Peter J. Bickel

In empirical research, when we have multiple estimators for the same parameter of interest, a central question arises: how do we combine unbiased but less precise estimators with biased but more precise ones to improve the inference? Under this setting, the point estimation problem has attracted considerable attention. In this paper, we focus on a less studied inference question: how can we conduct valid statistical inference in such settings with unknown bias? We propose a strategy to combine unbiased and biased estimators from a sensitivity analysis perspective. We derive a sequence of confidence intervals indexed by the magnitude of the bias, which enable researchers to assess how conclusions vary with the bias levels. Importantly, we introduce the notion of the b-value, a critical value of the unknown maximum relative bias at which combining estimators does not yield a significant result. We apply this strategy to three canonical combined estimators: the precision-weighted estimator, the pretest estimator, and the soft-thresholding estimator. For each estimator, we characterize the sequence of confidence intervals and determine the bias threshold at which the conclusion changes. Based on the theory, we recommend reporting the b-value based on the soft-thresholding estimator and its associated confidence intervals, which are robust to unknown bias and achieve the lowest worst-case risk among the alternatives.

We develop new semiparametric methods for estimating treatment effects. We focus on settings where the outcome distributions may be thick tailed, where treatment effects may be small, where sample sizes are large and where assignment is completely random. This setting is of particular interest in recent online experimentation. We propose using parametric models for the treatment effects, leading to semiparametric models for the outcome distributions. We derive the semiparametric efficiency bound for the treatment effects for this setting, and propose efficient estimators. In the leading case with constant quantile treatment effects one of the proposed efficient estimators has an interesting interpretation as a weighted average of quantile treatment effects, with the weights proportional to minus the second derivative of the log of the density of the potential outcomes. Our analysis also suggests an extension of Huber's model and trimmed mean to include asymmetry.

Peter J Bickel, Derek Bean, Aiyou Chen, Purnamrita Sarkar; Peter J Bickel, Derek Bean, Aiyou Chen and Purnamrita Sarkar’s contribution to the Discussion of “Vin

Significance: In this paper, we present two divide-and-conquer algorithms for clustering large graphs. Both algorithms apply a base algorithm on several small subgraphs and then use these individual local clusterings to obtain a global clustering. We show that our methods help scale computationally intensive base clustering algorithms to large networks, and improve the algorithmic stability of some well-known algorithms.

In a challenging paper 20 years ago, Leo Breiman challenged the statistical culture of his time. Some perceptive comments by David Cox and Brad Efron appeared with it. In this paper I try to look at this work in the light of modern culture and find much to agree but also much to disagree with. It's still a pleasure to read.

Recently, Chatterjee has introduced a new coefficient of correlation which has several natural properties. In particular, the coefficient attains its maximal value if and only if one variable is a measurable function of the other variable. In this paper, we seek to define correlations which have a similar property, except now the measurable function must belong to a pre-specified class, which amounts to a shape restriction on the function. We will then look specifically at the correlation corresponding to the class of monotone nondecreasing functions, in which case we can prove various asymptotic results, as well as perform local power calculations.

Chromosome conformation capture experiments such as Hi-C are used to map the three-dimensional spatial organization of genomes. One specific feature of the 3D organization is known as topologically associating domains (TADs), which are densely interacting, contiguous chromatin regions playing important roles in regulating gene expression. A few algorithms have been proposed to detect TADs. In particular, the structure of Hi-C data naturally inspires application of community detection methods. However, one of the drawbacks of community detection is that most methods take exchangeability of the nodes in the network for granted; whereas the nodes in this case, i.e. the positions on the chromosomes, are not exchangeable. We propose a network model for detecting TADs using Hi-C data that takes into account this non-exchangeability. In addition, our model explicitly makes use of cell-type specific CTCF binding sites as biological covariates and can be used to identify conserved TADs across multiple cell types. The model leads to a likelihood objective that can be efficiently optimized via relaxation. We also prove that when suitably initialized, this model finds the underlying TAD structure with high probability. Using simulated data, we show the advantages of our method and the caveats of popular community detection methods, such as spectral clustering, in this application. Applying our method to real Hi-C data, we demonstrate the domains identified have desirable epigenetic features and compare them across different cell types.

A new approach to the sparse Canonical Correlation Analysis (sCCA)is proposed with the aim of discovering interpretable associations in very high-dimensional multi-view, i.e.observations of multiple sets of variables on the same subjects, problems. Inspired by the sparse PCA approach of Journee et al. (2010), we also show that the sparse CCA formulation, while non-convex, is equivalent to a maximization program of a convex objective over a compact set for which we propose a first-order gradient method. This result helps us reduce the search space drastically to the boundaries of the set. Consequently, we propose a two-step algorithm, where we first infer the sparsity pattern of the canonical directions using our fast algorithm, then we shrink each view, i.e. observations of a set of covariates, to contain observations on the sets of covariates selected in the previous step, and compute their canonical directions via any CCA algorithm. We also introduceDirected Sparse CCA, which is able to find associations which are aligned with a specified experiment design, andMulti-View sCCA which is used to discover associations between multiple sets of covariates. Our simulations establish the superior convergence properties and computational efficiency of our algorithm as well as accuracy in terms of the canonical correlation and its ability to recover the supports of the canonical directions. We study the associations between metabolomics, trasncriptomics and microbiomics in a multi-omic study usingMuLe, which is an R-package that implements our approach, in order to form hypotheses on mechanisms of adaptations of Drosophila Melanogaster to high doses of environmental toxicants, specifically Atrazine, which is a commonly used chemical fertilizer.