• 응용통계연구
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• 제30권5호
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• pp.733-745
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• 2017

국소복합분위수 회귀모형을 활용한 비모수적 함수 추정방법이 높은 효율성과 더불어 활발히 연구되고 있다. 이러한 추정과정에 커널을 사용한 자료 평활방법이 대표적으로 사용되고 있으며, 그 성능은 커널보다는 평활계수의 선택 크게 의존한다. 한편, 회귀함수 추정방법의 성능을 평가하는 기준으로는 통상적으로 $L_2$-노름이 사용되어 평균제곱오차 또는 평균적분제곱오차를 최소화하는 평활계수의 선택에 대한 많은 연구가 진행되어 왔다. 본 논문에서는 국소선형 복합 분위수 회귀방법을 활용한 비모수 회귀모형 추정량의 성능을 결정하는 평활계수 선택의 최적성에 관해 연구하였다. 특히, 여러 장점을 가졌으나 수리적 어려움으로 연구가 미흡한 평균절대오차 및 평균적분절대오차를 최적의 기준으로 삼아 최적의 평활계수를 구하고 그 유일성에 관해 연구하였다. 나아가 기존의 평가기준인 평균제곱오차 및 평균적분제곱오차를 사용한 선택과의 관계를 파악하고 그 성능을 비교하였다. 이러한 과정에서 다양한 상황에서의 모의실험을 통해 제안한 방법의 특성을 규명하였다.

• Journal of the Korean Data and Information Science Society
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• 제25권4호
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• pp.931-939
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• 2014

In this paper we propose the iteratively reweighted least squares procedure to solve the quadratic programming problem of support vector expectile regression with an asymmetrically weighted squares loss function. The proposed procedure enables us to select the appropriate hyperparameters easily by using the generalized cross validation function. Through numerical studies on the artificial and the real data sets we show the effectiveness of the proposed method on the estimation performances.

• Journal of the Korean Data and Information Science Society
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• 제27권5호
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• pp.1433-1441
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• 2016

Small area model provides reliable and accurate estimations when the sample size is not sufficient. Our dataset has an inherent nonlinear pattern which signicantly affects our inference. In this case, we could consider semiparametric models such as truncated polynomial basis function and radial basis function. In this paper, we study four Bayesian semiparametric models for small areas to handle this point. Four small area models are based on two kinds of basis function and different knots positions. To evaluate the different estimates, four comparison measurements have been employed as criteria. In these comparison measurements, the truncated polynomial basis function with equal quantile knots has shown the best result. In Bayesian calculation, we use Gibbs sampler to solve the numerical problems.

• International Journal of Reliability and Applications
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• 제17권1호
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• pp.65-84
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• 2016

Motivated by the recent work of Cordeiro and Castro (2011), we study the Kumaraswamy exponentiated Frechet distribution (KEF). We derive some mathematical properties of the (KEF) including moment generating function, moments, quantile function and incomplete moment. We provide explicit expressions for the density function of the order statistics and their moments. In addition, the method of maximum likelihood and least squares and weighted least squares estimators are discuss for estimating the model parameters. A real data set is used to illustrate the importance and flexibility of the new distribution.

• Communications for Statistical Applications and Methods
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• 제23권2호
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• pp.147-161
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• 2016

This paper introduces the four parameter new generalized inverse Weibull distribution and investigates the potential usefulness of this model with application to reliability data from engineering studies. The new extended model has upside-down hazard rate function and provides an alternative to existing lifetime distributions. Various structural properties of the new distribution are derived that include explicit expressions for the moments, moment generating function, quantile function and the moments of order statistics. The estimation of model parameters are performed by the method of maximum likelihood and evaluate the performance of maximum likelihood estimation using simulation.

• 대한수학회지
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• 제35권3호
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• pp.741-753
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• 1998

Let G(*) be a Borel function applied to a stationary long memory sequence {X$_{i}$} of standard Gaussian random variables. Focusing on the process {G(X$_{i}$)}, the present paper establishes the almost sure representation for the empirical quantile process, that is, Bahadur's representation, and for the empirical process with respect to sample mean. Statistical applications of the representations are also addressed.sed.

• Communications for Statistical Applications and Methods
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• 제10권3호
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• pp.1017-1024
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• 2003

An estimation problem of treatment effect for bivariate censored survival data is considered under location shift model between two sample. The proposed estimator is very intuitive and can be obtained in a closed form. Asymptotic results of the proposed estimator are discussed and simulation studies are performed to show the strength of the proposed estimator.

• Journal of the Korean Data and Information Science Society
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• 제1권
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• pp.47-57
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• 1990

A method which determines the number of replications in the simulation is proposed, particularly for small-sample comparison of estimators. This method takes the smallest number of replications that makes the difference of mean square errors be statistically significant and provides an efficient algorithm for calculating the standard error of the mean square error. Two examples are illustrated, the first one is on comparison of mean and median ; the second, the Kaplan-Meier type and Buckley-James type estimators of a quantile function with censored data.

• Communications for Statistical Applications and Methods
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• 제12권2호
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• pp.443-451
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• 2005

The studied in this paper is a new algorithm for searching the maximum likelihood estimate(MLE) in which probability density function is not explicitly expressed. Newton-Raphson's root-finding routine and a nonlinear numerical optimization algorithm with constraint (so-called feasible sequential quadratic programming) are used. This algorithm is applied to the Wakeby distribution which is importantly used in hydrology and water resource research for analysis of extreme rainfall. The performance comparison between maximum likelihood estimates and method of L-moment estimates (L-ME) is studied by Monte-carlo simulation. The recommended methods are L-ME for up to 300 observations and MLE for over the sample size, respectively. Methods for speeding up the algorithm and for computing variances of estimates are discussed.

• 대한수학회지
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• 제61권4호
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• pp.713-742
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• 2024

From the ordinary notion of upper-tail quantitle function, a new concept called conditionally upper-tail quantitle function given a σ-algebra is proposed. Some basic properties of this terminology and further properties of conditionally strictly stationary sequences are derived. By means of these properties, several conditional central limit theorems for a sequence of conditionally strong mixing and conditionally strictly stationary random variables are established, some of which are the conditional versions corresponding to earlier results under non-conditional case.