• Title/Summary/Keyword: empirical processes

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ON THE EMPIRICAL MEAN LIFE PROCESSES FOR RIGHT CENSORED DATA

  • Park, Hyo-Il
    • Journal of the Korean Statistical Society
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    • v.32 no.1
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    • pp.25-32
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    • 2003
  • In this paper, we define the mean life process for the right censored data and show the asymptotic equivalence between two kinds of the mean life processes. We use the Kaplan-Meier and Susarla-Van Ryzin estimates as the estimates of survival function for the construction of the mean life processes. Also we show the asymptotic equivalence between two mean residual life processes as an application and finally discuss some difficulties caused by the censoring mechanism.

RESIDUAL EMPIRICAL PROCESS FOR DIFFUSION PROCESSES

  • Lee, Sang-Yeol;Wee, In-Suk
    • Journal of the Korean Mathematical Society
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    • v.45 no.3
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    • pp.683-693
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    • 2008
  • In this paper, we study the asymptotic behavior of the residual empirical process from diffusion processes. For this task, adopting the discrete sampling scheme as in Florens-Zmirou [9], we calculate the residuals and construct the residual empirical process. It is shown that the residual empirical process converges weakly to a Brownian bridge.

Weak Convergence of U-empirical Processes for Two Sample Case with Applications

  • Park, Hyo-Il;Na, Jong-Hwa
    • Journal of the Korean Statistical Society
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    • v.31 no.1
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    • pp.109-120
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    • 2002
  • In this paper, we show the weak convergence of U-empirical processes for two sample problem. We use the result to show the asymptotic normality for the generalized dodges-Lehmann estimates with the Bahadur representation for quantifies of U-empirical distributions. Also we consider the asymptotic normality for the test statistics in a simple way.

WEAK CONVERGENCE FOR STATIONARY BOOTSTRAP EMPIRICAL PROCESSES OF ASSOCIATED SEQUENCES

  • Hwang, Eunju
    • Journal of the Korean Mathematical Society
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    • v.58 no.1
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    • pp.237-264
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    • 2021
  • In this work the stationary bootstrap of Politis and Romano [27] is applied to the empirical distribution function of stationary and associated random variables. A weak convergence theorem for the stationary bootstrap empirical processes of associated sequences is established with its limiting to a Gaussian process almost surely, conditionally on the stationary observations. The weak convergence result is proved by means of a random central limit theorem on geometrically distributed random block size of the stationary bootstrap procedure. As its statistical applications, stationary bootstrap quantiles and stationary bootstrap mean residual life process are discussed. Our results extend the existing ones of Peligrad [25] who dealt with the weak convergence of non-random blockwise empirical processes of associated sequences as well as of Shao and Yu [35] who obtained the weak convergence of the mean residual life process in reliability theory as an application of the association.

Rate of Convergence of Empirical Distributions and Quantiles in Linear Processes with Applications to Trimmed Mean

  • Lee, Sangyeol
    • Journal of the Korean Statistical Society
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    • v.28 no.4
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    • pp.435-441
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    • 1999
  • A 'convergence in probability' rate of the empirical distributions and quantiles of linear processes is obtained. As an application of the limit theorems, a trimmed mean for the location of the linear process is considered. It is shown that the trimmed mean is asymptotically normal. A consistent estimator for the asymptotic variance of the trimmed mean is provided.

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Choice of the Kernel Function in Smoothing Moment Restrictions for Dependent Processes

  • Lee, Jin
    • Communications for Statistical Applications and Methods
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    • v.16 no.1
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    • pp.137-141
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    • 2009
  • We study on selecting the kernel weighting function in smoothing moment conditions for dependent processes. For hypothesis testing in Generalized Method of Moments or Generalized Empirical Likelihood context, we find that smoothing moment conditions by Bartlett kernel delivers smallest size distortions based on empirical Edgeworth expansions of the long-run variance estimator.

ON THE GOODNESS OF FIT TEST FOR DISCRETELY OBSERVED SAMPLE FROM DIFFUSION PROCESSES: DIVERGENCE MEASURE APPROACH

  • Lee, Sang-Yeol
    • Journal of the Korean Mathematical Society
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    • v.47 no.6
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    • pp.1137-1146
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    • 2010
  • In this paper, we study the divergence based goodness of fit test for partially observed sample from diffusion processes. In order to derive the limiting distribution of the test, we study the asymptotic behavior of the residual empirical process based on the observed sample. It is shown that the residual empirical process converges weakly to a Brownian bridge and the associated phi-divergence test has a chi-square limiting null distribution.

CENTRAL LIMIT THEOREMS FOR BELLMAN-HARRIS PROCESSES

  • Kang, Hye-Jeong
    • Journal of the Korean Mathematical Society
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    • v.36 no.5
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    • pp.923-943
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    • 1999
  • In this paper we consider functionals of the empirical age distribution of supercritical Bellman-Harris processes. Let f : R+ longrightarrow R be a measurable function that integrates to zero with respect to the stable age distribution in a supercritical Bellman-Harris process with no extinction. We present sufficient conditions for the asymptotic normality of the mean of f with respect to the empirical age distribution at time t.

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A Test for Independence between Two Infinite Order Autoregressive Processes

  • Kim, Eun-Hee;Lee, Sang-Yeol
    • Proceedings of the Korean Statistical Society Conference
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    • 2003.05a
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    • pp.191-197
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    • 2003
  • This paper considers the independence test for two stationary infinite order autoregressive processes. For a test, we follow the empirical process method devised by Hoeffding (1948) and Blum, Kiefer and Rosenblatt (1961), and construct the Cram${\acute{e}}$r-von Mises type test statistics based on the least squares residuals. It is shown that the proposed test statistics behave asymptotically the same as those based on true errors.

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