On the role of parameterization in models with a misspecified nuisance component.

The paper is concerned with inference for a parameter of interest in models that share a common interpretation for that parameter but that may differ appreciably in other respects. We study the general structure of models under which the maximum likelihood estimator of the parameter of interest is consistent under arbitrary misspecification of the nuisance part of the model. A specialization of the general results to matched-comparison and two-groups problems gives a more explicit and easily checkable condition in terms of a notion of symmetric parameterization, leading to a broadening and unification of existing results in those problems. The role of a generalized definition of parameter orthogonality is highlighted, as well as connections to Neyman orthogonality. The issues involved in obtaining inferential guarantees beyond consistency are briefly discussed.

DISTRIBUTED TESTING AND ESTIMATION UNDER SPARSE HIGH DIMENSIONAL MODELS.

This paper studies hypothesis testing and parameter estimation in the context of the divide-and-conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various statistics from k subsamples of size n/k, where n is the sample size. In both low dimensional and sparse high dimensional settings, we address the important question of how large k can be, as n grows large, such that the loss of efficiency due to the divide-and-conquer algorithm is negligible. In other words, the resulting estimators have the same inferential efficiencies and estimation rates as an oracle with access to the full sample. Thorough numerical results are provided to back up the theory.

Individual versus systemic risk and the Regulator's Dilemma.

The global financial crisis of 2007-2009 exposed critical weaknesses in the financial system. Many proposals for financial reform address the need for systemic regulation--that is, regulation focused on the soundness of the whole financial system and not just that of individual institutions. In this paper, we study one particular problem faced by a systemic regulator: the tension between the distribution of assets that individual banks would like to hold and the distribution across banks that best supports system stability if greater weight is given to avoiding multiple bank failures. By diversifying its risks, a bank lowers its own probability of failure. However, if many banks diversify their risks in similar ways, then the probability of multiple failures can increase. As more banks fail simultaneously, the economic disruption tends to increase disproportionately. We show that, in model systems, the expected systemic cost of multiple failures can be largely explained by two global parameters of risk exposure and diversity, which can be assessed in terms of the risk exposures of individual actors. This observation hints at the possibility of regulatory intervention to promote systemic stability by incentivizing a more diverse diversification among banks. Such intervention offers the prospect of an additional lever in the armory of regulators, potentially allowing some combination of improved system stability and reduced need for additional capital.

Seizure outcomes of large volume temporo-parieto-occipital and frontal surgery in children with drug-resistant epilepsy.

OBJECTIVE: In this study, we investigate the seizure outcomes of temporo-parieto-occipital (TPO) and frontal disconnections or resections in children with drug-resistant epilepsy (DRE) in order to determine factors which may predict surgical results. METHODS: Children with DRE, who underwent either TPO or frontal disconnection or resection at Great Ormond Street Hospital for Children between 2000 and 2017, were identified from a prospectively collated operative database. Demographic data, age at surgery, type of surgery, scalp EEGs and operative histopathology were collected. Magnetic resonance imaging (MRI) was assessed to determine completeness of disconnection and presence of radiological lesion beyond the disconnection margins. Seizure outcome at 6, 12, and 24 months post-surgery was assessed using the Engel Scale (ES). Logistic regression was used to identify relationships between data variables and seizure outcome. RESULTS: 46 children (males = 28, females = 18; age range 0.5-16.6 years) who underwent TPO (n = 32, including a re-do disconnection) or frontal disconnection or resection (n = 15) were identified. Patients in the TPO treatment group had more favourable seizure outcomes than those in the frontal treatment group (ES I-II in 56 %vs 47 % at 6 months, 52 % vs 46 % at 12 months). Presence of the lesion beyond disconnection boundaries and older age at the time of surgery were associated with poorer seizure outcome. Gender, surgery type, completeness of disconnection, scalp EEG findings and underlying pathology were not related to seizure outcome, but subgroup numbers were small. CONCLUSIONS: Both TPO and frontal disconnection are effective treatments for selected children with posterior multi-lobar or diffuse frontal lobe epilepsy. Confinement of the MRI lesion within the disconnection margins and a younger age at surgery are associated with favourable seizure outcomes. Further studies are required to elucidate these findings.

An unethical optimization principle.

If an artificial intelligence aims to maximize risk-adjusted return, then under mild conditions it is disproportionately likely to pick an unethical strategy unless the objective function allows sufficiently for this risk. Even if the proportion η of available unethical strategies is small, the probability p U of picking an unethical strategy can become large; indeed, unless returns are fat-tailed p U tends to unity as the strategy space becomes large. We define an unethical odds ratio, Υ (capital upsilon), that allows us to calculate p U from η, and we derive a simple formula for the limit of Υ as the strategy space becomes large. We discuss the estimation of Υ and p U in finite cases and how to deal with infinite strategy spaces. We show how the principle can be used to help detect unethical strategies and to estimate η. Finally we sketch some policy implications of this work.

Robust estimation of high-dimensional covariance and precision matrices.

High-dimensional data are often most plausibly generated from distributions with complex structure and leptokurtosis in some or all components. Covariance and precision matrices provide a useful summary of such structure, yet the performance of popular matrix estimators typically hinges upon a sub-Gaussianity assumption. This paper presents robust matrix estimators whose performance is guaranteed for a much richer class of distributions. The proposed estimators, under a bounded fourth moment assumption, achieve the same minimax convergence rates as do existing methods under a sub-Gaussianity assumption. Consistency of the proposed estimators is also established under the weak assumption of bounded 2 + ε moments for ε ∈ (0, 2). The associated convergence rates depend on ε.