On LASSO Inference for High Dimensional Predictive Regression

• URL: http://arxiv.org/abs/2409.10030v1
• Date: Mon, 16 Sep 2024 06:41:58 GMT
• Title: On LASSO Inference for High Dimensional Predictive Regression
• Authors: Zhan Gao, Ji Hyung Lee, Ziwei Mei, Zhentao Shi,
• Abstract summary: We propose a novel estimator called IVX-desparsified LASSO (XDlasso) XDlasso eliminates the shrinkage bias simultaneously. We investigate the predictability of the U.S. stock returns based on the earnings-price ratio, and the predictability of the U.S. inflation using the unemployment rate.
• Score: 4.658398919599387
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: LASSO introduces shrinkage bias into estimated coefficients, which can adversely affect the desirable asymptotic normality and invalidate the standard inferential procedure based on the $t$-statistic. The desparsified LASSO has emerged as a well-known remedy for this issue. In the context of high dimensional predictive regression, the desparsified LASSO faces an additional challenge: the Stambaugh bias arising from nonstationary regressors. To restore the standard inferential procedure, we propose a novel estimator called IVX-desparsified LASSO (XDlasso). XDlasso eliminates the shrinkage bias and the Stambaugh bias simultaneously and does not require prior knowledge about the identities of nonstationary and stationary regressors. We establish the asymptotic properties of XDlasso for hypothesis testing, and our theoretical findings are supported by Monte Carlo simulations. Applying our method to real-world applications from the FRED-MD database -- which includes a rich set of control variables -- we investigate two important empirical questions: (i) the predictability of the U.S. stock returns based on the earnings-price ratio, and (ii) the predictability of the U.S. inflation using the unemployment rate.

Related papers

• Distributionally Robust Instrumental Variables Estimation [10.765695227417865]
  We propose a distributionally robust framework for instrumental variables (IV) estimation. We show that Wasserstein DRIVE could be preferable in practice, particularly when the practitioner is uncertain about model assumptions or distributional shifts in data.
  arXiv  Detail & Related papers  (2024-10-21T04:33:38Z)
• Method-of-Moments Inference for GLMs and Doubly Robust Functionals under Proportional Asymptotics [30.324051162373973]
  We consider the estimation of regression coefficients and signal-to-noise ratio in high-dimensional Generalized Linear Models (GLMs) We derive Consistent and Asymptotically Normal (CAN) estimators of our targets of inference. We complement our theoretical results with numerical experiments and comparisons with existing literature.
  arXiv  Detail & Related papers  (2024-08-12T12:43:30Z)
• Model-Based Epistemic Variance of Values for Risk-Aware Policy Optimization [59.758009422067]
  We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. We propose a new uncertainty Bellman equation (UBE) whose solution converges to the true posterior variance over values. We introduce a general-purpose policy optimization algorithm, Q-Uncertainty Soft Actor-Critic (QU-SAC) that can be applied for either risk-seeking or risk-averse policy optimization.
  arXiv  Detail & Related papers  (2023-12-07T15:55:58Z)
• Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability [50.44439018155837]
  We propose to include a calibration term directly into the training objective of the neural model. By introducing a relaxation of the classical formulation of calibration error we enable end-to-end backpropagation. It is directly applicable to existing computational pipelines allowing reliable black-box posterior inference.
  arXiv  Detail & Related papers  (2023-10-20T10:20:45Z)
• Selective Nonparametric Regression via Testing [54.20569354303575]
  We develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor.
  arXiv  Detail & Related papers  (2023-09-28T13:04:11Z)
• Quantifying predictive uncertainty of aphasia severity in stroke patients with sparse heteroscedastic Bayesian high-dimensional regression [47.1405366895538]
  Sparse linear regression methods for high-dimensional data commonly assume that residuals have constant variance, which can be violated in practice. This paper proposes estimating high-dimensional heteroscedastic linear regression models using a heteroscedastic partitioned empirical Bayes Expectation Conditional Maximization algorithm.
  arXiv  Detail & Related papers  (2023-09-15T22:06:29Z)
• On LASSO for High Dimensional Predictive Regression [0.0]
  This paper examines LASSO, a widely-used $L_1$-penalized regression method, in high dimensional linear predictive regressions. The consistency of LASSO is contingent upon two key components: the deviation bound of the cross product of the regressors and the error term. Using machine learning and macroeconomic domain expertise, LASSO demonstrates strong performance in forecasting the unemployment rate.
  arXiv  Detail & Related papers  (2022-12-14T06:14:58Z)
• Learning Probabilistic Ordinal Embeddings for Uncertainty-Aware Regression [91.3373131262391]
  Uncertainty is the only certainty there is. Traditionally, the direct regression formulation is considered and the uncertainty is modeled by modifying the output space to a certain family of probabilistic distributions. How to model the uncertainty within the present-day technologies for regression remains an open issue.
  arXiv  Detail & Related papers  (2021-03-25T06:56:09Z)
• STELAR: Spatio-temporal Tensor Factorization with Latent Epidemiological Regularization [76.57716281104938]
  We develop a tensor method to predict the evolution of epidemic trends for many regions simultaneously. STELAR enables long-term prediction by incorporating latent temporal regularization through a system of discrete-time difference equations. We conduct experiments using both county- and state-level COVID-19 data and show that our model can identify interesting latent patterns of the epidemic.
  arXiv  Detail & Related papers  (2020-12-08T21:21:47Z)
• The Reciprocal Bayesian LASSO [0.0]
  We consider a fully Bayesian formulation of the rLASSO problem, which is based on the observation that the rLASSO estimate for linear regression parameters can be interpreted as a Bayesian posterior mode estimate. On simulated and real datasets, we show that the Bayesian formulation outperforms its classical cousin in estimation, prediction, and variable selection.
  arXiv  Detail & Related papers  (2020-01-23T01:21:59Z)
• On Low-rank Trace Regression under General Sampling Distribution [9.699586426043885]
  We show that cross-validated estimators satisfy near-optimal error bounds on general assumptions. We also show that the cross-validated estimator outperforms the theory-inspired approach of selecting the parameter.
  arXiv  Detail & Related papers  (2019-04-18T02:56:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.