Study GLS estimator properties in multivariate regression with heteroskedastic and autocorrelated errors.
problem Asymptotic properties of GLS estimator in multivariate regression with specific error structures.
method Derive Wald statistics for linear restrictions and assess their performance.
result Wald statistics remain robust to heteroskedasticity and autocorrelation.
Adaptive regularization tackles heteroskedastic and imbalanced datasets in deep learning.
problem Heteroskedastic and imbalanced datasets challenge deep learning due to varying label uncertainty and long-tailed label distributions.
method Data-dependent adaptive regularization that applies stronger regularization to higher-uncertainty, lower-density regions.
result Significant improvement in noise-robust deep learning over other methods on benchmark tasks.
Improved CI test for heteroskedastic data enhances causal discovery.
problem CI testing assumptions fail in heteroskedastic data.
method Adapted partial correlation CI test for heteroskedastic noise.
result The adapted test outperforms standard CI test in heteroskedastic cases.
A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance matrix to remove estimation bias due to heteroskedasticity. This procedure is com…
Doubly-stochastic normalization improves robustness to heteroskedastic noise.
problem Robustness to heteroskedastic noise in affinity matrix construction.
method Doubly-stochastic normalization of the Gaussian kernel.
result Doubly-stochastic normalization converges to clean matrix with rate m−1/2 under heteroskedastic noise. Paper develops methods for PCA inference with missing data and heteroskedastic noise.
problem Constructing confidence regions for PCA in high dimensions with missing data and heteroskedastic noise.
method Proposes HeteroPCA and develops non-asymptotic distributional guarantees for valid inference.
result Valid inference on principal subspace and spiked covariance matrix with missing data.
This paper improves prediction intervals for heteroskedastic regression.
problem Adaptive prediction intervals for heteroskedastic regression.
method Normalized and Mondrian conformal prediction methods.
result Conditional validity of chosen conformal predictors related to data-generating assumptions.
New financial volatility models capture dynamic volatility better.
problem Traditional volatility models miss important volatility dynamics.
method Integrate recurrent neural networks into GARCH models.
result Improved in-sample and out-of-sample volatility forecasting.
Heteroskedasticity biases uplift model rankings, leading to inefficient treatment allocation.
problem Bias in uplift model rankings due to heteroskedasticity.
method Theoretical analysis and simulation on real-world data.
result Heteroskedasticity can cause individuals with high treatment effects to be ranked at the bottom, leading to inefficient treatment allocation.
A new algorithm reduces regret in bandit problems with adversarial corruptions.
problem Optimizing decision-making in bandit problems with variable uncertainties and adversarial interference.
method Proposes HCW-GLB-OMD, an OMD-based estimator with Hessian-based confidence weights for robustness.
result Achieves instance-wise minimax optimality with a κ-factor in the corruption term. This study was conducted to find an appropriate statistical model to forecast the volatilities of PSEi using the model Generalized Autoregressive Conditional Heteroskedasticity (GARCH). Using the R software, the log returns of PSEi is modeled using various ARIMA models and with the presence of heteroskedasticity, the l…
Deep heteroskedastic models overfit, showing a phase transition with regularization strength.
problem Overfitting in deep heteroskedastic regression models.
method Theoretical framework based on statistical field theory, empirical verification, and hyperparameter simplification.
result A phase transition in model behavior with varying regularization strength.
A new estimator improves financial econometrics by providing reliable inference.
problem Poor performance of standard regression methods in financial economics with thick-tailed predictors.
method Developed an unbiased, consistent, and asymptotically normal estimator for linear regression.
result The new method delivers reliable inference under heteroskedasticity and quantile regression.
Paper relaxes factor analysis for noisy data, improving robustness.
problem Challenges in finding robust low dimensional approximations for data with heteroskedastic noise.
method Introduces a relaxed version of Minimum Trace Factor Analysis (MTFA) as a convex optimization method.
result Effective at not overfitting to heteroskedastic perturbations and addressing common issues in factor analysis.
The paper shows how sketching data can simplify regression inference even when errors are heteroskedastic.
problem Performing robust inference with heteroskedastic errors using sketched data.
method Using random projections to sketch data, the paper shows that sketched estimates behave as if errors are homoskedastic.
result Estimation by random sampling does not have the same property, and sketched estimates are asymptotically normal with homoskedastic variance.
New algorithm improves heteroskedastic PCA performance.
problem Estimating low-rank matrix subspace from noisy data.
method Deflated-HeteroPCA algorithm, dividing spectrum into subblocks.
result Near-optimal and condition-number-free statistical guarantees.
