specified at each time point. We study the multiply robust estimators of Rotnitzky et al. (2017) in the context of a survival outcome. Specifically, we compare various estimators of the g‐formula for survival outcomes in order to (1) understand how the estimators may be related to one another, (2) understand each estimator's robustness to model misspecification, and (3) construct estimators that can be more efficient than others in certain model misspecification scenarios. We propose a modification of the multiply robust estimators to gain efficiency under misspecification of the outcome model by using calibrated propensity scores over non‐calibrated propensity scores at each time point. Theoretical results are confirmed via simulation studies, and a practical comparison of these estimators is conducted through an application to the US Veterans Aging Cohort Study.
On the basis of conditional expectation of a random variable function, we present few characterization findings in this study. For a given function g,
, we present necessary and sufficient conditions ...for characterization results in terms of a single function
. Some of these findings are completely novel, while others are expansions of previously published characterizations.
We establish several deep existence criteria for conditional expectations on von Neumann algebras, and then apply this theory to develop a noncommutative theory of representing measures of characters ...of a function algebra. Our main cycle of results describes what may be understood as a ‘noncommutative Hoffman-Rossi theorem’ giving the existence of weak* continuous ‘noncommutative representing measures’ for so-called D-characters. These results may also be viewed as ‘module’ Hahn-Banach extension theorems for weak* continuous ‘characters’ into possibly noninjective von Neumann algebras. In closing we introduce the notion of ‘noncommutative Jensen measures’, and show that as in the classical case representing measures of logmodular algebras are Jensen measures. The proofs of the two main cycles of results rely on the delicate interplay of Tomita-Takesaki theory, noncommutative Radon-Nikodym derivatives, Connes cocycles, Haagerup noncommutative Lp-spaces, Haagerup's reduction theorem, etc.
This study bridges the gap between Real-Time Risk Assessment (RTRA) and its practical implications by following the post-hoc interpretability approach and utilizing black-box graphical tools for ...safety data visualization. The real-time traffic-related crash contributing factors were detected using the matched-case control design on 402-miles Interstate 80 in Wyoming. Four black-box visualization tools, including Partial Dependence Plot (PDP), Individual Conditional Expectation (ICE), centered ICE, and Accumulated Local Effect (ALE), were scrutinized to interpret the causal effect of these factors on crash probabilities. The results revealed that these techniques have many advantages, disadvantages, and unanswered questions that must be recognized by Active Traffic Management. PDPs must be accompanied by ICEs that explain the heterogeneity across observations. ALE is the most reliable technique in one-dimensional plots for highly correlated space of variables. However, there is a substantial distinction between PDP and ALE in two-dimensional plots that may make ALE an unreliable method.
In this paper, we study the least squares estimator for sublinear expectations. Under some mild assumptions, we prove the existence and uniqueness of the least squares estimator. The relationship ...between the least squares estimator and the conditional coherent risk measure (resp. the conditional g-expectation) is also explored. Then some characterizations of the least squares estimator are given.
•An efficient method to estimate variance-based sensitivity indices is proposed.•Multiplication approximation of the response function is employed.•All the order effects can be simultaneously ...estimated by the same sample points.•The efficiency, the accuracy and the robustness of the method are excellent.
In order to improve the efficiency, the accuracy and the robustness of the sampling-based methods for estimating the variance-based sensitivity indices, a new efficient method based on the combination of the unconditional expectation, the conditional expectation and the multiplication approximation of the response function is proposed in this paper. By the new equivalent forms of the variance-based sensitivity indices and the multiplication approximation of the response function, the proposed method can simultaneously estimate all the order effects by repeatedly making use of the same sample points. Through three typical test examples and an engineering application, the efficiency, the accuracy and the robustness of the proposed method are demonstrated in comparison with other existing sampling-based methods.
The gross calorific value (GCV) of coal is important in both the direct use and conversion into other fuel forms of coals. The measurement of GCV usually requires sophisticated bomb calorimetric ...experimental apparatus and expertise, whereas proximate analysis is much cheaper, easier and faster to conduct. This paper presents the application of three regression models, i.e., support vector machine (SVM), alternating conditional expectation (ACE) and back propagation neural network (BPNN) to predict the GCV of coals based on proximate analysis information. Analytical data of 76 Chinese coal samples, with a large variation in rank were acquired and used as input into these models. The modeling results show that: 1) all three methods are generally capable of tracking the variation trend of GCV with the proximate analysis parameters; 2) SVM performs the best in terms of generalization capability among the models investigated; 3) BPNN has the potential to outperform SVM in the training stage and ACE in both training and testing stages; however, its prediction accuracy is dramatically affected by the model parameters including hidden neuron number, learning rate and initial weights; 4) ACE performs slightly better with respect to the generalization capability than does BPNN, on an averaged scale.
•All methods perform better in the training than in the testing stage.•SVM performs the best in terms of generalization capability.•The performance of BPNN is significantly affected by its parameter initialization.•BPNN has the potential to outperform ACE if initialized properly.
Multivariate normal mean–variance mixture (NMVM) distributions are alternatives to the multivariate normal distribution when, in practice, we encounter data sets possessing large skewness and/or ...kurtosis measures. In this paper, we focus on truncated forms of NMVM distributions and derive explicit expressions for the first two moments. Our results are general which can be applied for any NMVM distribution. In particular, we derive explicit expressions for the first two moments of doubly truncated multivariate generalized hyperbolic (GH) distribution. We show that by using the results established here, the multivariate tail conditional expectation (MTCE) can be obtained for any NMVM distribution.
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