Semiparametric minimax rates

We consider the minimax rate of testing (or estimation) of nonlinear functionals defined on semiparametric models. Existing methods appear not capable of determining a lower bound on the minimax rate of testing (or estimation) for certain functionals of interest. In particular, if the semiparametric model is indexed by several infinite-dimensional parameters. To cover these examples we extend the approach of [1], which is based on comparing a “true distribution” to a convex mixture of perturbed distributions to a comparison of two convex mixtures. The first mixture is obtained by perturbing a first parameter of the model, and the second by perturbing in addition a second parameter. We apply the new result to two examples of semiparametric functionals:the estimation of a mean response when response data are missing at random, and the estimation of an expected conditional covariance functional

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

Citizen engagement in spatial planning, shaping places together

This paper explores the roles and practices of collective citizen engagement in spatial planning. Drawing on a selection of core articles in planning scholarship, it investigates how citizens (re-)shape urban places by responding to perceived flaws in how spatial planning addresses societal challenges. Formal planning interventions are often spatially and socially selective, ineffective, or even non-existent due to a lack of institutional capacities and resources. Consequently, citizens take on roles that they consider as missing, underperformed or ineffective. The paper shows that this results in a variety of practices complementary to, independent from, or opposing formal planning actors and interventions. Five dilemmas citizens face are identified, highlighting the tensions that surface on exclusion, participation, and governmental responsibilities when citizens claim their role in urban governance

Sequential Data-Adaptive Bandwidth Selection by Cross-Validation for Nonparametric Prediction

We consider the problem of bandwidth selection by cross-validation from a sequential point of view in a nonparametric regression model. Having in mind that in applications one often aims at estimation, prediction and change detection simultaneously, we investigate that approach for sequential kernel smoothers in order to base these tasks on a single statistic. We provide uniform weak laws of large numbers and weak consistency results for the cross-validated bandwidth. Extensions to weakly dependent error terms are discussed as well. The errors may be {\alpha}-mixing or L2-near epoch dependent, which guarantees that the uniform convergence of the cross validation sum and the consistency of the cross-validated bandwidth hold true for a large class of time series. The method is illustrated by analyzing photovoltaic data.Comment: 26 page

Fisher information and asymptotic normality in system identification for quantum Markov chains

This paper deals with the problem of estimating the coupling constant $\theta$ of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular we obtain a simple estimator of $\theta$ whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system, is itself asymptotically Gaussian and compute its quantum Fisher information which sets an absolute bound to the estimation error. The classical and quantum Fisher informations are compared in a simple example. In the vicinity of $\theta=0$ we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localised in the system, while the output is independent of the parameter.Comment: 10 pages, 2 figures. final versio

Serious complication 1 year after sacrospinous ligament fixation

Myositis of the gluteal region caused by group A streptococci 1 year after a sacrospinous ligament fixation was recognised as a serious complication of this procedure. Most likely, the infection was spread to the gluteal region through a port d’entree caused by vaginal atrophy, via the non-resorbable sutures. The patient was treated successfully with antibiotics intravenous and local estrogens