ProbRes calibrates probabilistic forecasts by learning volatility dynamics.
problem Quantifying risk and uncertainty in time series forecasting.
method ProbRes learns conditional mean and volatility separately, generating well-calibrated prediction intervals.
result ProbRes accurately captures predictive distributions and produces well-calibrated prediction intervals.
An algorithm for efficient experimentation in a dynamic environment with personalized preferences and context drifts.
problem Efficiently recommending decisions to users with personalized preferences in a context where the environment is changing over time.
method Dri-MED, inspired from the linear version of the MED strategy, adapted to handle non-stationary heteroskedastic noise.
result The instance-dependent regret scales as $ ilde{\mathcal O}\left(\fracκ{ ildeΔ}d^2(\log(T)
ight)$, with ildeΔ being the constraint-aware sub-optimality gap. Neural GARCH models financial time series with time-varying coefficients.
problem Modeling conditional heteroskedasticity in financial time series.
method Neural network adaptation of GARCH and BEKK models with time-varying coefficients parameterized by a recurrent neural network.
result Neural Students t model consistently outperforms other models on financial time series.
New method clusters tensors with heteroskedastic noise.
problem Clustering tensors with varying noise levels.
method Two-stage method: subspace estimation followed by approximate k-means. result Proves exact clustering for SNR above computational limit.
Truncated Lévy flights are random walks in which the arbitrarily large steps of a Lévy flight are eliminated. Since this makes the variance finite, the central limit theorem applies, and as time increases the probability distribution of the increments becomes Gaussian. Here, truncated Lévy flights with correlated fluct…
We propose parametric copulas that capture serial dependence in stationary heteroskedastic time series. We develop our copula for first order Markov series, and extend it to higher orders and multivariate series. We derive the copula of a volatility proxy, based on which we propose new measures of volatility dependence…
Conditions for geometric ergodicity of multivariate autoregressive conditional heteroskedasticity (ARCH) processes, with the so-called BEKK (Baba, Engle, Kraft, and Kroner) parametrization, are considered. We show for a class of BEKK-ARCH processes that the invariant distribution is regularly varying. In order to accou…
Paper proposes a robust test for high-dimensional models with large covariates and instruments.
problem Testing high-dimensional linear instrumental variable models with large covariates and instruments.
method Introduces a test based on the maximum norm of multiple parameters and a power-enhanced test.
result The proposed test is robust to heteroskedastic errors and has higher power than existing tests.
We address noisy Euclidean distances in high dimensions, estimating noise levels and correcting distances.
problem Distorted pairwise Euclidean distances due to heteroskedastic noise.
method Developed a hyperparameter-free approach to jointly estimate noise magnitudes and correct distances.
result Our method provides accurate noise magnitude estimates and corrected distances in high-dimensional settings.
Algorithm estimates common mean from Gaussian variables with unknown variances.
problem Estimating common mean from Gaussian variables with different unknown variances.
method Intuitive and efficient algorithm using Subset-of-Signals model as benchmark.
result Improved estimation error by polynomial factors compared to previous work.
Analyzed US firm data 1970-2019, identifying scale effects and distributional forms.
problem Understanding differences between small and large firms over time.
method Examined all public US firms, used stylized facts and DLN distribution analysis.
result Small firms are systematically different from large firms, with scale-dependent heteroskedasticity.
In this paper we consider a Lagrange Multiplier-type test (LM) to detect change in the mean of time series with heteroskedasticity of unknown form. We derive the limiting distribution under the null, and prove the consistency of the test against the alternative of either an abrupt or smooth changes in the mean. We perf…
In this manuscript, we analytically and numerically study statistical properties of an heteroskedastic process based on the celebrated ARCH generator of random variables whose variance is defined by a memory of qm-exponencial, form (eqm=1x=ex). Specifically, we inspect the self-correlation function o…
New method estimates bidirectional causal effects in large-scale systems.
problem Estimating bidirectional causal effects in systems with mutual dependence and heteroskedasticity.
method Heteroskedasticity-based identification with online kernel learning and random Fourier features.
result Superior accuracy and stability compared to single equation and polynomial approximations.
A new method improves treatment effect inferences in RCTs by adjusting for covariates and heteroskedasticity.
problem Improving treatment effect inferences in RCTs with efficient and powerful methods.
method Weighted Prognostic Covariate Adjustment Method (Weighted PROCOVA) for heteroskedasticity.
result The method reduces variance, maintains Type I error rate, and increases test power for treatment effect.
