arXiv subjects

Yoshimasa Uematsu

Publications and source records attributed to Yoshimasa Uematsu.

13 recordsLinked to original sources

arXiv2026

Moment-Based Adjustments of Statistical Inference in High-Dimensional Generalized Linear Models

We develop a statistical inference method for generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients $p$ is of the same order as the sample size $n$. In this regime, constructing confidence intervals requires estimating unknown hyperparameters, such as the signal strength. However, existing estimators for the hyperparameters are not stably applicable to GLMs when $p/n$ is close to or greater than $1$, both theoretically and empirically. In this study, we develop an estimator for the hyperparameter that addresses the issue and establish an inferential framework, provided that the link function of the GLM exhibits an asymmetry property. The proposed estimator utilizes the moments of the output variable of GLMs and a convex surrogate loss. Our framework is theoretically valid even when the limit of $p/n$ exceeds $1$, ensuring the strong consistency of the hyperparameter estimator and asymptotically attaining the exact coverage probability of the confidence intervals. Our numerical experiments support these theoretical results.

math.ST↗

arXiv2026

High-Dimensional Single-Index Models: Link Estimation and Marginal Inference

This study proposes a novel method for estimation and hypothesis testing in high-dimensional single-index models. We address a common scenario where the sample size and the dimension of regression coefficients are large and comparable. Unlike previous approaches, which often overlook the estimation of the unknown link function, we introduce a new method for link function estimation. Leveraging the information from the estimated link function, we propose more efficient estimators that are better aligned with the underlying model. Furthermore, we rigorously establish the asymptotic normality of each coordinate of the estimator. This provides a valid construction of confidence intervals and $p$-values for any finite collection of coordinates. Numerical experiments validate our theoretical results.

math.ST↗

arXiv2026

Revisiting Asymptotic Theory for Principal Component Estimators of Approximate Factor Models

It is well known that approximate factor models exhibit rotation indeterminacy. Principal component (PC) estimators are typically analyzed relative to a rotated factor-loading representation, but the commonly used rotation depends on the estimator itself, leaving unclear which fixed population parameters are estimated. We show that any starting representation of the common component can be mapped by a rotation matrix $\bH$, constructed without using the PC estimator or the idiosyncratic errors and unique up to column signs, to a population representation satisfying the same PC normalization as the estimator. Although $\bH$ depends on the starting representation, the resulting representation is invariant to that choice up to simultaneous column sign changes. We call the resulting factors and loadings the pseudo-true (PC-normalized) parameters. Under a general weak factor model allowing signal eigenvalues to diverge at possibly different rates, we establish consistency and asymptotic normality of the PC estimators for these fixed, estimator-independent targets, together with fixed-target asymptotic theory for factor-augmented regressions. The theory thereby justifies confidence intervals for PC-normalized factors, gives loading profiles a fixed-target interpretation, and identifies the population coefficients associated with estimated PC factors in factor-augmented regressions.

math.ST↗

arXiv2026

Post-Screening Portfolio Selection

We propose post-screening portfolio selection (PS$^2$), a two-step framework for high-dimensional mean--variance investing. First, assets are screened by Lasso-type regression of a constant on excess returns without an intercept. Second, portfolio weights are estimated on the selected set using standard low-dimensional methods. Because strong factors can destroy sparsity in real data, we further introduce PS$^2$ with factors (FPS$^2$), which defactors returns before screening and allows factor investing in the final step. We establish theoretical guarantees, and simulations and an empirical application show competitive performance, especially when sparse screening is appropriate or strong factors are explicitly accommodated.

q-fin.PM↗

arXiv2026

Testing Conditional Independence via the Spectral Generalized Covariance Measure: Beyond Euclidean Data

