• Title/Summary/Keyword: consistency of estimator

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Consistency of the Periodogram When the Long-Run Variance is Degenerate

  • Lee, Jin
    • Communications for Statistical Applications and Methods
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    • v.19 no.2
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    • pp.287-292
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    • 2012
  • Sample periodogram is widely known as an inconsistent estimator for true spectral density. We show that it becomes consistent when the true spectrum at the zero frequency (often known as long-run variance) equals zero. Asymptotic results for consistency of the periodogram as well as the rate of convergence are formally derived.

Nonparametric Estimation of Bivariate Mean Residual Life Function under Univariate Censoring

  • Dong-Myung Jeong;Jae-Kee Song;Joong Kweon Sohn
    • Journal of the Korean Statistical Society
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    • v.25 no.1
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    • pp.133-144
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    • 1996
  • We, in this paper, propose a nonparametric estimator of bivariate mean residual life function based on Lin and Ying's (1993) bivariate survival function estimator of paired failure times under univariate censoring and prove the uniform consistency and the weak convergence result of this estimator. Through Monte Carlo simulation, the performances of the proposed estimator are tabulated and are illustrated with the skin grafts data.

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The Nonparametric Deconvolution Problem with Gaussian Error Distribution

  • Cho, Wan-Hyun;Park, Jeong-Soo
    • Journal of the Korean Statistical Society
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    • v.25 no.2
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    • pp.265-276
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    • 1996
  • The nonparametric deconvolution problems are studied to recover an unknown density when the data are contaminated with Gaussian error. We propose the estimator which is a linear combination of kernel type estimates of derivertives of the observed density function. We show that this estimator is consistent and also consider the properties of estimator at small sample by simulation.

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A Study on Estimating Mean Lifetime After Modifying Censored Observations

  • Kim, Jinh-eum;Kim, Jee-hoon
    • Journal of Korean Society for Quality Management
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    • v.26 no.1
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    • pp.161-171
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    • 1998
  • Kim and Kim (1997) developed a method of estimating the mean lifetime based on the augmented data after imputing censored observations. Assuming the linear relationship between lifetime and covariates, and then introducing the procedure of Buckley and James (1979) to estimate the mean lifetimes of censored observations, they proposed a mean lifetime estimator and its consistency under the regularity conditions. In this article, the Kim and Kim's estimator is compared with the estimator introduced by Gill (1983) through simulations under the various configurations. Also, their estimator is illustrated with two real data sets.

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A Change-point Estimator with Unsymmetric Fourier Series

  • Kim, Jaehee
    • Journal of the Korean Statistical Society
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    • v.31 no.4
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    • pp.533-543
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    • 2002
  • In this paper we propose a change-point estimator with left and right regressions using the sample Fourier coefficients on the orthonormal bases. The window size is different according to the data in the left side and in the right side at each point. The asymptotic properties of the proposed change-point estimator are established. The limiting distribution and the consistency of the estimator are derived.

Asymptotic Properties of a Robust Estimator for Regression Models with Random Regressor

  • Chang, Sook-Hee;Kim, Hae-Kyung
    • Communications for Statistical Applications and Methods
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    • v.6 no.2
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    • pp.345-356
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    • 1999
  • This paper deals with the problem of estimating regression coefficients in nonlinear regression model having random regressor. The sufficient conditions for consistency of the $L_1$-estimator with random regressor are given and discussed in this paper. An example is given to illustrate the application of the main results.

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A Note On L$_1$ Strongly Consistent Wavelet Density Estimator for the Deconvolution Problems

  • Lee, Sungho
    • Communications for Statistical Applications and Methods
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    • v.8 no.3
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    • pp.859-866
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    • 2001
  • The problem of wavelet density estimation is studied when the sample observations are contaminated with random noise. In this paper a linear wavelet estimator based on Meyer-type wavelets is shown to be L$_1$ strongly consistent for f(x) with bounded support when Fourier transform of random noise has polynomial descent or exponential descent.

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A Kernel Estimator of Hazard Ratio (위험비(危險比)의 커널추정량(推定量))

  • Choi, Myong-Hui;Lee, In-Suk;Song, Jae-Kee
    • Journal of the Korean Data and Information Science Society
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    • v.3 no.1
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    • pp.79-90
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    • 1992
  • We consider hazard ratio as a descriptive measure to compare the hazard experience of a treatment group with that of a control group with censored survival data. In this paper, we propose a kernel estimator of hazard ratio. The uniform consistency and asymptotic normality of a kernel estimator are proved by using counting process approach via martingale theory and stochastic integrals.

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A Simple Estimator of Mean Residual Life Function under Random Censoring

  • Jeong, Dong-Myung;Song, Myung-Unn;Song, Jae-Kee
    • Journal of the Korean Data and Information Science Society
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    • v.8 no.2
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    • pp.225-230
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    • 1997
  • We, in this paper, propose an estimator of mean residual life function by using the residual survival function under random censoring and prove the uniform consistency and weak convergence result of this estimator. Also an example is illustrated by the real data.

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Asymptotic Properties of Least Square Estimator of Disturbance Variance in the Linear Regression Model with MA(q)-Disturbances

  • Jong Hyup Lee;Seuck Heum Song
    • Communications for Statistical Applications and Methods
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    • v.4 no.1
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    • pp.111-117
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    • 1997
  • The ordinary least squares estimator $S^2$ for the variance of the disturbances is considered in the linear regression model with sutocorrelated disturbances. It is proved that the OLS-estimator of disturbance variance is asymptotically unbiased and weakly consistent, when the distrubances are generated by an MA(q) process. In particular, the asymptotic unbiasedness and consistency of $S^2$ is satisfied without any restriction on the regressor matrix.

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