• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.403-412
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• 2004

We obtain a kernel quantile process based on the kernel quantile estimator and prove the uniform consistency of the kernel quantile process by developing that of the usual sample quantile process. We apply our result to the classical kernel type processes.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1539-1547
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• 2014

In this paper we apply the autoregressive process to the nonlinear quantile regression in order to infer nonlinear quantile regression models for the autocorrelated data. We propose a kernel method for the autoregressive data which estimates the nonlinear quantile regression function by kernel machines. Artificial and real examples are provided to indicate the usefulness of the proposed method for the estimation of quantile regression function in the presence of autocorrelation between data.

• Asian Journal of Innovation and Policy
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• v.12 no.2
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• pp.155-176
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• 2023

This paper employs datasets from the Enterprise Survey conducted by the World Bank to examine the relationship between four types of innovation defined by the Oslo Manual (OECD, 2005): product innovation, process innovation, marketing innovation, organization innovation, and the firm performance in the selected developing ASEAN economies. The main objective of this paper is to understand the characteristics of innovation activities at the firm level and how various innovation types affect firm performance. The empirical results from ASEAN manufacturing firms reveal that product innovation positively affects firms' performance, while non-technological innovations are negatively related to the performance of firms. The further employed quantile regression provides more insights into the roles of innovation types on different levels of firm performance: while product and process innovations actively contribute to the small and medium-size firms (below 25^th quantile and median), organizational and marketing innovations negatively affect them. Interestingly, the role of process innovation decreases when firm performance grows.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.473-481
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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. Kim(2001) proposed a modified Shapiro-Wilk's test statistic based on the ratio of tow asymptotically efficient estimates of scale. In this paper, we study the asymptotic behavior of the statistic using the approximation of the quantile process by a sequence of Brownian bridges and represent the limit null distribution as an integral of a Brownian bridge.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.179-186
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• 1996

Bioequivanence models arise typically in bioassays when new preparations are compared against standard ones by means of responses on some biological organisms. Relative potency measures provide nice interpretations for such bioequivalence and their estimation constitutes the prime interest of such studies. A conditional quantile process based on the k-nearest neighbor method is proposed for this purpose. An alternative procedure based on Kolmogrov-Smirnov type estimator has also been considered along with. ARIC ultrasound data are analyzed as examples.

• Genomics & Informatics
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• v.6 no.4
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• pp.231-234
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• 2008

Precise and reliable identification of CNV is still important to fully understand the effect of CNV on genetic diversity and background of complex diseases. SNP marker has been used frequently to detect CNVs, but the analysis of SNP chip data for identifying CNV has not been well established. We compared various normalization methods for CNV analysis and suggest optimal normalization procedure for reliable CNV call. Four normal Koreans and NA10851 HapMap male samples were genotyped using Affymetrix Genome-Wide Human SNP array 5.0. We evaluated the effect of median and quantile normalization to find the optimal normalization for CNV detection based on SNP array data. We also explored the effect of Robust Multichip Average (RMA) background correction for each normalization process. In total, the following 4 combinations of normalization were tried: 1) Median normalization without RMA background correction, 2) Quantile normalization without RMA background correction, 3) Median normalization with RMA background correction, and 4) Quantile normalization with RMA background correction. CNV was called using SW-ARRAY algorithm. We applied 4 different combinations of normalization and compared the effect using intensity ratio profile, box plot, and MA plot. When we applied median and quantile normalizations without RMA background correction, both methods showed similar normalization effect and the final CNV calls were also similar in terms of number and size. In both median and quantile normalizations, RMA backgroundcorrection resulted in widening the range of intensity ratio distribution, which may suggest that RMA background correction may help to detect more CNVs compared to no correction.

• 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.18 no.4
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• pp.527-535
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• 2011

This study proposes a modified definition about $C_{pk}$ based on median as the centering parameter in order to more easily control the process since the mean does not represent any quantile of the asymmetric process distribution. Then we consider an estimate and derive the asymptotic normality for the estimate of the modified $C_{pk}$. In addition, we provide an example with asymmetric distributions and discuss the estimation for the limiting variance that are followed by some concluding remarks.

• Communications for Statistical Applications and Methods
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• v.15 no.3
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• pp.421-427
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• 2008

This paper deals with the problem of testing for the existence of change in mean and estimating the change-point when the data are from the exponential distributions. The likelihood ratio test statistic and Gombay and Horvath (1990) test statistic are compared in a power study when there exists one change-point in the exponential means. Also the change-point estimator using the likelihood ratio and the change-point estimators based on Gombay and Horvath (1990) statistic are compared for their detecting capability via simulation.

• 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.