Conditional expectation ≈ Conditional expectation
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Quantile regression: A short story on how and why Open
Quantile regression quantifies the association of explanatory variables with a conditional quantile of a dependent variable without assuming any specific conditional distribution. It hence models the quantiles, instead of the mean as done …
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Weak value beyond conditional expectation value of the pointer readings Open
It is argued that a weak value of an observable is a robust property of a\nsingle pre- and post-selected quantum system rather than a statistical\nproperty. During an infinitesimal time a system with a given weak value affects\nother syste…
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Generalized Method of Integrated Moments for High-Frequency Data Open
We propose a semiparametric two-step inference procedure for a finite-dimensional parameter based on moment conditions constructed from high-frequency data. The population moment conditions take the form of temporally integrated functional…
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THE ROLE OF INITIAL VALUES IN CONDITIONAL SUM-OF-SQUARES ESTIMATION OF NONSTATIONARY FRACTIONAL TIME SERIES MODELS Open
In this paper, we analyze the influence of observed and unobserved initial values on the bias of the conditional maximum likelihood or conditional sum-of-squares (CSS, or least squares) estimator of the fractional parameter, d , in a nonst…
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Conditionals, Causality and Conditional Probability Open
The appropriateness, or acceptability, of a conditional does not just ‘go with’ the corresponding conditional probability. A condition of dependence is required as well (cf. Douven in Synthese 164:19–44, 2008, The epistemology of indicativ…
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Causal effects of the United States and Japan on Pacific-Rim stock markets: nonparametric quantile causality approach Open
This article adopts a nonparametric quantile causality approach to examine the causal effects of the U.S. and Japan stock markets on the stock markets of the Pacific-Rim region. This approach allows us to detect not only nonlinear causalit…
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The EffectLiteR Approach for Analyzing Average and Conditional Effects Open
We present a framework for estimating average and conditional effects of a discrete treatment variable on a continuous outcome variable, conditioning on categorical and continuous covariates. Using the new approach, termed the EffectLiteR …
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Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications Open
We consider the optimal control problem for a linear conditional\nMcKean-Vlasov equation with quadratic cost functional. The coefficients of the\nsystem and the weigh-ting matrices in the cost functional are allowed to be\nadapted processe…
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Conditional Gaussian Systems for Multiscale Nonlinear Stochastic Systems: Prediction, State Estimation and Uncertainty Quantification Open
A conditional Gaussian framework for understanding and predicting complex multiscale nonlinear stochastic systems is developed. Despite the conditional Gaussianity, such systems are nevertheless highly nonlinear and are able to capture the…
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MEAN‐VARIANCE POLICY FOR DISCRETE‐TIME CONE‐CONSTRAINED MARKETS: TIME CONSISTENCY IN EFFICIENCY AND THE MINIMUM‐VARIANCE SIGNED SUPERMARTINGALE MEASURE Open
The discrete‐time mean‐variance portfolio selection formulation, which is a representative of general dynamic mean‐risk portfolio selection problems, typically does not satisfy time consistency in efficiency (TCIE), i.e., a truncated preco…
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SIZE-BIASED TRANSFORM AND CONDITIONAL MEAN RISK SHARING, WITH APPLICATION TO P2P INSURANCE AND TONTINES Open
Using risk-reducing properties of conditional expectations with respect to convex order, Denuit and Dhaene [Denuit, M. and Dhaene, J. (2012). Insurance: Mathematics and Economics 51, 265–270] proposed the conditional mean risk sharing rule…
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Augmented minimax linear estimation Open
Many statistical estimands can expressed as continuous linear functionals of a conditional expectation function. This includes the average treatment effect under unconfoundedness and generalizations for continuous-valued and personalized t…
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Estimating the Marginal Likelihood Using the Arithmetic Mean Identity Open
In this paper we propose a conceptually straightforward method to estimate the marginal data density value (also called the marginal likelihood). We show that the marginal likelihood is equal to the prior mean of the conditional density of…
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Robust learning for optimal treatment decision with NP-dimensionality Open
In order to identify important variables that are involved in making optimal treatment decision, Lu, Zhang and Zeng (2013) proposed a penalized least squared regression framework for a fixed number of predictors, which is robust against th…
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Conditional mean and quantile dependence testing in high dimension Open
Motivated by applications in biological science, we propose a novel test to assess the conditional mean dependence of a response variable on a large number of covariates. Our procedure is built on the martingale difference divergence recen…
