Yanqin Fan, Fang Han, Wei Li, Xiao-Hua Zhou
arXiv 14 Aug 2019 · Mathematics — Statistics Theory · publishedJournal of Econometrics (2019) · 19 citations (OpenAlex)
arXiv:1908.05255 · PDF · DOI · OpenAlex · Extracted main text
The family of rank estimators, including Han's maximum rank correlation (Han, 1987) as a notable example, has been widely exploited in studying regression problems. For these estimators, although the linear index is introduced for alleviating the impact of dimensionality, the effect of large dimension on inference is rarely studied. This paper fills this gap via studying the statistical properties of a larger family of M-estimators, whose objective functions are formulated as U-processes and may be discontinuous in increasing dimension set-up where the number of parameters, $p_{n}$, in the model is allowed to increase with the sample size, $n$. First, we find that often in estimation, as $p_{n}/n\rightarrow 0$, $(p_{n}/n)^{1/2}$ rate of convergence is obtainable. Second, we establish Bahadur-type bounds and study the validity of normal approximation, which we find often requires a much stronger scaling requirement than $p_{n}^{2}/n\rightarrow 0.$ Third, we state conditions under which the numerical derivative estimator of asymptotic covariance matrix is consistent, and show that the step size in implementing the covariance estimator has to be adjusted with respect to $p_{n}$. All theoretical results are further backed up by simulation studies.
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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 | Khan, S. and Tamer, E (2007) Partial rank estimation of duration models with general forms of censoring | 1.000 | 7 | 3 | 100% |
| 2 | Sherman, R. P (1993) The limiting distribution of the maximum rank correlation estimator | 0.965 | 10 | 4 | 90% |
| 3 | Abrevaya, J. and Shin, Y (2011) Rank estimation of partially linear index models | 0.928 | 4 | 3 | 100% |
| 4 | Han, A. K (1987) Non-parametric analysis of a generalized regression model: the maximum rank correlation estimator | 0.928 | 4 | 3 | 100% |
| 5 | Sherman, R. P (1994) Maximal inequalities for degenerate U-processes with applications to optimization estimators | 0.874 | 6 | 2 | 100% |
| 6 | Cavanagh, C. and Sherman, R. P (1998) Rank estimators for monotonic index models | 0.843 | 3 | 3 | 100% |
| 7 | Pakes, A. and Pollard, D (1989) Simulation and the asymptotics of optimization estimators | 0.737 | 3 | 3 | 67% |
| 8 | Spokoiny, V (2012) Parametric estimation. Finite sample theory | 0.737 | 3 | 2 | 100% |
| 9 | van der Vaart, A. and Wellner, J (1996) Weak Convergence and Empirical Processes | 0.737 | 3 | 2 | 100% |
| 10 | Nolan, D. and Pollard, D (1987) U-processes: rates of convergence | 0.550 | 8 | 2 | 25% |
Showing the top 10 of 50 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Estimating High Dimensional Monotone Index Models by Iterative Convex Optimization | 0.585 | 3 | 1 |
| 2 | Exact Computation of Maximum Rank Correlation Estimator | 0.405 | 1 | 1 |
| 3 | Stochastic Learning of Semiparametric Monotone Index Models with Large Sample Size | 0.405 | 1 | 1 |
| 4 | Online Learning in Semiparametric Econometric Models | 0.405 | 1 | 1 |