• International Journal of Reliability and Applications
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• v.8 no.2
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• pp.125-135
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• 2007

In this paper, testing exponentiality against new better than used in convex average and denote by (NBUCA), or its dual (NWUCA) is investigated through the U-test. The percentiles of these tests are tabulated for samples sizes n = 5(1)40. The power estimates of the test are simulated for some commonly used distributions in reliability. Pitman's asymptotic efficiency of the test is calculated and compared. Data of 40 patients suffering from blood cancer disease (Leukemia) is considered as a practical application of the proposed test in the medical sciences.

• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.47-64
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• 2003

In this paper, we consider the asymptotic properties of asymmetric least squares estimators for nonlinear regression models. This paper provides sufficient conditions for strong consistency and asymptotic normality of the proposed estimators and derives asymptotic relative efficiency of the pro-posed estimators to the regression quantile estimators. We give some examples and results of a Monte Carlo simulation to compare the asymmetric least squares estimators with the regression quantile estimators.

• International Journal of Reliability and Applications
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• v.16 no.2
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• pp.113-122
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• 2015

In this paper, we introduce U-statistics approach to generalized Hollander-Proschan test for new better than used (NBUE) alternative. We prove, the proposed test is equivalent to test was introduced by Anis and Mitra (2011) and includes test was introduced by Hollander Proschan (1975). Also, the asymptotic properties are studied. The powers of our test are estimated. The Pitman asymptotic efficiencies of proposed test are also calculated. Finally, the test is applied to some real data.

• Journal of the Korean Statistical Society
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• v.29 no.2
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• pp.187-199
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• 2000

In this paper, we deal with the asymptotic properties of the least absolute deviation estimators in the nonlinear time series regression model. For the sinusodial model which frequently appears in a time series analysis, we study the strong consistency and asymptotic normality of least absolute deviation estimators. And using the derived limiting distributions we show that the least absolute deviation estimators is more efficient than the least squared estimators when the error distribution of the model has heavy tails.

• Proceedings of the Korean Statistical Society Conference
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• 2005.11a
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• pp.55-58
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• 2005

This paper discusses the asymptotic efficiency of estimators for optimal portfolios when returns are vector-valued non-Gaussian stationary processes. We give the asymptotic distribution of portfolio estimators ${\hat{g}}$ for non-Gaussian dependent return processes. Next we address the problem of asymptotic efficiency for the class of estimators ${\hat{g}}$ First, it is shown that there are some cases when the asymptotic variance of ${\hat{g}}$ under non-Gaussianity can be smaller than that under Gaussianity. The result shows that non-Gaussianity of X(t) does not always affect worse. Second, we give a necessary and sufficient condition for ${\hat{g}}$ to be asymptotically efficient when the return process is Gaussian, which shows that ${\hat{g}}$ is not asymptotically efficient generally. From this point of view we propose to use maximum likelihood type estimators for g, which are asymptotically efficient. We examine our approach numerically.

• International Journal of Reliability and Applications
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• v.4 no.4
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• pp.171-181
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• 2003

This paper proposes a U-test statistic for the problem of testing that a life distribution is exponential against the alternative that it is harmonic new better (worse) than used in expectation upper tail HNBUET (HNWUET), but not exponential on complete data. Selected critical values are tabulated for sample sizes n =5(1)60. The asymptotic normality of the statistic is proved and a comparison is made of the asymptotic efficiency between the statistic and other statistics. The power of the test is studied by simulation. A test for HNBUET in the case of randomly right-censored data is also considered. An application of the proposed test statistic in medical sciences is given.

• Journal of the Korean Statistical Society
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• v.31 no.2
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• pp.251-259
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• 2002

Lagged regressor models with general stationary errors independent of the regressors are considered. The regressor process is unstable having characteristic roots on the unit circle. If the order of the lag matches the number of roots on the unit circle, the ordinary least squares estimator (OLSE) is asymptotically efficient in that it has the same limiting distribution as the generalized least squares estimator (GLSE) under the same normalization. This result extends the well-known result of Grenander and Rosenblatt (1957) for asymptotic efficiency of the OLSE in deterministic polynomial and/or trigonometric regressor models to a class of models with stochastic regressors.

• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.121-128
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• 2002

In this paper we provide a new proof of the asymptotic distributions of LAD estimators using the martingale limit theorem and show the efficiency of LAD estimators in a stationary AR(1) model setting.

• Journal of the Korean Statistical Society
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• v.25 no.3
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• pp.337-346
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• 1996

The chi-squared type statistic generated from the empirical process can be used for testing the goodness of fit hypothesis on iid random sample. Lee (1995) showed that under some conditions, the chi-squared type statistic is asymptotically maximin in the sense of Strasser (1985). Since the chi-squared type statistic depends on the choice of *points in the unit interval, it is worth investigating the points yielding more efficient tests. Motivated by this viewpoint, we are led to study the asymptotic relative efficiency of chi-squared type tests in the same setting of Lee (1995). Some examples are given for illustration.

• International Journal of Reliability and Applications
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• v.1 no.2
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• pp.115-121
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• 2000

The trend change in aging properties, such as failure rate and mean residual life, of a life distribution is important to engineers and reliability analysts. In this paper we develop a test statistic for testing whether or not the failure rate changes its trend using censored data. The asymptotic normality of the test statistics is established. We discuss the efficiency values of loss due to censoring.