Semiparametric theory and empirical processes in causal inference

In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss estimation and inference for causal effects under semiparametric models, which allow parts of the data-generating process to be unrestricted if they are not of particular interest (i.e., nuisance functions). These models are very useful in causal problems because the outcome process is often complex and difficult to model, and there may only be information available about the treatment process (at best). Semiparametric theory gives a framework for benchmarking efficiency and constructing estimators in such settings. In the second part of the paper we discuss empirical process theory, which provides powerful tools for understanding the asymptotic behavior of semiparametric estimators that depend on flexible nonparametric estimators of nuisance functions. These tools are crucial for incorporating machine learning and other modern methods into causal inference analyses. We conclude by examining related extensions and future directions for work in semiparametric causal inference

Minimax estimation of a functional on a structured high-dimensional model

Analysis and Stochastic

Buttock pain after sacrospinous hysteropexy: reply to Wallner

We greatly appreciate the comment by Dr. Wallner [1] on the new insight into the positioning of the pudendal and levator ani nerves in relation to the complaint of buttock pain after sacrospinous hysteropexy [2]

Naturally occurring C-terminal splice variants of nuclear receptors

Alternative mRNA splicing in the region encoding the C-terminus of nuclear receptors results in receptor variants lacking the entire ligand-binding domain (LBD), or a part of it, and instead contain a sequence of splice variant-specific C-terminal amino acids. A total of thirteen such splice variants have been shown to occur in vertebrates, and at least nine occur in humans. None of these receptor variants appear to be able to bind endogenous ligands and to induce transcription on promoters containing the response element for the respective canonical receptor variant. Interestingly, ten of these C-terminal splice variants have been shown to display dominant-negative activity on the transactivational properties of their canonical equivalent. Research on most of these splice variants has been limited, and the dominant-negative effect of these receptor variants has only been demonstrated in reporter assays in vitro, using transiently transfected receptors and reporter constructs. Therefore, the in vivo function and relevance of most C-terminal splice variants remains unclear. By reviewing the literature on the human glucocorticoid receptor β-isoform (hGRβ), we show that the dominant-negative effect of hGRβ is well established using more physiologically relevant readouts. The hGR β-isoform may alter gene transcription independent from the canonical receptor and increased hGRβ levels correlate with glucocorticoid resistance and the occurrence of several immune-related diseases. Thus, available data suggests that C-terminal splice variants of nuclear receptors act as dominant-negative inhibitors of receptor-mediated signaling in vivo, and that aberrant expression of these isoforms may be involved in the pathogenesis of a variety of diseases

Fractional plateaus in the Coulomb blockade of coupled quantum dots

Ground-state properties of a double-large-dot sample connected to a reservoir via a single-mode point contact are investigated. When the interdot transmission is perfect and the dots controlled by the same dimensionless gate voltage, we find that for any finite backscattering from the barrier between the lead and the left dot, the average dot charge exhibits a Coulomb-staircase behavior with steps of size e/2 and the capacitance peak period is halved. The interdot electrostatic coupling here is weak. For strong tunneling between the left dot and the lead, we report a conspicuous intermediate phase in which the fractional plateaus get substantially altered by an increasing slope.Comment: 6 pages, 4 figures, final versio

Effective action and interaction energy of coupled quantum dots

We obtain the effective action of tunnel-coupled quantum dots, by modeling the system as a Luttinger liquid with multiple barriers. For a double dot system, we find that the resonance conditions for perfect conductance form a hexagon in the plane of the two gate voltages controlling the density of electrons in each dot. We also explicitly obtain the functional dependence of the interaction energy and peak-splitting on the gate voltage controlling tunneling between the dots and their charging energies. Our results are in good agreement with recent experimental results, from which we obtain the Luttinger interaction parameter $K=0.74$.Comment: 5 pgs,latex,3 figs,revised version to be publshed in Phys.Rev.

Empirical Phi-Discrepancies and Quasi-Empirical Likelihood: Exponential Bounds

We review some recent extensions of the so-called generalized empirical likelihood method, when the Kullback distance is replaced by some general convex divergence. We propose to use, instead of empirical likelihood, some regularized form or quasi-empirical likelihood method, corresponding to a convex combination of Kullback and χ2 discrepancies. We show that for some adequate choice of the weight in this combination, the corresponding quasi-empirical likelihood is Bartlett-correctable. We also establish some non-asymptotic exponential bounds for the confidence regions obtained by using this method. These bounds are derived via bounds for self-normalized sums in the multivariate case obtained in a previous work by the authors. We also show that this kind of results may be extended to process valued infinite dimensional parameters. In this case some known results about self-normalized processes may be used to control the behavior of generalized empirical likelihood

Microbiota promote secretory cell determination in the intestinal epithelium by modulating host Notch signaling

Resident microbes promote many aspects of host development, although the mechanisms by which microbiota influence host tissues remain unclear. We showed previously that the microbiota is required for allocation of appropriate numbers of secretory cells in the zebrafish intestinal epithelium. Because Notch signaling is crucial for secretory fate determination, we conducted epistasis experiments to establish whether the microbiota modulates host Notch signaling. We also investigated whether innate immune signaling transduces microbiota cues via the Myd88 adaptor protein. We provide the first evidence that microbiota-induced, Myd88-dependent signaling inhibits host Notch signaling in the intestinal epithelium, thereby promoting secretory cell fate determination. These results connect microbiota activity via innate immune signaling to the Notch pathway, which also plays crucial roles in intestinal homeostasis throughout life and when impaired can result in chronic inflammation and cancer.Animal science