• International Journal of Reliability and Applications
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• v.1 no.1
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• pp.39-47
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• 2000

In a resent paper, Na and Kim(2000) develop a family of test statistics for testing whether or not the mean residual life changes its trend based on complete data and show that the new tests perform better than previously known tests. In this paper, we extend their tests to the randomly censored data. The asymptotic normality of the test statistics is established. Monte Carlo simulations are conducted to compare our tests with a previously known test by the power of tests.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.561-570
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• 2003

We propose a nonparametric test procedure for checking the proportionality assumption between hazard functions using a functional equation. Because of the involvement of censoring distribution function, we consider the large sample case only and obtain the asymptotic normality of the proposeed test statistic. Then we discuss the rationale of the use of the functional equation, give some examples and compare the performances with Andersen's procedure by computing powers through simulations.

• Proceedings of the Korean Reliability Society Conference
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• 2000.11a
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• pp.365-371
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• 2000

The problem of trend change in the failure rate is great interest in the reliability and survival analysis. In this paper we develop a test statistic for testing whether or not the failure rate changes its trend using random censored data. The asymptotic normality of the test statistic is established. We discuss the efficiency values of loss due to censoring.

• International Journal of Quality Innovation
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• v.1 no.1
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• pp.58-63
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• 2000

The problem of trend change in the failure rate is great interest in the reliability and survival analysis. In this paper we develop a test statistic for testing whether or not the failure rate changes its trend using random censored data. The asymptotic normality of the test statistic is established. The efficiency values of loss due to censoring are discussed.

• Journal of the Korean Statistical Society
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• v.26 no.3
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• pp.319-332
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• 1997

The application of multivariate linear rank statistics to data with item nonresponse is considered. Only a modest extension of the complete data techniques is required when the missing data may be thought of as a random sample, and an appropriate modification of the covariances is derived. A proof of the asymptotic multivariate normality is given. A review of some related results in the literature is presented and applications including longitudinal and repeated measures designs are discussed.

• 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.

• 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.

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.161-173
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• 1996

When we deal with a Hilbert space-valued Stochastic Differential Equation (SDE) (or Stochastic Partial Differential Equation (SPDE)), depending on some unknown parameters, the solution usually has a Fourier series expansion. In this situation we consider the maximum likelihood method for the statistical estimation problem and derive the asymptotic properties (consistency and normality) of the Maximum Likelihood Estimator (MLE).

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.789-798
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• 2000

The mean residual function is the expected remaining life of an item at age x. The problem of trend change in the mean residual life is great interest in the reliability and survival analysis. In this paper, we develop a family of test statistics for testing whether or not the mean residual life changes its trend. The asymptotic normality of the test statistics is established. Monte Carlo simulations are conducted to study the performance of our test statistics.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.57-65
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• 1999

In a resent paper, Na, Lee and Kim(1998) develop a test statistic for testing whether or not the mean residual life changes its trend based on complete data and show that the new test performs better than previously known tests. In this paper, we extend their test to the randomly censored data. The asymptotic normality of the test statistic is established. Monte Carlo simulations are conducted to compare our test with a previously known test by the power of tests.