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Semiparametric Estimation with Data Missing Not at Random Using an Instrumental Variable Open
Missing data occur frequently in empirical studies in health and social sciences, often compromising our ability to make accurate inferences. An outcome is said to be missing not at random (MNAR) if, conditional on the observed variables, …
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Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression Open
We design a numerical scheme for solving a Dynamic Programming equation with Malliavin weights arising from the time-discretization of backward stochastic differential equations with the integration by parts-representation of the $Z$-compo…
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Parametric g‐formula implementations for causal survival analyses Open
The g‐formula can be used to estimate the survival curve under a sustained treatment strategy. Two available estimators of the g‐formula are noniterative conditional expectation and iterative conditional expectation. We propose a version o…
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Formula for success: Multilevel modelling of Formula One Driver and Constructor performance, 1950–2014 Open
This paper uses random-coefficient models and (a) finds rankings of who are the best formula 1 (F1) drivers of all time, conditional on team performance; (b) quantifies how much teams and drivers matter; and (c) quantifies how team and dri…
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True to the Model or True to the Data? Open
A variety of recent papers discuss the application of Shapley values, a concept for explaining coalitional games, for feature attribution in machine learning. However, the correct way to connect a machine learning model to a coalitional ga…
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Conditional Superior Predictive Ability Open
This article proposes a test for the conditional superior predictive ability (CSPA) of a family of forecasting methods with respect to a benchmark. The test is functional in nature: under the null hypothesis, the benchmark’s conditional ex…
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Learning L2 Continuous Regression Functionals via Regularized Riesz Representers Open
Many objects of interest can be expressed as an L2 continuous functional of a regression, including average treatment effects, economic average consumer surplus, expected conditional covariances, and discrete choice parameters that depend …
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Finite‐Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness Open
We consider estimation and inference on average treatment effects under unconfoundedness conditional on the realizations of the treatment variable and covariates. Given nonparametric smoothness and/or shape restrictions on the conditional …
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Telling Cause from Effect Using MDL-Based Local and Global Regression Open
We consider the fundamental problem of inferring the causal direction between\ntwo univariate numeric random variables $X$ and $Y$ from observational data.\nThe two-variable case is especially difficult to solve since it is not possible\nt…
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Bounds on the conditional and average treatment effect with unobserved confounding factors Open
For observational studies, we study the sensitivity of causal inference when treatment assignments may depend on unobserved confounders. We develop a loss minimization approach for estimating bounds on the conditional average treatment eff…
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CARD: Classification and Regression Diffusion Models Open
Learning the distribution of a continuous or categorical response variable $\boldsymbol y$ given its covariates $\boldsymbol x$ is a fundamental problem in statistics and machine learning. Deep neural network-based supervised learning algo…
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A Quasi-Monte-Carlo Comparison of Parametric and Semiparametric Regression Methods for Heavy-tailed and Non-normal Data: an Application to Healthcare Costs Open
Summary We conduct a quasi-Monte-Carlo comparison of the recent developments in parametric and semiparametric regression methods for healthcare costs, both against each other and against standard practice. The population of English Nationa…
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Inference and testing for structural change in general Poisson autoregressive models Open
We consider here together the inference questions and the change-point problem in a large class of Poisson autoregressive models (see Tjøstheim, 2012 [34]). The conditional mean (or intensity) of the process is involved as a non-linear fun…
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A Rigorous Theory of Conditional Mean Embeddings Open
Conditional mean embeddings (CMEs) have proven themselves to be a powerful\ntool in many machine learning applications. They allow the efficient\nconditioning of probability distributions within the corresponding reproducing\nkernel Hilber…
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Debiased machine learning of conditional average treatment effects and other causal functions Open
Summary This paper provides estimation and inference methods for the best linear predictor (approximation) of a structural function, such as conditional average structural and treatment effects, and structural derivatives, based on modern …