The Empirical Characteristic Function and Its Applications

By Andrey Feuerverger, R. Mureika. 1977

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “Given an i.i.d. sample x1, . . . ,xn, the empirical estimate µ̂P(t) = 1n ∑n i=1 exp(ix ⊤ i t) becomes an empirical characteristic function (ECF).”
Optimal Rates for Random Fourier Features (2015, background): “(i) Theorem 1 shows that̂k is a consistent estimator ofk in the topology of compact convergence as m → ∞ with the rate of a.s. convergence being √ m−1 log |S| (almost sure convergence is guaranteed by the first Borel-Cantelli lemma).”
Empirical Characteristic Function Estimation and Its Applications (2004, unknown): “Denote the covariance matrix of Vn by Ω and it has been shown that (see, for example, Feuerverger and Mureika (1977)) Ω = ΩRR ΩRI ΩIR ΩII , where the elements in the partitions associated with rj and rk are given by (ΩRR)jk = 1 2 (Re[c(rj + rk)] +Re[c(rj − rk)])−Re[c(rj)]Re[c(rk)], (ΩRI)jk = 1 2…”
Estimation of Continuous-Time Processes via the Empirical Characteristic Function (2002, methodology): “The basic idea of the empirical characteristic function estimation method for time series models was rst proposed by Feuerverger (1990), who extended earlier results on the ECF method (see Feuerverger and Mureika, 1977; Feuerverger and McDunnough, 1981) to estimate stationary stochastic processes.”
Bayesian Predictive Beamforming for Vehicular Networks: A Low-Overhead Joint Radar-Communication Approach (2020, unknown): “According to the characteristic function [29], the expectation of e jθ given θ ∼ N ( θ ; 0 , λ θ ) is E [ e jθ ] = e 0+( jθ ) 2 / 2 = e − λ θ / 2 .”
Diverging Moments and Parameter Estimation (2005, methodology): “It is also shown in Feuerverger and Mureika (1977) that YN (u) converges weakly towardsY (u) in any finite interval, provided that IE|X|1+δ < ∞.”
Bibliography on stable distributions, processes and related topics (2004, methodology): “Empirical characteristic function methods: Koutrouvelis (1980), Koutrouvelis (1981), Csorgo (1981), Feuerverger and Mureika (1977), Feuerverger and McDunnough (1981b), Feuerverger and McDunnough (1981a), Kogon and Williams (1998), Yu (2004), Besbeas and Morgan (2008), Bibalan et al. (2017),…”
Applications of distance correlation to time series (2016, background): “al characteristic functions for inference problems, including estimation in some special parametric settings and testing for goodness of t, has a long history dating back to the 70s (see for example, Feuerverger and Mureika (1977), Csorg}o (1981a,1981b,1981c) Feuerverger (1993)). More recently, ther”
Estimation of Nonlinear Models with Measurement Error Using Marginal Information1 (2004, background): “…(1996), Lemma 1, p. 164, claim that sup |t|<∞ ¯̄̄ φ̂(t)− φ(t) ¯̄̄ = o Ãr logn n ! a.s. (58) This cannot be correct, because it would imply uniform convergence of the empirical characteristic function without bounds on t, a result that does not hold (see e.g. Feuerverger and Mureika (1977), p. 89).”
EMPIRICAL CHARACTERISTIC FUNCTION IN TIME SERIES ESTIMATION (2001, unknown): “…the inference based on the ECF should work as well as that based on the empirical DF+ The theory for the ECF in the i+i+d+ case is well understood ~Feuerverger and Mureika, 1977; Csörgő, 1981!+ Surprisingly, however, the ECF in the dependent case has received much less attention, and…”
A test for the two-sample problem based on empirical characteristic functions (2008, background): “Attending to the a.s. convergence of the e.c.f to the population c.f. (see for example Feuerverger and Mureika (1977) and Csörgő (1981a,b)), for testing H0 we consider the following test function Φn,m = { 1 if N Dn,m ≥ dn,m,α 0 otherwise, (2) where Dn,m is the sample version of D2, Dn,m = ∫…”