Central limit theorems for empirical andU-processes of stationary mixing sequences

Arcones, Miguel A.; Yu, Bin

doi:10.1007/bf02213360

Cited by 136 publications

(108 citation statements)

References 25 publications

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“…Therefore, Assumptions D1 and F2 permit the use of uniform central limit theorem of Arcones and Yu (1994), which implies that F n,δ converges in distribution to a Gaussian process with uniformly bounded paths, which confirms that (36) is…”

Section: Proofsupporting

confidence: 56%

“…The main tools in achieving this are the (uniform) law of large numbers (Andrews, 1988 and1992) and the uniform central limit theorem (Arcones andYu, 1994, andYu, 1994) for mixing processes. On the other hand, computational issues and robustness properties of GTE, which are analogous to LTS, LTA, and MTLE and motivate the use of trimmed estimators also as tools for regression diagnostics, are not discussed here to a larger extent because of a large number of existing studies that address the computation and breakdown behavior of trimmed estimator.…”

Section: Introductionmentioning

confidence: 99%

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General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models

Čı́žek

2008

Econom. Theory

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High breakdown-point regression estimators protect against large errors and data contamination. Motivated by some -the least trimmed squares and maximum trimmed likelihood estimators -we propose a general trimmed estimator, which unifies and extends many existing robust procedures. We derive here the consistency and rate of convergence of the proposed general trimmed estimator under mild β-mixing conditions and demonstrate its applicability in nonlinear regression, time series, limited dependent variable models, and panel data.

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Section: Proofsupporting

confidence: 56%

Section: Introductionmentioning

confidence: 99%

General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models

Čı́žek

2008

Econom. Theory

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“…Further properties of U -processes were investigated by Dehling, Denker and Philipp [17], Helmers, Janssen and Serfling [28], Nolan and Pollard [36], and others. For weakly dependent observations, weak convergence of U -processes has been established by Arcones and Yu [3] and Borovkova [10]. Their results hold for absolutely regular processes.…”

Section: Motivation and Examplesmentioning

confidence: 93%

Limit theorems for functionals of mixing processes with applications to $U$-statistics and dimension estimation

Borovkova

Burton

Dehling

2001

Trans. Amer. Math. Soc.

124

137

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Abstract. In this paper we develop a general approach for investigating the asymptotic distribution of functionals Xn = f ((Z n+k ) k∈Z ) of absolutely regular stochastic processes (Zn) n∈Z . Such functionals occur naturally as orbits of chaotic dynamical systems, and thus our results can be used to study probabilistic aspects of dynamical systems. We first prove some moment inequalities that are analogous to those for mixing sequences. With their help, several limit theorems can be proved in a rather straightforward manner. We illustrate this by re-proving a central limit theorem of Ibragimov and Linnik. Then we apply our techniques to U -statisticswith symmetric kernel h : R × R → R. We prove a law of large numbers, extending results of Aaronson, Burton, Dehling, Gilat, Hill and Weiss for absolutely regular processes. We also prove a central limit theorem under a different set of conditions than the known results of Denker and Keller. As our main application, we establish an invariance principle for U -processes (Un(h)) h , indexed by some class of functions. We finally apply these results to study the asymptotic distribution of estimators of the fractal dimension of the attractor of a dynamical system.

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“…In addition to the reprojected volatilities from Heston's model, Chernov and Ghysels produce a set of daily implied Black-Scholes volatilities de ned from equation (3). In addition to the two volatility series calculated from option prices, we apply two volatility measures based on the historical daily returns data.…”

Section: Application To Daily Returns On the Sandp500mentioning

confidence: 99%

Testing and comparing Value-at-Risk measures

Christoffersen

Hahn

Inoue

2001

Journal of Empirical Finance

176

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Central limit theorems for empirical andU-processes of stationary mixing sequences

Cited by 136 publications

References 25 publications

General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models

General Trimmed Estimation: Robust Approach to Nonlinear and Limited Dependent Variable Models

Limit theorems for functionals of mixing processes with applications to $U$-statistics and dimension estimation

Testing and comparing Value-at-Risk measures

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