This paper sets fundamental limits for rank-one matrix estimation with varying noise levels.
problem Estimating a rank-one matrix from Gaussian observations with different noise levels across blocks.
method Novel reduction from heterogeneous noise to homogeneous noise, proving asymptotic error bounds.
result Asymptotically exact formulas for minimum mean-squared error in estimating rank-one matrix and factors.
Bayesian inference for stochastic differential equations using Wishart diffusions.
problem Inferring stochastic differential equations for regression and dynamical modeling.
method Bayesian non-parametric approach with semi-parametric Wishart processes.
result Modeling diffusion in stochastic differential equations improves performance and avoids overfitting.
Improved multivariate conformal prediction by standardizing residuals.
problem Weak conditional coverage in heteroskedastic multivariate settings.
method Natural extension of univariate normalization to multivariate setting, whitening residuals and standardizing local variance.
result Standardized residuals yield asymptotic conditional coverage under certain distributions.
We propose a new class of models specifically tailored for spatio-temporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, i.e. SARAR(1,1), by exploiting the recent advancements in Score Driven (SD) models typically used in time series eco…
New algorithm broadens BART models applicability.
problem Limited applicability of Bayesian additive regression trees (BART) models due to conditional conjugacy.
method Introduces a reversible jump Markov chain Monte Carlo algorithm for generalized BART models.
result Extends BART models to arbitrary generalized BART models without conditional conjugacy.
Unified framework detects shifts in climate boundaries using GP regression and MAD test.
problem Challenges in quantifying and testing for temporal shifts in spatial boundaries from noisy data.
method Combines heteroskedastic GP regression with scaled MAD GET.
result No significant decade-scale changes in arid and semi-arid interfaces, but localized shifts during extreme droughts identified.
Develops abstention procedure for nonparametric regression via variance testing.
problem Prediction with selective abstention in error-critical machine learning.
method Nonparametric heteroskedastic regression via testing hypothesis on conditional variance.
result Non-asymptotic risk bounds and convergence regimes for the estimator.
Online algorithm for probabilistic forecasting of conditional moments.
problem Probabilistic forecasting needs accurate learning of expected value and conditional heteroskedasticity.
method Combines online LASSO estimation with GAMLSS framework.
result Competitive performance in day-ahead electricity price forecasting.
A new model integrates covariates with grade of membership analysis for better latent structure recovery.
problem Improving latent structure recovery in multivariate categorical data analysis.
method Covariate-assisted grade of membership model exploiting shared low-rank simplex geometry.
result Auxiliary covariates can provably improve latent structure recovery, leading to faster convergence rates.
A standard model of (conditional) heteroscedasticity, i.e., the phenomenon that the variance of a process changes over time, is the Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) model, which is especially important for economics and finance. GARCH models are typically estimated by the Quasi-Maximum …
The asymptotic distribution of the Markowitz portfolio is derived, for the general case (assuming fourth moments of returns exist), and for the case of multivariate normal returns. The derivation allows for inference which is robust to heteroskedasticity and autocorrelation of moments up to order four. As a side effect…
Robustly infers manifold density and geometry under high-dimensional noise.
problem Inaccurate kernel density estimation under high-dimensional noise.
method Doubly stochastic normalization of Gaussian kernel.
result Robust tools for density estimation, noise magnitude estimation, and distance approximation.
In this paper, non-linear time series models are used to describe volatility in financial time series data. To describe volatility, two of the non-linear time series are combined into form TAR (Threshold Auto-Regressive Model) with AARCH (Asymmetric Auto-Regressive Conditional Heteroskedasticity) error term and its par…
CAESar improves risk forecasting by combining VaR and ES estimates.
problem Lack of tail risk measures in financial risk management.
method Conditional Autoregressive Expected Shortfall model, combining VaR and ES estimates.
result CAESar outperforms existing methods in risk forecasting.
Proposes a method to estimate drug sensitivity uncertainty using deep regression forests.
problem Lack of confidence intervals in deep learning models for critical tasks.
method Uses Deep Regression Forests to estimate variance and uncertainty for drug sensitivity prediction.
result Improves efficiency and coverage of uncertainty estimates for drug sensitivity predictions.
Paper tightens optimization bounds using conformal prediction.
problem Lack of practical informiveness in dual bounds from optimization solvers.
method Introduces conformal prediction framework to tighten loose primal and dual bounds.
result Proposed method produces tighter, more informative prediction intervals.
Introduces CCR for constructing confidence regions from conformal predictions.
problem Challenges in constructing confidence regions for model parameters.
method Combines conformal prediction intervals for model outputs to establish confidence regions for parameters under minimal assumptions.
result Valid coverage guarantees for finite sample regime, applicable to various model types.