• The Korean Journal of Applied Statistics
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• v.30 no.5
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• pp.733-745
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• 2017

Local composite quantile regression is a useful non-parametric regression method widely used for its high efficiency. Data smoothing methods using kernel are typically used in the estimation process with performances that rely largely on the smoothing parameter rather than the kernel. However, $L_2$-norm is generally used as criterion to estimate the performance of the regression function. In addition, many studies have been conducted on the selection of smoothing parameters that minimize mean square error (MSE) or mean integrated square error (MISE). In this paper, we explored the optimality of selecting smoothing parameters that determine the performance of non-parametric regression models using local linear composite quantile regression. As evaluation criteria for the choice of smoothing parameter, we used mean absolute error (MAE) and mean integrated absolute error (MIAE), which have not been researched extensively due to mathematical difficulties. We proved the uniqueness of the optimal smoothing parameter based on MAE and MIAE. Furthermore, we compared the optimal smoothing parameter based on the proposed criteria (MAE and MIAE) with existing criteria (MSE and MISE). In this process, the properties of the proposed method were investigated through simulation studies in various situations.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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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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• v.27 no.5
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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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• v.17 no.1
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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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• v.23 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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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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• v.10 no.3
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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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• v.1
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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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• v.12 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.61 no.4
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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.