A Cautionary Note on Doubly Robust Estimators Involving Continuous-time Structure

Nowadays, more literature estimates their parameters of interest relying on estimating equations with two or more nuisance parameters. In some cases, one might be able to find a population-level doubly (or possibly multiply) robust estimating equation which has zero mean provided one of the nuisance parameters is correctly specified, without knowing which. This property is appealing in practice because it suggests "model doubly robust" estimators that entail extra protection against model misspecification. Typically asymptotic inference of such a doubly robust estimator is relatively simple through classical Z-estimation theory under standard regularity conditions. In other cases, machine learning techniques are leveraged to achieve "rate double robustness", with cross fitting. However, the classical theory might be insufficient when all nuisance parameters involve complex time structures and are possibly in the form of continuous-time stochastic nuisance processes. In such cases, we caution that extra assumptions are needed, especially on total variation. In this paper, as an example, we consider a general class of double robust estimating equations and develop generic assumptions on the asymptotic properties of the estimators of nuisance parameters such that the resulted estimator for the parameter of interest is consistent and asymptotically normal. We illustrate our framework in some examples. We also caution a gap between population double robustness and rate double robustness

Causality of Functional Longitudinal Data

"Treatment-confounder feedback" is the central complication to resolve in longitudinal studies, to infer causality. The existing frameworks for identifying causal effects for longitudinal studies with discrete repeated measures hinge heavily on assuming that time advances in discrete time steps or treatment changes as a jumping process, rendering the number of "feedbacks" finite. However, medical studies nowadays with real-time monitoring involve functional time-varying outcomes, treatment, and confounders, which leads to an uncountably infinite number of feedbacks between treatment and confounders. Therefore more general and advanced theory is needed. We generalize the definition of causal effects under user-specified stochastic treatment regimes to longitudinal studies with continuous monitoring and develop an identification framework, allowing right censoring and truncation by death. We provide sufficient identification assumptions including a generalized consistency assumption, a sequential randomization assumption, a positivity assumption, and a novel "intervenable" assumption designed for the continuous-time case. Under these assumptions, we propose a g-computation process and an inverse probability weighting process, which suggest a g-computation formula and an inverse probability weighting formula for identification. For practical purposes, we also construct two classes of population estimating equations to identify these two processes, respectively, which further suggest a doubly robust identification formula with extra robustness against process misspecification. We prove that our framework fully generalize the existing frameworks and is nonparametric

Cloaking the Clock: Emulating Clock Skew in Controller Area Networks

Automobiles are equipped with Electronic Control Units (ECU) that communicate via in-vehicle network protocol standards such as Controller Area Network (CAN). These protocols are designed under the assumption that separating in-vehicle communications from external networks is sufficient for protection against cyber attacks. This assumption, however, has been shown to be invalid by recent attacks in which adversaries were able to infiltrate the in-vehicle network. Motivated by these attacks, intrusion detection systems (IDSs) have been proposed for in-vehicle networks that attempt to detect attacks by making use of device fingerprinting using properties such as clock skew of an ECU. In this paper, we propose the cloaking attack, an intelligent masquerade attack in which an adversary modifies the timing of transmitted messages in order to match the clock skew of a targeted ECU. The attack leverages the fact that, while the clock skew is a physical property of each ECU that cannot be changed by the adversary, the estimation of the clock skew by other ECUs is based on network traffic, which, being a cyber component only, can be modified by an adversary. We implement the proposed cloaking attack and test it on two IDSs, namely, the current state-of-the-art IDS and a new IDS that we develop based on the widely-used Network Time Protocol (NTP). We implement the cloaking attack on two hardware testbeds, a prototype and a real connected vehicle, and show that it can always deceive both IDSs. We also introduce a new metric called the Maximum Slackness Index to quantify the effectiveness of the cloaking attack even when the adversary is unable to precisely match the clock skew of the targeted ECU.Comment: 11 pages, 13 figures, This work has been accepted to the 9th ACM/IEEE International Conference on Cyber-Physical Systems (ICCPS

Magnetic field effects on TcT_c and the pseudogap onset temperature in cuprate superconductors

We study the sensitivity of $T_c$ and the pseudogap onset temperature, $T^*$, to low fields, $H$, for cuprate superconductors, using a BCS-based approach extended to arbitrary coupling. We find that $T^*$ and $T_c$, which are of the same superconducting origin, have very different $H$ dependences. The small coherence length makes $T^*$ rather insensitive to the field. However, the presence of the pseudogap at $T_c$ makes $T_c$ more sensitive to $H$. Our results for the coherence length $\xi$ fit well with existing experiments. We predict that very near the insulator $\xi$ will rapidly increase.Comment: 4 pages, 1 figure, contribution to the PPHMF-IV conference, Oct. 200