We proceed to compute the variances of each estimator. The proof also holds for the non-zero mean case trivially. Causal model details for Section 5.2 In Section 5.2, We include a wide range of machine learning-based causal inference methods to evaluate the performance of causal error estimators. Others configs are kept as default. The others are kept as default.

Heatwaves, intensified by climate change and rapid urbanisation, pose significant threats to urban systems, particularly in the Global South, where adaptive capacity is constrained. This study investigates the relationship between heatwaves and nighttime light (NTL) radiance, a proxy of nighttime economic activity, in four hyperdense cities: Delhi, Guangzhou, Cairo, and Sao Paulo. We hypothesised that heatwaves increase nighttime activity. Using a double machine learning (DML) framework, we analysed data from 2013 to 2019 to quantify the impact of heatwaves on NTL while controlling for local climatic confounders. Results revealed a statistically significant increase in NTL intensity during heatwaves, with Cairo, Delhi, and Guangzhou showing elevated NTL on the third day, while S\~ao Paulo exhibits a delayed response on the fourth day. Sensitivity analyses confirmed the robustness of these findings, indicating that prolonged heat stress prompts urban populations to shift activities to night. Heterogeneous responses across cities highlight the possible influence of urban morphology and adaptive capacity to heatwave impacts. Our findings provide a foundation for policymakers to develop data-driven heat adaptation strategies, ensuring that cities remain liveable and economically resilient in an increasingly warming world.

This thesis contains a series of independent contributions to statistics, unified by a model-free perspective. The first chapter elaborates on how a model-free perspective can be used to formulate flexible methods that leverage prediction techniques from machine learning. Mathematical insights are obtained from concrete examples, and these insights are generalized to principles that permeate the rest of the thesis. The second chapter studies the concept of local independence, which describes whether the evolution of one stochastic process is directly influenced by another. To test local independence, we define a model-free parameter called the Local Covariance Measure (LCM). We formulate an estimator for the LCM, from which a test of local independence is proposed. We discuss how the size and power of the proposed test can be controlled uniformly and investigate the test in a simulation study. The third chapter focuses on covariate adjustment, a method used to estimate the effect of a treatment by accounting for observed confounding. We formulate a general framework that facilitates adjustment for any subset of covariate information. We identify the optimal covariate information for adjustment and, based on this, introduce the Debiased Outcome-adapted Propensity Estimator (DOPE) for efficient estimation of treatment effects. An instance of DOPE is implemented using neural networks, and we demonstrate its performance on simulated and real data. The fourth and final chapter introduces a model-free measure of the conditional association between an exposure and a time-to-event, which we call the Aalen Covariance Measure (ACM). We develop a model-free estimation method and show that it is doubly robust, ensuring $\sqrt{n}$-consistency provided that the nuisance functions can be estimated with modest rates. A simulation study demonstrates the use of our estimator in several settings.

This paper explores the use of unstructured, multimodal data, namely text and images, in causal inference and treatment effect estimation. We propose a neural network architecture that is adapted to the double machine learning (DML) framework, specifically the partially linear model. An additional contribution of our paper is a new method to generate a semi-synthetic dataset which can be used to evaluate the performance of causal effect estimation in the presence of text and images as confounders. The proposed methods and architectures are evaluated on the semi-synthetic dataset and compared to standard approaches, highlighting the potential benefit of using text and images directly in causal studies. Our findings have implications for researchers and practitioners in economics, marketing, finance, medicine and data science in general who are interested in estimating causal quantities using non-traditional data.

Understanding why travel behavior differs between residents of urban centers and suburbs is key to sustainable urban planning. Especially in light of rapid urban growth, identifying housing locations that minimize travel demand and induced CO2 emissions is crucial to mitigate climate change. While the built environment plays an important role, the precise impact on travel behavior is obfuscated by residential self-selection. To address this issue, we propose a double machine learning approach to obtain unbiased, spatially-explicit estimates of the effect of the built environment on travel-related CO2 emissions for each neighborhood by controlling for residential self-selection. We examine how socio-demographics and travel-related attitudes moderate the effect and how it decomposes across the 5Ds of the built environment. Based on a case study for Berlin and the travel diaries of 32,000 residents, we find that the built environment causes household travel-related CO2 emissions to differ by a factor of almost two between central and suburban neighborhoods in Berlin. To highlight the practical importance for urban climate mitigation, we evaluate current plans for 64,000 new residential units in terms of total induced transport CO2 emissions. Our findings underscore the significance of spatially differentiated compact development to decarbonize the transport sector.

Structural equation models provide a quintessential framework for conducting causal inference in statistics, econometrics, machine learning (ML), and other data sciences. The package DoubleML for R (R Core Team, 2020) implements partially linear and interactive structural equation and treatment effect models with high-dimensional confounding variables as considered in Chernozhukov et al. (2018). Estimation and tuning of the machine learning models is based on the powerful functionalities provided by the mlr3 package and the mlr3 ecosystem (Lang et al., 2019). A key element of double machine learning (DML) models are score functions identifying the estimates for the target parameter. These functions play an essential role for valid inference with machine learning methods because they have to satisfy a property called Neyman orthogonality. With the score functions as key elements, DoubleML implements double machine learning in a very general way using object orientation based on the R6 package (Chang, 2020). Currently, DoubleML implements the double / debiased machine learning framework as established in Chernozhukov et al. (2018) for - partially linear regression models (PLR), - partially linear instrumental variable regression models (PLIV), - interactive regression models (IRM), and - interactive instrumental variable regression models (IIVM). The object-oriented implementation of DoubleML is very flexible. The model classes DoubleMLPLR, DoubleMLPLIV, DoubleMLIRM and DoubleIIVM implement the estimation of the nuisance functions via machine learning methods and the computation of the Neyman-orthogonal score function.

We consider the problem of using observational data to learn treatment assignment policies that satisfy certain constraints specified by a practitioner, such as budget, fairness, or functional form constraints. This problem has previously been studied in economics, statistics, and computer science, and several regret-consistent methods have been proposed. However, several key analytical components are missing, including a characterization of optimal methods for policy learning, and sharp bounds for minimax regret. In this paper, we derive lower bounds for the minimax regret of policy learning under constraints, and propose a method that attains this bound asymptotically up to a constant factor. Whenever the class of policies under consideration has a bounded Vapnik-Chervonenkis dimension, we show that the problem of minimax-regret policy learning can be asymptotically reduced to first efficiently evaluating how much each candidate policy improves over a randomized baseline, and then maximizing this value estimate. Our analysis relies on uniform generalizations of classical semiparametric efficiency results for average treatment effect estimation, paired with sharp concentration bounds for weighted empirical risk minimization that may be of independent interest.