We propose a conditional independence (CI) test based on a new measure, the \emph{spectral generalized covariance measure} (SGCM). The SGCM is constructed by expressing the squared norm of the conditional cross-covariance operator in spectral coordinates and approximating it in finite dimensions using data-dependent bases obtained from empirical covariance operators. This avoids direct estimation of conditional mean embeddings and reduces nuisance estimation to a finite collection of scalar-valued regressions. On the theoretical side, under a doubly robust product-bias condition, we establish uniform bootstrap validity and uniform asymptotic size control, and derive nontrivial uniform power and uniform consistency over classes of projected separated alternatives. The analysis also clarifies the role of spectral truncation: stronger truncation relaxes nuisance-estimation requirements, whereas weaker truncation retains more of the projected signal. To support applications beyond Euclidean data, we develop characteristic-kernel constructions on general Polish spaces via a pullback principle and non-constant completely monotone transforms of continuous negative-type semimetrics, with closure under finite tensor products. These constructions cover examples such as distribution-valued data, curves in metric spaces, and manifold-valued observations. Simulations show near-nominal size in the main settings and competitive power across a range of challenging scenarios.

stat.ME↗

arXiv2025

Bias Correction in Factor-Augmented Regression Models with Weak Factors

In this paper, we study the asymptotic bias of the factor-augmented regression estimator and its reduction, which is augmented by the $r$ factors extracted from a large number of $N$ variables with $T$ observations. In particular, we consider general weak latent factor models with $r$ signal eigenvalues that may diverge at different rates, $N^{α_{k}}$, $0<α_{k}\leq 1$, $k=1,\dots,r$. In the existing literature, the bias has been derived using an approximation for the estimated factors with a specific data-dependent rotation matrix $\hat{H}$ for the model with $α_{k}=1$ for all $k$, whereas we derive the bias for weak factor models. In addition, we derive the bias using the approximation with a different rotation matrix $\hat{H}_q$, which generally has a smaller bias than with $\hat{H}$. We also derive the bias using our preferred approximation with a purely signal-dependent rotation $H$, which is unique and can be regarded as the population version of $\hat{H}$ and $\hat{H}_q$. Since this bias is parametrically inestimable, we propose a split-panel jackknife bias correction, and theory shows that it successfully reduces the bias. The extensive finite-sample experiments suggest that the proposed bias correction works very well, and the empirical application illustrates its usefulness in practice.

stat.ME↗

arXiv2025

Sequential Correct Screening and Post-Screening Inference

Selecting the top-$m$ variables with the $m$ largest population parameters from a larger set of candidates is a fundamental problem in statistics. In this paper, we propose a novel methodology called Sequential Correct Screening (SCS), which sequentially screens out variables that are not among the top-$m$. A key feature of our method is its anytime validity; it provides a sequence of variable subsets that, with high probability, always contain the true top-$m$ variables. Furthermore, we develop a post-screening inference (PSI) procedure to construct confidence intervals for the selected parameters. Importantly, this procedure is designed to control the false coverage rate (FCR) whenever it is conducted -- an aspect that has been largely overlooked in the existing literature. We establish theoretical guarantees for both SCS and PSI, and demonstrate their performance through simulation studies and an application to a real-world dataset on suicide rates.

stat.ME↗

arXiv2024

Discovering the Network Granger Causality in Large Vector Autoregressive Models

This paper proposes novel inferential procedures for discovering the network Granger causality in high-dimensional vector autoregressive models. In particular, we mainly offer two multiple testing procedures designed to control the false discovery rate (FDR). The first procedure is based on the limiting normal distribution of the $t$-statistics with the debiased lasso estimator. The second procedure is its bootstrap version. We also provide a robustification of the first procedure against any cross-sectional dependence using asymptotic e-variables. Their theoretical properties, including FDR control and power guarantee, are investigated. The finite sample evidence suggests that both procedures can successfully control the FDR while maintaining high power. Finally, the proposed methods are applied to discovering the network Granger causality in a large number of macroeconomic variables and regional house prices in the UK.

stat.ME↗

arXiv2024

Robust Reproducible Network Exploration

We propose a novel methodology for discovering the presence of relationships realized as binary time series between variables in high dimension. To make it visually intuitive, we regard the existence of a relationship as an edge connection, and call a collection of such edges a network. Our objective is thus rephrased as uncovering the network by selecting relevant edges, referred to as the network exploration. Our methodology is based on multiple testing for the presence or absence of each edge, designed to ensure statistical reproducibility via controlling the false discovery rate (FDR). In particular, we carefully construct $p$-variables, and apply the Benjamini-Hochberg (BH) procedure. We show that the BH with our $p$-variables controls the FDR under arbitrary dependence structure with any sample size and dimension, and has asymptotic power one under mild conditions. The validity is also confirmed by simulations and a real data example.

