A generic nonparametric value-at-risk estimator for high dimensions

High-Dimensional Variance Estimation for the Generalized Regression Estimator

In survey sampling, the goal is to estimate finite population parameters such as totals, means, and proportions. At the estimation stage, it is common to have access to auxiliary information in the form of covariates known either in aggregate form or for each population unit. These covariates are often used, through models relating them to the variable of interest, to improve efficiency; this approach is known as model-assisted estimation. Modern applications increasingly involve settings where a large number of covariates are observed, sometimes of the same order as the sample size. While this setting offers greater modeling flexibility, it also creates important challenges for inference. In this article, we study variance estimation for the generalized regression (GREG) estimator in high-dimensional regimes. We derive new theoretical results that characterize the high-dimensional asymptotic bias of commonly used variance estimators, including those based on Taylor linearization. Furthermore, under suitable distributional assumptions on the covariates, we show that a cross-validated variance estimator is naturally asymptotically unbiased.

Conditional projection methods for large-scale Bayesian VARs

We develop fast methods for conditional forecasting and structural scenario analysis with high-dimensional Bayesian vector autoregressions (VARs). Our general framework features a factor structure on the reduced-form errors, which enables fast and order-invariant equation-by-equation estimation; suitably identified factors admit a structural interpretation. The scenarios are defined through separate distributional restrictions on observables, structural shocks and idiosyncratic components. The computational cost of our proposed algorithm is cubic only in the number of restrictions, while the dimension of the forecasted system enters linearly. In our application with $33$ macroeconomic and financial variables and ten set-identified structural shocks for the US, we compute counterfactual predictions for oil price scenarios in the context of the 2026 closure of the Strait of Hormuz. The same oil price path is consistent with outcomes ranging from a mostly benign episode to pronounced stagflation, depending on which structural and idiosyncratic shocks are allowed to deliver it.

Multi-horizon uniform superior predictive ability revisited: A size-exploiting and consistent test

An Empirical Study of Robust Portfolios Based on Statistical Noise Reduction and Regularization Constraints

This research paper discusses the issue of out-of-sample robustness of portfolio optimization within a complex market environment. Within the mean-variance framework, we compare four methods for covariance estimation and weighting: a baseline model based on sample covariances, the Ledoit-Wolf shrinkage estimator, Garber's robust covariance estimator, and a minimum-variance model incorporating an L2 regularization term. This study uses data from 60 American stocks from 2019 to 2021, with four rebalancing cycles (5, 20, 60, and 100 days) were established, and a moving-window backtesting method was applied to evaluate the performance of the various methods in terms of returns, risk, and out-of-sample stability. The empirical results indicate that the L2 normalization model generates higher cumulative returns and Sharpe ratios during most rebalancing periods, demonstrating effective stabilization of the weights; Garbner's robust covariance technique demonstrates consistent resilience to downturns in high-volatility market environments; And Reduit-Wolf's contraction estimates also show a relatively stable improvement in sample skewness compared to the benchmark model. These results suggest that including a covariance noise or normalization term in the traditional expected value and variance-based approach to portfolio management helps reduce the impact of estimation error and market volatility on portfolio performance. The period of analysis for this paper is specified. Furthermore, it covers the observation period, highlights limitations related to market comprehensiveness and parameter selection, and provides guidance for future research by incorporating financial data from diverse sources and more advanced robust optimization techniques.

Modelling of Regression with Non-Gaussian AR Errors

Hansen-Jagannathan distance with many assets

This paper proposes methods to estimate and compare asset pricing models in settings with a large number of test assets. Models are specified through a linear stochastic discount factor (SDF). We propose two regularization schemes to extend the Hansen-Jagannathan distance to high-dimensional environments. In addition to stabilizing the inversion of the covariance matrix, the proposed regularizations admit an economic interpretation as relaxing the exact pricing restrictions, thereby accommodating market frictions. We derive the asymptotic properties of the SDF parameter estimator under a double asymptotic framework in which both the cross-sectional and time dimensions grow. These results allow for inference on whether individual factors are priced. We further develop tests for comparing competing asset pricing models under misspeci…cation, providing a formal procedure to identify the least misspecified model. The analysis covers both nested and non-nested specifications. An empirical application compares 4 models using a dataset of 647 test portfolios.