We consider logistic regression including two sets of discrete or categorical covariates that are missing at random (MAR) separately or simultaneously. We examine the asymptotic properties of two multiple imputation (MI) estimators, given in the study of Lee at al. (2023), for the parameters of the logistic regression model with both sets of discrete or categorical covariates that are MAR separately or simultaneously. The proposed estimated asymptotic variances of the two MI estimators address a limitation observed with Rubin's type estimated variances, which lead to underestimate the variances of the two MI estimators (Rubin, 1987). Simulation results demonstrate that our two proposed MI methods outperform the complete-case, semiparametric inverse probability weighting, random forest MI using chained equations, and stochastic approximation of expectation-maximization methods. To illustrate the methodology's practical application, we provide a real data example from a survey conducted in the Feng Chia night market in Taichung City, Taiwan.
相關內容
We propose a new concept of lifts of reversible diffusion processes and show that various well-known non-reversible Markov processes arising in applications are lifts in this sense of simple reversible diffusions. Furthermore, we introduce a concept of non-asymptotic relaxation times and show that these can at most be reduced by a square root through lifting, generalising a related result in discrete time. Finally, we demonstrate how the recently developed approach to quantitative hypocoercivity based on space-time Poincar\'e inequalities can be rephrased and simplified in the language of lifts and how it can be applied to find optimal lifts.
We perform a quantitative assessment of different strategies to compute the contribution due to surface tension in incompressible two-phase flows using a conservative level set (CLS) method. More specifically, we compare classical approaches, such as the direct computation of the curvature from the level set or the Laplace-Beltrami operator, with an evolution equation for the mean curvature recently proposed in literature. We consider the test case of a static bubble, for which an exact solution for the pressure jump across the interface is available, and the test case of an oscillating bubble, showing pros and cons of the different approaches.
We consider nonparametric Bayesian inference in a multidimensional diffusion model with reflecting boundary conditions based on discrete high-frequency observations. We prove a general posterior contraction rate theorem in $L^2$-loss, which is applied to Gaussian priors. The resulting posteriors, as well as their posterior means, are shown to converge to the ground truth at the minimax optimal rate over H\"older smoothness classes in any dimension. Of independent interest and as part of our proofs, we show that certain frequentist penalized least squares estimators are also minimax optimal.
The interest in network analysis of bibliographic data has grown substantially in recent years, yet comprehensive statistical models for examining the complete dynamics of scientific networks based on bibliographic data are generally lacking. Current empirical studies often focus on models restricting analysis either to paper citation networks (paper-by-paper) or author networks (author-by-author). However, such networks encompass not only direct connections between papers, but also indirect relationships between the references of papers connected by a citation link. In this paper, we extend recently developed relational hyperevent models (RHEM) for analyzing scientific networks. We introduce new covariates representing theoretically meaningful and empirically interesting sub-network configurations. The model accommodates testing hypotheses considering: (i) the polyadic nature of scientific publication events, and (ii) the interdependencies between authors and references of current and prior papers. We implement the model using purpose-built, publicly available open-source software, demonstrating its empirical value in an analysis of a large publicly available scientific network dataset. Assessing the relative strength of various effects reveals that both the hyperedge structure of publication events, as well as the interconnection between authors and references significantly improve our understanding and interpretation of collaborative scientific production.
Logical characterisations, rule formats and compositionality for input-output conformance simulation
Input-output conformance simulation (iocos) has been proposed by Gregorio-Rodr\'iguez, Llana and Mart\'inez-Torres as a simulation-based behavioural preorder underlying model-based testing. This relation is inspired by Tretmans' classic ioco relation, but has better worst-case complexity than ioco and supports stepwise refinement. The goal of this paper is to develop the theory of iocos by studying logical characterisations of this relation, rule formats for it and its compositionality. More specifically, this article presents characterisations of iocos in terms of modal logics and compares them with an existing logical characterisation for ioco proposed by Beohar and Mousavi. It also offers a characteristic-formula construction for iocos over finite processes in an extension of the proposed modal logics with greatest fixed points. A precongruence rule format for iocos and a rule format ensuring that operations take quiescence properly into account are also given. Both rule formats are based on the GSOS format by Bloom, Istrail and Meyer. The general modal decomposition methodology of Fokkink and van Glabbeek is used to show how to check the satisfaction of properties expressed in the logic for iocos in a compositional way for operations specified by rules in the precongruence rule format for iocos .
