RATES OF CONVERGENCE FOR EMPIRICAL PROCESSES OF STATIONARY MIXING SEQUENCES

By Bin Yu. 1994

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Citations in the corpus

Rates of uniform convergence of empirical means with mixing processes (2002, background): “The above bound may be compared with the bounds derived by Yu (1994), especially Eq.”
Inference on Causal and Structural Parameters using Many Moment Inequalities (2013, unknown): “/3{1 ∨log(p/∆)b}2/3, where ∆ = maxb 1≤j,k≤p |(1/(mq)) Pm l=1(SljSlk −E[SljSlk])|. Hence it suﬃces to prove that P(∆b>C′n−c′ log−2 p) ≤ Cn−c + (m− 1)b r with suitable c,c′,C,C′. By Corollary 2.7 in Yu (1994), for every t>0, P(∆b>t) ≤ P(∆e>t)+(m−1)br, where∆ = maxe 1≤j,k≤p |(1/(mq)) Pm l=1”
Uniform convergence of Vapnik–Chervonenkis classes under ergodic sampling (2010, background): “Yu [27] extends these results to β-mixing (absolutely regular) processes X and and classes F satisfying metric entropy conditions.”
Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification (2018, methodology): “The most well-established technique in the statistics literature for dealing with non-independent, time-series data is the use of mixing-time arguments [Yu, 1994].”
Learning from Limited Demonstrations (2013, background): “In the vehicle brake control simulation [21], the agent’s goal is reach a target velocity, then maintain that target.”
Of Copulas, Quantiles, Ranks and Spectra - An L1-Approach to Spectral Analysis (2011, methodology): “11) In this proof, we use a blocking argument by Yu [42] – call it the independent blocks argument.”
Statistical linear estimation with penalized estimators: an application to reinforcement learning (2012, background): “This can be arranged for example if the features φi(Xt) and rewards Rt+1 are a.s. bounded, and if we assume appropriate mixing, such as exponential β-mixing (Yu, 1994), or when the Markov chain (Xt)t≥0 forgets its past sufficiently rapidly (Samson, 2000).”
Estimation and Inference about Heterogeneous Treatment Effects in High-Dimensional Dynamic Panels. (2017, background): “nductive hypothesis. The bound iiifollows from Lemma 7.8 with n= Nand i= ( X i1;X i2;:::;X (L 1)) ( X iL) and i= ( X i1;X i2;:::;X iL), and Condition (7.20). Lemma 7.10 (Extension of Lemma 2.6 from Yu (1994)). Let Q i:= ( X i1;X i2;:::;X iL);i2 f1;2;:::;Ngwith marginals Q il;1 6 l6 L. Suppose for so”
Rademacher Complexity Bounds for Non-I.I.D. Processes (2008, methodology): “analyses [7, 9, 10, 15], we use a technique transferring the original problem based on dependent points to one based on a sequence of independent blocks .”
Testing Many Moment Inequalities (2013, unknown): “7 in Yu (1994), for every t > 0, P(∆̂ > t) ≤ P(∆̃ > t) + (m− 1)br, where ∆̃ = max1≤j,k≤p |(1/(mq)) ∑m l=1(S̃ljS̃lk−E[SljSlk])| (recall that S̃l, 1 ≤ l ≤ m, are independent with S̃l d = Sl).”
Quantile spectral analysis for locally stationary time series (2014, methodology): “The existence of such a sequence and the measurability issues that arise are addressed in Yu (1994). The Γ- and ∆-block subsequences are denoted by XΓ, YΓ, X∆ and Y∆, respectively: for instance, XΓ := X(Γ1), X(Γ2), . . . , X(Γμn). We obtain XΓ by leaving out every other block in the original sequenc”
Time series prediction and online learning (2016, background): “Keywords: time series prediction, on-line learning, generalization bounds, regret minimization, validation, model selection, ensembles, stability, non-stationary, non-mixing.”
Regularization in reinforcement learning (2011, methodology): “process to more general mixing processes [Doukhan, 1994; Yu, 1994].”
Modelling multivariate volatilities via conditionally uncorrelated components (2008, background): “Under the additional condition E|XtiXtj|2p ∞ and the mixing condition that is given in condition (d), theorem 1 of Arcones and Yu (1994) implies that the set of functions {XtiXtj I.Xt−k ∈ B/, B ∈B} is Conditionally Uncorrelated Components 701 a Donsker class, and hence the process {Δn,k.”
Fitted Q-iteration in continuous action-space MDPs (2007, methodology): “, ZN ∈ Z is a stationary β-mixing process with mixing coefficients {βm}, Z ′ t ∈ Z (t ∈ H) are the block-independent “ghost” samples as done by [23], H = { 2ikN + j : 0 ≤ i < mN , 1 ≤ j ≤ kN } and F is a permissible class of Z → [−K, K] functions.”
Finite-sample analysis of least-squares policy iteration (2012, methodology): “Proposition 15 (Yu, 1994) Let X1, .”