A Test for Normality Based on Sample Entropy

By Oldrich A. Vasicek. 1976

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Citations in the corpus

Distinguishing Cause from Effect Using Observational Data: Methods and Benchmarks (2014, neutral): “As covariance function for HSIC, we use the popular Gaussian kernel: κ` : (x, x ′) 7→ exp ( −(x− x ′)2 `2 ) , with bandwidths selected by the median heuristic (Schölkopf and Smola, 2002), i.e., we take ˆ̀(u) := median{‖ui − uj‖ : 1 ≤ i j ≤ N, ‖ui − uj‖ 6= 0}, and similarly for ˆ̀(v).”
Fast Multidimensional Entropy Estimation by $k$-d Partitioning (2009, background): “Indeed, in one dimension this approach leads to estimators such as the " -spacing " estimator of [10] (see also [11]).”
Correcting moments for goodness of fit tests based on two entropy estimates (2003, methodology): “While Vasicek (1976) and Ebrahimi et al. (1994) directly obtained the nonparametric entropy estimators, Theil (1980), Dudewicz and van der Meulen (1987) and Bowman (1992) derived the nonparametric entropy estimators from the nonparametric distribution functions.”
Methods of Microarray Data Analysis III (2003, methodology): “Jung et al. [2004] (see Chapter 8 of this book) presented power analyses by setting the first D genes to be prognostic with some correlation, say, r, with log survival time and suggested that this inferential method should serve as an helpful tool for sample size and power calculations in designing ”
An Appraisal and Bibliography of Tests for Multivariate Normality (2004, methodology): “One was based on sample entropy, extending the univariate test of Vasicek (1976); the other was an integrated squared error statistic.”
Detecting Out-of-Distribution Inputs to Deep Generative Models Using Typicality (2019, background): “for normal [59], uniform [18], and exponential [15] distributions.”
Nonparametric entropy estimation. An overview (1997, background): “¿From a different point of view, and independently, Vasicek [63] introduced his test statistic Ĥn = 1 n n ∑”
On the Kozachenko-Leonenko entropy estimator (2016, methodology): “[18] O. Vasicek, A test for normality based on sample entropy, J. Roy.”
A comparison of various tests of normality (2007, background): “Three years later, a new normality test ‘Vasicek’s test of normality’ was suggested [12].”
Testing exponentiality based on characterizations of the exponential distribution (2011, background): “where Hmn = 1 n ∑n i=1 log { n 2m(x(i+m) − x(i−m)) } is Vasicek’s [29] entropy estimator and the window size m is a positive integer smaller than n/2, x(i) = x(1) if i < 1, x(i) = x(n) if i > n.”
A new class of random vector entropy estimators and its applications in testing statistical hypotheses (2005, methodology): “by Vasicek [9] and compare it with the simulated power of some well-known goodness-offit tests.”
Efficient multivariate entropy estimation via $k$-nearest neighbour distances (2016, background): “…2017 In statistical contexts, it is often the estimation of entropy that is of primary interest, for instance in goodness-of-fit tests of normality (Vasicek, 1976) or uniformity (Cressie, 1976), tests of independence (Goria et al., 2005), independent component analysis (Miller and Fisher, 2003)…”