Phillips and Solo (1992, Annals of Statistics 20, 971–2001) provided sets of conditions concerning the summability of coefficients and the properties of innovations in discrete-time linear processes such that normalized sums satisfy certain asymptotic properties, such as laws of large numbers, central limit theorems, and invariance principles. In this article, we consider ARMA processes in continuous time that are sampled at discrete-time intervals and provide conditions on the continuous-time process such that the results of Phillips and Solo can be utilized for normalized sums of the discrete-time observations. We utilize a state-space representation in the case of stock and flow variables, both of which are a linear combination of the state vector, and derive the relevant asymptotics based on multivariate extensions of the Phillips–Solo results. An illustrative application of the results to unit (zero) root testing is provided.
Infinite-order U -statistics play a vital role in modern statistics. However, given their degree k n $k_n$ k Subscript n depends on the sample size n , quantifying their variability is quite challenging, as fixed-degree theories cannot be directly adopted. In this article, we propose a jackknife empirical likelihood (EL) framework that can be used to construct confidence intervals for an infinite-order U -statistic. We establish sufficient conditions for the limiting chi-squared distribution of the JEL ratio statistic and introduce an efficient partition-sampling realization for practical implementation. To evaluate the performance of the proposed methodology, we conduct simulation studies in the context of subsampling-based ensemble methods and the maximum test, respectively, comparing its performance with four competing methods. The simulation studies yield satisfactory results across the board. Finally, we demonstrate the practical application of our method using a United States Forest Service timber auctions dataset to predict the highest bid at an auction.
This study examines the large-sample behavior of an ordinary least squares (OLS) estimator within a correctly specified nonlinear autoregressive distributed lag (NARDL) model for nonstationary data. Although the OLS estimator suffers from an asymptotically singular matrix problem, it remains consistent for unknown model parameters and asymptotically follows a mixed normal distribution. Additionally, we examine the large-sample behavior of the standard Wald test, as defined by the OLS estimator, for asymmetries in long- and short-run NARDL parameters, and enhance this analysis with a super-consistent long-run parameter estimator. We then confirm the theory on the Wald test using Monte Carlo simulations. Finally, using U.S. GDP and exogenous fiscal shock data, we demonstrate the use of the OLS estimator and show statistical evidence of long- and short-run symmetries between the effects of tax increases and decreases on U.S. GDP.
Abstract We develop a convex-analytic framework for constructing and analyzing a broad class of penalized estimators. Our method defines penalized estimators by applying proximal operators to benchmark estimators, rather than by penalizing the benchmark criterion itself. We establish general finite-sample properties, derive unified asymptotic distribution results, and provide tractable conditions for oracle selection and oracle asymptotic efficiency. We then apply the framework to linear regression with irregular designs, including singular and nearly-singular cases. In this setting, where the coefficient vector need not be point identified, we motivate the Ridgeless estimand as the inferential target, construct a n $\sqrt {n}$ StartRoot n EndRoot -consistent modified Ridgeless benchmark estimator, and combine it with adaptive proximal penalization to obtain, to the best of our knowledge, the first penalized estimator achieving the oracle property under both regular and irregular designs.
Many real-world policies and business interventions require assessing short-term effects to inform timely decisions, even though most causal inference methods focus on long-term average treatment effects. In this paper, we introduce average treatment effect localization (ATEL), which captures localized, short-term policy impacts in panel data settings with a single treated unit and provides early indicators of policy impact. To accommodate both time-varying and nonlinear effects of observed and unobserved covariates, we propose a nonparametric model for untreated outcome, interpreted as a time-varying factor model via sieve approximation. Estimating the time-varying factor model is challenging due to the boundary bias and identification. Our estimation method based on diversified projection can effectively address these issues. We develop an asymptotic distribution theory to facilitate inference for the ATEL estimator. In an empirical application, we apply our proposed methodology to assess the impact of right-to-carry laws on violent crime rate.
