On the rosenthal inequality for mixing fields

Fazekas, István; Kukush, Alexander; Tómács, Tibor

doi:10.1007/bf02529642

Cited by 6 publications

(7 citation statements)

References 2 publications

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“…The result follows from a Rosenthal type inequality for mixing random fields, which was first suggested in this setting by Doukhan (1994). However, we have based our result on the slightly weaker version derived by Fazekas et al (2000), in order to control the constant C 1 more precisely. The theorem shows that the constant only depends on the mixing coefficients in a monotone fashion.…”

Section: C1 Technical Prerequisitesmentioning

confidence: 99%

Validating Approximate Slope Homogeneity in Large Panels

Kutta¹,

Dette²

2022

Preprint

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Statistical inference for large data panels is omnipresent in modern economic applications. An important benefit of panel analysis is the possibility to reduce noise and thus to guarantee stable inference by intersectional pooling. However, it is wellknown that pooling can lead to a biased analysis if individual heterogeneity is too strong. In classical linear panel models, this trade-off concerns the homogeneity of slope parameters, and a large body of tests has been developed to validate this assumption. Yet, such tests can detect inconsiderable deviations from slope homogeneity, discouraging pooling, even when practically beneficial.In order to permit a more pragmatic analysis, which allows pooling when individual heterogeneity is sufficiently small, we present in this paper the concept of approximate slope homogeneity. We develop an asymptotic level α test for this hypothesis, that is uniformly consistent against classes of local alternatives. In contrast to existing methods, which focus on exact slope homogeneity and are usually sensitive to dependence in the data, the proposed test statistic is (asymptotically) pivotal and applicable under simultaneous intersectional and temporal dependence. Moreover, it can accommodate the realistic case of panels with large intersections. A simulation study and a data example underline the usefulness of our approach.

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Section: C1 Technical Prerequisitesmentioning

confidence: 99%

Validating Approximate Slope Homogeneity in Large Panels

Kutta¹,

Dette²

2022

Preprint

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“…In addition, by (3), the last expression in the inequality is bounded. We may then adapt Theorem 1 in Fazekas, Kukush, and Tómács (2000) to the lattice s n Z d and so there exists a constant c 2 > 0 such that…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…Then, by (2) and (C2), we may apply Theorem 1 in Fazekas et al (2000), which states the existence of c 1 > 0 such that…”

Section: Assumption (I)mentioning

confidence: 99%

A general central limit theorem and a subsampling variance estimator for α‐mixing point processes

Biscio

Waagepetersen

2019

Scandinavian J Statistics

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We establish a central limit theorem for multivariate summary statistics of nonstationary α‐mixing spatial point processes and a subsampling estimator of the covariance matrix of such statistics. The central limit theorem is crucial for establishing asymptotic properties of estimators in statistics for spatial point processes. The covariance matrix subsampling estimator is flexible and model free. It is needed, for example, to construct confidence intervals and ellipsoids based on asymptotic normality of estimators. We also provide a simulation study investigating an application of our results to estimating functions.

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“…Bolthausen [1] and Guyon [11] extended it to˛-mixing random fields. Fazekas [10] and Fazekas and Kukush [8] presented the so-called infill-increasing versions of Guyon's result for the bounded and the uniformly integrable cases, respectively. These papers do not contain the proofs of the theorems mentioned (a sketch of the proof can be found in [9]).…”

Section: Introductionmentioning

confidence: 99%

“…Then there is a constant c such that for any finite subset D of Z d .We remark that the proof of the Rosenthal inequality (2.11) follows from (2.12) below, by using the so-called interpolation lemma. Details and the general form of the Rosenthal inequality can be found, e. g., in[8].Remark 2. Using the notation of Lemma 2, let > 0, and assume that c…”

mentioning

confidence: 99%