stat.ME↗

arXiv2018

IPAD: Stable Interpretable Forecasting with Knockoffs Inference

Interpretability and stability are two important features that are desired in many contemporary big data applications arising in economics and finance. While the former is enjoyed to some extent by many existing forecasting approaches, the latter in the sense of controlling the fraction of wrongly discovered features which can enhance greatly the interpretability is still largely underdeveloped in the econometric settings. To this end, in this paper we exploit the general framework of model-X knockoffs introduced recently in Candès, Fan, Janson and Lv (2018), which is nonconventional for reproducible large-scale inference in that the framework is completely free of the use of p-values for significance testing, and suggest a new method of intertwined probabilistic factors decoupling (IPAD) for stable interpretable forecasting with knockoffs inference in high-dimensional models. The recipe of the method is constructing the knockoff variables by assuming a latent factor model that is exploited widely in economics and finance for the association structure of covariates. Our method and work are distinct from the existing literature in that we estimate the covariate distribution from data instead of assuming that it is known when constructing the knockoff variables, our procedure does not require any sample splitting, we provide theoretical justifications on the asymptotic false discovery rate control, and the theory for the power analysis is also established. Several simulation examples and the real data analysis further demonstrate that the newly suggested method has appealing finite-sample performance with desired interpretability and stability compared to some popularly used forecasting methods.

math.ST↗

arXiv2017

Penalized Likelihood Estimation in High-Dimensional Time Series Models and its Application

This paper presents a general theoretical framework of penalized quasi-maximum likelihood (PQML) estimation in stationary multiple time series models when the number of parameters possibly diverges. We show the oracle property of the PQML estimator under high-level, but tractable, assumptions, comprising the first half of the paper. Utilizing these results, we propose in the latter half of the paper a method of sparse estimation in high-dimensional vector autoregressive (VAR) models. Finally, the usability of the sparse high-dimensional VAR model is confirmed with a simulation study and an empirical analysis on a yield curve forecast.

math.ST↗

arXiv2017

SOFAR: large-scale association network learning

Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network structures via layers of sparse latent factors ranked by importance. Yet sparsity and orthogonality have been two largely incompatible goals. To accommodate both features, in this paper we suggest the method of sparse orthogonal factor regression (SOFAR) via the sparse singular value decomposition with orthogonality constrained optimization to learn the underlying association networks, with broad applications to both unsupervised and supervised learning tasks such as biclustering with sparse singular value decomposition, sparse principal component analysis, sparse factor analysis, and spare vector autoregression analysis. Exploiting the framework of convexity-assisted nonconvex optimization, we derive nonasymptotic error bounds for the suggested procedure characterizing the theoretical advantages. The statistical guarantees are powered by an efficient SOFAR algorithm with convergence property. Both computational and theoretical advantages of our procedure are demonstrated with several simulation and real data examples.

stat.ME↗

arXiv2017

Macroeconomic Forecasting and Variable Selection with a Very Large Number of Predictors: A Penalized Regression Approach

This paper studies macroeconomic forecasting and variable selection using a folded-concave penalized regression with a very large number of predictors. The penalized regression approach leads to sparse estimates of the regression coefficients, and is applicable even if the dimensionality of the model is much larger than the sample size. The first half of the paper discusses the theoretical aspects of a folded-concave penalized regression when the model exhibits time series dependence. Specifically, we show the oracle inequality and the oracle property for ultrahigh-dimensional time-dependent regressors. The latter half of the paper shows the validity of the penalized regression using two motivating empirical applications. The first forecasts U.S. GDP with the FRED-MD data using the MIDAS regression framework, where there are more than 1000 covariates, while the sample size is at most 200. The second examines how well the penalized regression screens the hidden portfolio with around 40 stocks from more than 1800 potential stocks using NYSE stock price data. Both applications reveal that the penalized regression provides remarkable results in terms of forecasting performance and variable selection.

stat.AP↗