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This paper demonstrates the advantages of sharing information about unknown features of covariates across multiple model components in various nonparametric regression problems including multivariate, heteroscedastic, and semicontinuous responses. In this paper, we present a methodology which allows for information to be shared nonparametrically across various model components using Bayesian sum-of-tree models. Our simulation results demonstrate that sharing of information across related model components is often very beneficial, particularly in sparse high-dimensional problems in which variable selection must be conducted. We illustrate our methodology by analyzing medical expenditure data from the Medical Expenditure Panel Survey (MEPS). To facilitate the Bayesian nonparametric regression analysis, we develop two novel models for analyzing the MEPS data using Bayesian additive regression trees—a heteroskedastic log-normal hurdle model with a “shrinktoward-homoskedasticity” prior and a gamma hurdle model.

We propose a method to analyze interval-censored data using a multiple imputation based on a Heteroskedastic Interval regression approach. The proposed model aims to obtain a synthetic dataset that can be used for standard analysis, including standard linear regression, quantile regression, or poverty and inequality estimation. We present two applications to show the performance of our method. First, we run a Monte Carlo simulation to show the method's performance under the assumption of multiplicative heteroskedasticity, with and without conditional normality. Second, we use the proposed methodology to analyze labor income data in Grenada for 2013-2020, where the salary data are interval-censored according to the salary intervals prespecified in the survey questionnaire. The results obtained are consistent across both exercises.

This paper introduces a new econometric framework for modeling fractional outcomes bounded between zero and one. We propose the Fractional Probit with Cross-Sectional Volatility (FPCV), which specifies the conditional mean through a probit link and allows the conditional variance to depend on observable heterogeneity. The model extends heteroskedastic probit methods to fractional responses and unifies them with existing approaches for proportions. Monte Carlo simulations demonstrate that the FPCV estimator achieves lower bias, more reliable inference, and superior predictive accuracy compared with standard alternatives. The framework is particularly suited to empirical settings where fractional outcomes display systematic variability across units, such as participation rates, market shares, health indices, financial ratios, and vote shares. By modeling both mean and variance, FPCV provides interpretable measures of volatility and offers a robust tool for empirical analysis and policy evaluation.

We consider the problem of calibrating range measurements of a Light Detection and Ranging (lidar) sensor that is dealing with the sensor nonlinearity and heteroskedastic, range-dependent, measurement error. We solved the calibration problem without using additional hardware, but rather exploiting assumptions on the environment surrounding the sensor during the calibration procedure. More specifically we consider the assumption of calibrating the sensor by placing it in an environment so that its measurements lie in a 2D plane that is parallel to the ground. Then, its measurements come from fixed objects that develop orthogonally w.r.t. the ground, so that they may be considered as fixed points in an inertial reference frame. Moreover, we consider the intuition that moving the distance sensor within this environment implies that its measurements should be such that the relative distances and angles among the fixed points above remain the same. We thus exploit this intuition to cast the sensor calibration problem as making its measurements comply with this assumption that \"fixed features shall have fixed relative distances and angles\". The resulting calibration procedure does thus not need to use additional (typically expensive) equipment, nor deploy special hardware. As for the proposed estimation strategies, from a mathematical perspective we consider models that lead to analytically solvable equations, so to enable deployment in embedded systems. Besides proposing the estimators we moreover analyze their statistical performance both in simulation and with field tests. We report the dependency of the MSE performance of the calibration procedure as a function of the sensor noise levels, and observe that in field tests the approach can lead to a tenfold improvement in the accuracy of the raw measurements.

This paper empirically tests housing market efficiency in the spatial dimension by using the spatial autoregressive conditional heteroskedastic (ARCH) and spatial quantile regression models. The tests were conducted in terms of both housing returns and squared returns (volatility). The sale price data used is from Cook County residential MLS for the years 2010–2016. The main findings are that housing returns are not spatially correlated but squared returns are spatially correlated, and the spatial dependence of squared returns seems to be stronger for higher squared return quantiles.