Constant (naive) imputation is still widely used in practice as this is a first easy-to-use technique to deal with missing data. Yet, this simple method could be expected to induce a large bias for prediction purposes, as the imputed input may strongly differ from the true underlying data. However, recent works suggest that this bias is low in the context of high-dimensional linear predictors when data is supposed to be missing completely at random (MCAR). This paper completes the picture for linear predictors by confirming the intuition that the bias is negligible and that surprisingly naive imputation also remains relevant in very low dimension.To this aim, we consider a unique underlying random features model, which offers a rigorous framework for studying predictive performances, whilst the dimension of the observed features varies.Building on these theoretical results, we establish finite-sample bounds on stochastic gradient (SGD) predictors applied to zero-imputed data, a strategy particularly well suited for large-scale learning.If the MCAR assumption appears to be strong, we show that similar favorable behaviors occur for more complex missing data scenarios.
Municipalities are vulnerable to cyberattacks with devastating consequences, but they lack key information to evaluate their own risk and compare their security posture to peers. Using data from 83 municipalities collected via a cryptographically secure computation platform about their security posture, incidents, security control failures, and losses, we build data-driven cyber risk models and cyber security benchmarks for municipalities. We produce benchmarks of the security posture in a sector, the frequency of cyber incidents, forecasted annual losses for organizations based on their defensive posture, and a weighting of cyber controls based on their individual failure rates and associated losses. Combined, these four items can help guide cyber policymaking by quantifying the cyber risk in a sector, identifying gaps that need to be addressed, prioritizing policy interventions, and tracking progress of those interventions over time. In the case of the municipalities, these newly derived risk measures highlight the need for continuous measured improvement of cybersecurity readiness, show clear areas of weakness and strength, and provide governments with some early targets for policy focus such as security education, incident response, and focusing efforts first on municipalities at the lowest security levels that have the highest risk reduction per security dollar invested.
We explore a linear inhomogeneous elasticity equation with random Lam\'e parameters. The latter are parameterized by a countably infinite number of terms in separated expansions. The main aim of this work is to estimate expected values (considered as an infinite dimensional integral on the parametric space corresponding to the random coefficients) of linear functionals acting on the solution of the elasticity equation. To achieve this, the expansions of the random parameters are truncated, a high-order quasi-Monte Carlo (QMC) is combined with a sparse grid approach to approximate the high dimensional integral, and a Galerkin finite element method (FEM) is introduced to approximate the solution of the elasticity equation over the physical domain. The error estimates from (1) truncating the infinite expansion, (2) the Galerkin FEM, and (3) the QMC sparse grid quadrature rule are all studied. For this purpose, we show certain required regularity properties of the continuous solution with respect to both the parametric and physical variables. To achieve our theoretical regularity and convergence results, some reasonable assumptions on the expansions of the random coefficients are imposed. Finally, some numerical results are delivered.
Forecasts for key macroeconomic variables are almost always made simultaneously by the same organizations, presented together, and used together in policy analyses and decision-makings. It is therefore important to know whether the forecasters are skillful enough to forecast the future values of those variables. Here a method for joint evaluation of skill in directional forecasts of multiple variables is introduced. The method is simple to use and does not rely on complicated assumptions required by the conventional statistical methods for measuring accuracy of directional forecast. The data on GDP growth and inflation forecasts of three organizations from Thailand, namely, the Bank of Thailand, the Fiscal Policy Office, and the Office of the National Economic and Social Development Council as well as the actual data on GDP growth and inflation of Thailand between 2001 and 2021 are employed in order to demonstrate how the method could be used to evaluate the skills of forecasters in practice. The overall results indicate that these three organizations are somewhat skillful in forecasting the direction-of-changes of GDP growth and inflation when no band and a band of +/- 1 standard deviation of the forecasted outcome are considered. However, when a band of +/- 0.5% of the forecasted outcome is introduced, the skills in forecasting the direction-of-changes of GDP growth and inflation of these three organizations are, at best, little better than intelligent guess work.
Most of the existing Mendelian randomization (MR) methods are limited by the assumption of linear causality between exposure and outcome, and the development of new non-linear MR methods is highly desirable. We introduce two-stage prediction estimation and control function estimation from econometrics to MR and extend them to non-linear causality. We give conditions for parameter identification and theoretically prove the consistency and asymptotic normality of the estimates. We compare the two methods theoretically under both linear and non-linear causality. We also extend the control function estimation to a more flexible semi-parametric framework without detailed parametric specifications of causality. Extensive simulations numerically corroborate our theoretical results. Application to UK Biobank data reveals non-linear causal relationships between sleep duration and systolic/diastolic blood pressure.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191