• Journal of the Korean Statistical Society
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• 제25권4호
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• pp.603-611
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• 1996

In this article we consider a sequential procedure for the fixed width interval estimation of the means of two mutually independent linear processes. It is shown that the proposed stopping rule is asymptotically efficient as in iid samples (cf. Robbins, Simons and Starr(l967)).

• 한국통계학회:학술대회논문집
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• 한국통계학회 2005년도 추계 학술발표회 논문집
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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.

• 응용통계연구
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• 제7권2호
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• pp.173-182
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• 1994

Han(1993)의 임의의 오차분포하에서 회귀모형에의 기울기 추정법을 응용하여 회귀분위선(regression quantile)에 의해 적당한 상.하위절사가 주어질 때 점근적으로 최량의 회귀모형에서의 기울기 추정량을 구성할 수 있음을 보였다.

• Communications for Statistical Applications and Methods
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• 제4권2호
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• pp.345-351
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• 1997

This paper considers the problem of sequential fixed accuracy confidence set procedure of the aurocorrelations of stationary linear processes. The proposed procedure for fixed-width confidence set is shown to be both asymptotically consistent and asymptotically efficient as the size of the width approaches zero.

• Journal of the Korean Statistical Society
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• 제18권2호
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• pp.97-106
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• 1989

We consider two semiparametric regression lines where the density of the error terms are unknown. We give simultaneous estimatros of the differences of intercepts and slopes which turn out to be asymptotically minimax as well as efficient in semiparametric sense.

• 품질경영학회지
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• 제14권2호
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• pp.15-20
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• 1986

Using Fisher's method of combining two independent test statistics, we suggest a test for comparing two exponential populations with location and scale parameters and prove that it is asymptotically optimal in the sense of Bahadur efficiency.

• Communications for Statistical Applications and Methods
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• 제3권3호
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• pp.113-123
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• 1996

Data-dependent (adaptive) choice of asymptotically efficient score functions for rank estimators and M-estimators of regression parameters in a linear regression model with left-truncated and right-censored data are developed herein. The locally adaptive smoothing techniques of Muller and Wang (1990) and Uzunogullari and Wang (1992) provide good estimates of the hazard function h and its derivative h' from left-truncated and right-censored data. However, since we need to estimate h'/h for the asymptotically optimal choice of score functions, the naive estimator, which is just a ratio of estimated h' and h, turns out to have a few drawbacks. An altermative method to overcome these shortcomings and also to speed up the algorithms is developed. In particular, we use a subroutine of the PPR (Projection Pursuit Regression) method coded by Friedman and Stuetzle (1981) to find the nonparametric derivative of log(h) for the problem of estimating h'/h.

• Journal of the Korean Statistical Society
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• 제28권1호
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• pp.93-106
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• 1999

In this paper we consider estimation of a real valued parameter in the drift coefficient of a Hilbert space valued Ito stochastic differential equation. First we consider observation of the corresponding diffusion in a fixed time interval [0, T] and prove the Bernstein - von Mises theorem concerning the convergence of posterior distribution of the parameter given the observation, suitably normalised and centered at the MLE, to the normal distribution as Tlongrightarrow$\infty$. As a consequence, the Bayes estimator of the drift parameter becomes asymptotically efficient and asymptotically equivalent to the MLE as Tlongrightarrow$\infty$. Next, we consider observation in a random time interval where the random time is determined by a predetermined level of precision. We show that the sequential MLE is better than the ordinary MLE in the sense that the former is unbiased, uniformly normally distributed and efficient but is latter is not so.

• Communications for Statistical Applications and Methods
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• 제8권1호
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• pp.159-171
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• 2001

Shapiro and Wilk (1972) developed a test for exponentiality with origin and scale unknown. The procedure consists of comparing the generalized least squares estimate of scale with the estimate of scale given by the sample variance. However the test statistic is inconsistent ; that is, the power of the test will not approach 1 as the sample size increases. Hence we give a test based on the ratio of two asymptotically efficient estimates of scale. We also have conducted a power study to compare the test procedures, using Monte Carlo samples from a wide range of alternatives. It is found that the suggested statistics have higher power for the alternatives with the coefficient of variation greater that or equal to 1.

• 품질경영학회지
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• 제27권2호
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• pp.112-125
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• 1999

In a robust regression model, it is typically assumed that the errors are normally distributed. However, what if the error distribution is deviated from the normality and the response variables are not completely observable due to censoring? For complete data, Kim and Lai(1998) suggested a new adaptive M-estimator with an asymptotically efficient score function. The adaptive M-estimator is based on using B-splines to estimate the score function and simple cross validation to determine the knots of the B-splines, which are a modified version of Kun( 1992). We herein extend this method to right-censored data and study how well the adaptive M-estimator performs for various error distributions and censoring rates. Some impressive simulation results are shown.