Xuewen Li, Xiaojun Song, Xiaogang Wang, Feipeng Zhang
arXiv 20 Oct 2026 · Econometrics
arXiv:2610.28169 · PDF · Extracted main text
In this paper, we propose a simple score-based specification test for the Tobit regression model, implemented through a computationally efficient multiplier bootstrap. We test correct specification through the conditional moment restriction that the generalized Tobit residual has zero conditional mean, and construct a feasible score-based empirical process using the integrated conditional moments approach, conditioning on the estimated index so that no smoothing or tuning parameter is required. We derive a first-order uniform representation of the feasible process, showing how its limiting behavior is affected by maximum-likelihood estimation of the structural parameter, and obtain the asymptotic properties of the corresponding Kolmogorov--Smirnov statistic under the null, fixed alternatives, and a sequence of local alternatives. Since the limiting null distribution is non-pivotal, $p$-values are obtained from a multiplier bootstrap that mimics the first-order representation and therefore captures the parameter estimation uncertainty. Monte Carlo experiments, including an unknown-scale design, an index-visible/index-invisible power study, and comparisons with existing specification tests, confirm accurate size and competitive power across a range of designs and covariate dimensions. Two empirical applications further demonstrate the practical utility of our approach.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | H. L. Koul and W. X. Song and S. Liu (2014) Model checking in Tobit regression via nonparametric smoothing | 1.000 | 7 | 3 | 100% |
| 2 | Z. Sun and Y. Guo and T. Xie and M. Wang (2021) Model diagnostics of parametric Tobit model based on cumulative residuals | 1.000 | 7 | 3 | 100% |
| 3 | Greene, William H (2012) Econometric Analysis | 0.644 | 4 | 1 | 100% |
| 4 | V. Chernozhukov and D. Chetverikov and K. Kato (2013) Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors | 0.644 | 2 | 2 | 100% |
| 5 | M. A. Domínguez and I. N. Lobato (2020) Specification testing with estimated variables | 0.644 | 2 | 2 | 100% |
| 6 | Escanciano, Juan Carlos and Sant'Anna, Pedro H. C. and Song, Xiaojun (2026) Specification tests for generalised propensity scores using double projections self | 0.644 | 2 | 2 | 100% |
| 7 | A. W. van der Vaart and J. A. Wellner (1996) Weak Convergence and Empirical Processes: With Applications to Statistics | 0.550 | 12 | 2 | 25% |
| 8 | W. Stute (1997) Nonparametric model checks for regression | 0.511 | 2 | 1 | 100% |
| 9 | R. Winkelmann and S. Boes (2009) Analysis of Microdata | 0.511 | 2 | 1 | 100% |
| 10 | Santiago Acerenza and Otávio Bartalotti and Federico Veneri (2025) Testing identifying assumptions in Tobit models | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 36 scored citations.