• Title, Summary, Keyword: asymptotic distribution

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Asymptotic Distribution of a Nonparametric Multivariate Test Statistic for Independence

  • Um, Yong-Hwan
    • Journal of the Korean Data and Information Science Society
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    • v.12 no.1
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    • pp.135-142
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    • 2001
  • A multivariate statistic based on interdirection is proposed for detecting dependence among many vectors. The asymptotic distribution of the proposed statistic is derived under the null hypothesis of independence. Also we find the asymptotic distribution under the alternatives contiguous to the null hypothesis, which is needed for later use of computing relative efficiencies.

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Asymptotic Distribution in Estimating a Population Size

  • Choi, Ki-Heon
    • Journal of the Korean Data and Information Science Society
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    • v.10 no.2
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    • pp.313-318
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    • 1999
  • Suppose that there is a population of hidden objects of which the total number N is unknown. From such data, we derive an asymptotic distribution.

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ASYMPTOTIC DISTRIBUTION OF DEA EFFICIENCY SCORES

  • S.O.
    • Journal of the Korean Statistical Society
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    • v.33 no.4
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    • pp.449-458
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    • 2004
  • Data envelopment analysis (DEA) estimators have been widely used in productivity analysis. The asymptotic distribution of DEA estimator derived by Kneip et al. (2003) is too complicated and abstract for analysts to use in practice, though it should be appreciated in its own right. This paper provides another way to express the limit distribution of the DEA estimator in a tractable way.

ON ASYMPTOTIC OF EXTREMES FROM GENERALIZED MAXWELL DISTRIBUTION

  • Huang, Jianwen;Wang, Jianjun
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.3
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    • pp.679-698
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    • 2018
  • In this paper, with optimal normalized constants, the asymptotic expansions of the distribution and density of the normalized maxima from generalized Maxwell distribution are derived. For the distributional expansion, it shows that the convergence rate of the normalized maxima to the Gumbel extreme value distribution is proportional to 1/ log n. For the density expansion, on the one hand, the main result is applied to establish the convergence rate of the density of extreme to its limit. On the other hand, the main result is applied to obtain the asymptotic expansion of the moment of maximum.

Characterization of the Asymptotic Distributions of Certain Eigenvalues in a General Setting

  • Hwang, Chang-Ha
    • Journal of the Korean Statistical Society
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    • v.23 no.1
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    • pp.13-32
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    • 1994
  • Let A(n) and B(n) be sequences of $m \times m$ random matrices with a joint asymptotic distribution as $n \to \infty$. The asymptotic distribution of the ordered roots of $$\mid$A(n) - f B(n)$\mid$ = 0$ depends on the multiplicity of the roots of a determinatal equation involving parameter roots. This paper treats the asymptotic distribution of the roots of the above determinantal equation in the case where some of parameter roots are zero. Furthermore, we apply our results to deriving the asymptotic distributions of the eigenvalues of the MANOVA matrix in the noncentral case when the underlying distribution is not multivariate normal and some parameter roots are zero.

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Asymptotic Distribution of Sample Autocorrelation Function for the First-order Bilinear Time Series Model

  • Kim, Won-Kyung
    • Journal of the Korean Statistical Society
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    • v.19 no.2
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    • pp.139-144
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    • 1990
  • For the first-order bilinear time series model $X_t = aX_{t-1} + e_i + be_{t-1}X_{t-1}$ where ${e_i}$ is a sequence of independent normal random variables with mean 0 and variance $\sigma^2$, the asymptotic distribution of sample autocarrelation function is obtained and shown to follow a normal distribution. The variance of the asymptotic distribution is of a complicated form and hence a bootstrap estimate of the variance is proposed for large sample inference. This result can be used to distinguish between different bilinear models.

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Change-Point Problems in a Sequence of Binomial Variables

  • Jeong, Kwang-Mo
    • Communications for Statistical Applications and Methods
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    • v.3 no.2
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    • pp.175-185
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    • 1996
  • For the Change-point problem in a sequence of binomial variables we consider the maximum likelihood estimator (MLE) of unknown change-point. Its asymptotic distribution is quite limited in the case of binomial variables with different numver of trials at each time point. Hinkley and Hinkley (1970) gives an asymptotic distribution of the MLE for a sequence of Bernoulli random variables. To find the asymptotic distribution a numerical method such as bootstrap can be used. Another concern of our interest in the inference on the change-point and we derive confidence sets based on the liklihood ratio test(LRT). We find approximate confidence sets from the bootstrap distribution and compare the two results through an example.

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