UNIFORM CONVERGENCE RATES FOR KERNEL ESTIMATION WITH DEPENDENT DATA

By B. Hansen. Econometric Theory, 2008

476 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/49515776b8906ce6acf1189bdf115d2515d00a63

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In Artificial Intelligence

1. Aurore Delaigle
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3. Jiti Gao
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In Statistics and Probability

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Citations in the corpus

• NONPARAMETRIC SPECIFICATION TESTING FOR NONLINEAR TIME SERIES WITH NONSTATIONARITY (2009, background): “In the stationary time series case, Hansen (2008) establishes uniform strong convergence”
• A semiparametric spatial dynamic model (2014, result): “For example, if si’s were i.i.d. with joint density f(·), then condition (4) holds with probability one which can be obtained in a similar way to Hansen [7].”
• Threshold Regression With a Threshold Boundary (2020, background): “in Hirano and Porter (2003), Chernozhukov and Hong (2004) and Knight (2006) - the boundary there is de…ned by the jump in the conditional density of q "directly", while the boundary in threshold regression is de…ned "indirectly" by the jump in the conditional expectation of another variable y.”
• Moving Beyond Sub-Gaussianity in High-Dimensional Statistics: Applications in Covariance Estimation and Linear Regression (2018, background): “Under standard smoothness conditions and a q-th order kernel K(·), for some q ≥ 2, it can be shown that |E{ψ̂(x)}− ψ(x)| ≤ O(hq) uniformly in x (see, for instance, Hansen (2008) and references therein) and hence, a tail bound for |ψ̂(x)−ψ(x)| can also be obtained.”
• Filtering, Prediction and Simulation Methods for Noncausal Processes (2016, background): “…future vectors uTC1; : : : ; uTCH are recovered 5 As we focus on the filtering and prediction, the regularity conditions that ensure the uniform convergence of stochastic function O… on any bounded sets of values .uTC1; : : : ; uTCH / is out of the scope of this article (e.g. Hansen, 2004, 2008).”
• From Predictive to Prescriptive Analytics (2014, background): “Under these conditions, we have the following sufficient conditions for asymptotic optimality, which are proven as consequences of universal pointwise convergence results of related supervised learning problem of Walk (2010) and Hansen (2008).”
• Fast bivariate P‐splines: the sandwich smoother (2010, background): “By the uniform convergence theory for kernel density estimators and NadarayaWatson kernel regression estimators (see, for instance, Hansen (2008)), sup κ,l ∣ nκ,l/(nI )− f(x̃κ, z̃l) ∣ ∣ = Op { √ I lnn/n+ I }”
• Functional-coefficient models for nonstationary time series data (2009, background): “Note that under some regularity conditions (see, e.g., the assumptions of Theorem 2 in Hansen (2008)), and by following the same arguments as in Hansen (2008), one can show2 that (2.15) holds with an = n−4/5 log(n).”
• Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions (2014, background): “rm rate of n−p/(2p+d) with strictly stationary, exponentially beta-mixing (respectively algebraically beta-mixing at rate γ) regressors with p>0 (resp. p>d/(2γ)), while the power series LS 3See Hansen (2008), Kristensen (2009), Masry (1996), Tsybakov (2009), Cattaneo and Farrell (2013) and the”
• Nonparametric dynamic panel data models: Kernel estimation and specification testing (2013, methodology): “, Masry (1996), Hansen (2008)], supu∈U |VNT (u)| = (nh!)−1/2[log(n)]1/2 and supu∈U |BNT (u)| = khk .”
• Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing (2014, unknown): “, if we replaced (12) with Y = X> 0 e D, then this would be a semiparametric generalization of the standard Heckman’s (1979) selection model, and if we replaced (12) with Y = max X> 0 e; 0 D then this would be a semiparametric generalization of Cragg’s (1971) double hurdle model.”
• Specification Test for Panel Data Models with Interactive Fixed Effects (2014, unknown): “…k (u)]p. Noting that max1≤i≤N supxE[ Pτ t=1 Zi,t (x)] 2 ≤ C2τh! for some C2 <∞, we can apply the exponential inequality for strong mixing processes (e.g., Hansen, 2008, pp.739-740) to bound the left hand side of (D.4) from above by NQPr (|ϕiT (xl)| ≥ C1) = NQ max 1≤i≤N sup 1≤l≤Q Pr ï̄̄̄ ¯ TX…”
• Estimating Semi-Parametric Panel Multinomial Choice Models Using Cyclic Monotonicity (2016, methodology): “For example, if a kernel regression estimator is used, one can show using Theorem 2 of Hansen (2008) that it suffices to assume that the covariates have tails that are thinner than polynomial.”
• Classification of non‐parametric regression functions in longitudinal data models (2017, methodology): “Conditions 2 and 3 are standard-type smoothness and moment conditions that are needed to derive uniform convergence results for the kernel estimators on which our methods are based; see Hansen (2008) for similar assumptions.”
• Local Gaussian correlation: A new measure of dependence (2013, methodology): “However, this gives nonsensical results when used in an approximation context, as has been realised by Hjort and Jones (1996) and others.”
• Inferring Welfare Maximizing Treatment Assignment Under Budget Constraints (2012, background): “They imply sufficient moment and bandwidth conditions for a rate of uniform convergence, obtained in Hansen (2008) and Newey (1994).”