We contribute to the literature on empirical macroeconomic models with time-varying conditional moments, by introducing a heteroskedastic score-driven model with Student’s t -distributed innovations, named the heteroskedastic score-driven$t$-QVAR (quasi-vector autoregressive) model. The$t$-QVAR model is a robust nonlinear extension of the VARMA (VAR moving average) model. As an illustration, we apply the heteroskedastic$t$-QVAR model to a dynamic stochastic general equilibrium model, for which we estimate Gaussian-ABCD and$t$-ABCD representations. We use data on economic output, inflation, interest rate, government spending, aggregate productivity, and consumption of the USA for the period of 1954 Q3 to 2022 Q1. Due to the robustness of the heteroskedastic$t$-QVAR model, even including the period of the coronavirus disease of 2019 (COVID-19) pandemic and the start of the Russian invasion of Ukraine, we find a superior statistical performance, lower policy-relevant dynamic effects, and a higher estimation precision of the impulse response function for US gross domestic product growth and US inflation rate, for the heteroskedastic score-driven$t$-ABCD representation rather than for the homoskedastic Gaussian-ABCD representation.

Many financial time series have varying structures at different quantile levels, and also exhibit the phenomenon of conditional heteroskedasticity at the same time. However, there is presently no time series model that accommodates both of these features. This paper fills the gap by proposing a novel conditional heteroskedastic model called “quantile double autoregression”. The strict stationarity of the new model is derived, and self-weighted conditional quantile estimation is suggested. Two promising properties of the original double autoregressive model are shown to be preserved. Based on the quantile autocorrelation function and self-weighting concept, three portmanteau tests are constructed to check the adequacy of the fitted conditional quantiles. The finite sample performance of the proposed inferential tools is examined by simulation studies, and the need for use of the new model is further demonstrated by analyzing the S&P500 Index.

Spatial units typically vary over many of their characteristics, introducing potential unobserved heterogeneity which invalidates commonly used homoskedasticity conditions. In the presence of unobserved heteroskedasticity, methods based on the quasi-likelihood function generally produce inconsistent estimates of both the spatial parameter and the coefficients of the exogenous regressors. A robust generalized method of moments estimator as well as a modified likelihood method have been proposed in the literature to address this issue. The present paper constructs an alternative indirect inference (II) approach which relies on a simple ordinary least squares procedure as its starting point. Heteroskedasticity is accommodated by utilizing a new version of continuous updating that is applied within the II procedure to take account of the parameterization of the variance–covariance matrix of the disturbances. Finite-sample performance of the new estimator is assessed in a Monte Carlo study. The approach is implemented in an empirical application to house price data in the Boston area, where it is found that spatial effects in house price determination are much more significant under robustification to heterogeneity in the equation errors.

Background Sleep apnea patients on CPAP therapy exhibit differences in how they adhere to the therapy. Previous studies have demonstrated the benefit of describing adherence in terms of discernible longitudinal patterns. However, these analyses have been done on a limited number of patients, and did not properly represent the temporal characteristics and heterogeneity of adherence. Methods We illustrate the potential of identifying patterns of adherence with a latent-class heteroskedastic hurdle trajectory approach using generalized additive modeling. The model represents the adherence trajectories on three aspects over time: the daily hurdle of using the therapy, the daily time spent on therapy, and the day-to-day variability. The combination of these three characteristics has not been studied before. Results Applying the proposed model to a dataset of 10,000 patients in their first three months of therapy resulted in nine adherence groups, among which 49% of patients exhibited a change in adherence over time. The identified group trajectories revealed a non-linear association between the change in the daily hurdle of using the therapy, and the average time on therapy. The largest difference between groups was observed in the patient motivation score. The adherence patterns were also associated with different levels of high residual AHI, and day-to-day variability in leakage. Conclusion The inclusion of the hurdle model and the heteroskedastic model into the mixture model enabled the discovery of additional adherence patterns, and a more descriptive representation of patient behavior over time. Therapy adherence was mostly affected by a lack of attempts over time, suggesting that encouraging these patients to attempt therapy on a daily basis, irrespective of the number of hours used, could drive adherence. We believe the methodology is applicable to other domains of therapy or medication adherence.