Bounds on Expectations of Linear Systematic Statistics Based on Dependent Samples

By Barry C. Arnold, R. A. Groeneveld. 1979

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Fall of Empires: Breaking Byzantine-tolerant SGD by Inner Product Manipulation (2019, neutral): “9(a) from Arnold et al. (1979)), we have Remark 2.”
Adaptive Communication Strategies to Achieve the Best Error-Runtime Trade-off in Local-Update SGD (2018, background): “Then, The proof follows from the bound on expected order statistics given by (Arnold & Groeneveld, 1979).”
Coding for fast content download (2012, methodology): “Instead, we use the following upper bounds on the expectation and variance of S derived in [20] and [21].”
Anytime Minibatch: Exploiting Stragglers in Online Distributed Optimization (2020, methodology): “Using the result of Arnold & Groeneveld (1979); Bertsimas et al. (2006) we ﬁnd that where σ is the standard deviation of T i ( t ) .”
Estimating the Maximum Expected Value: An Analysis of (Nested) Cross Validation and the Maximum Sample Average (2013, background): “An upper bound for arbitrary means and variances is given by Aven [1985]: Bias(µ̂ME∗ ) ≤ √ √ √ √ M − 1 M M ∑ i Var (µ̂i) , (7) which is tight when the estimators are iid [Arnold and Groeneveld, 1979], indicating that iid variables are a worst-case setting.”
On the Delay-Storage Trade-Off in Content Download from Coded Distributed Storage Systems (2013, methodology): “The proof of (10) and (11) are given in [31] and [30] respectively.”