• The Korean Journal of Applied Statistics
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• v.26 no.4
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• pp.595-610
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• 2013

Testing of order-restricted alternative hypothesis in $2{\times}k$ contingency tables can be applied to various fields of medicine, sociology, and business administration. Most testing methods have been developed based on a large sample theory. In the case of a small sample size or unbalanced sample size, the Type I error rate of the testing method (based on a large sample theory) is very different from the target point of 5%. In this paper, the exact testing method is introduced in regards to the testing of an order-restricted alternative hypothesis in categorical data (particularly if a small sample size or extreme unbalanced data). Power and exact p-value are calculated, respectively.

• Communications for Statistical Applications and Methods
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• v.30 no.1
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• pp.37-48
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• 2023

Shape analysis is a method for measuring, describing and comparing the shape of objects in geometric space. An important aspect is to obtain Procrustes distance based on least square method. We note that the shape is all the geometrical information that remains when location, scale and rotational effects are filtered out from an object. However, and unfortunately, when we cannot measure some landmarks which are some biologically or geometrically meaningful points of any object, it is not possible to measure the variation of all shapes of an object, including that of the incomplete object. Hence, we need to replace the missing landmarks. In particular, Albers and Gower (2010) studied the missing rows of configurations in Procrustes analysis. They noted that the convergence of their approach can be quite slow. In this study, alternatively, we derive an algorithm for estimating the missing landmarks based on the pre-shapes. The pre-shape is invariant under the location and scaling of the original configuration with the centroid size of the pre-shape being one. Therefore we expect that we can reduce the amount of total computing time for obtaining the estimate of the missing landmarks.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.963-972
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• 2023

In this paper, geometrically convex and s-convex functions in third and fourth sense are merged to form (g, s)-convex function. Characterizations of (g, s)-convex function, algebraic and functional properties are presented. In addition, novel functions based on the integral of (g, s)-convex functions in the third sense are created, and inequality relations for these functions are explored and examined under particular conditions. Further, there are also some relationships between (g, s)-convex function and previously defined functions. The (g, s)-convex function and its derivatives will then be used to extend the well-known H-H and Fejer's type inequalities. In order to obtain the previously mentioned conclusions, several special cases from previous literature for extended H-H and Fejer's inequalities are also investigated. The relation between the average (mean) values and newly created H-H and Fejer's inequalities are also examined.

• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.159-174
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• 2015

Dragomiretskiy and Zosso (2014) developed a new decomposition method, termed variational mode decomposition (VMD), which is efficient for handling the tone detection and separation of signals. However, VMD may be inefficient in the presence of missing data since it is based on a fast Fourier transform (FFT) algorithm. To overcome this problem, we propose a new approach based on a novel combination of VMD and hierarchical (or h)-likelihood method. The h-likelihood provides an effective imputation methodology for missing data when VMD decomposes the signal into several meaningful modes. A simulation study and real data analysis demonstrates that the proposed method can produce substantially effective results.

• The Korean Journal of Applied Statistics
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• v.35 no.3
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• pp.395-406
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• 2022

This paper studies the outlier detection method for multivariate long memory time series. The existing outlier detection methods are based on a short memory VARMA model, so they are not suitable for multivariate long memory time series. It is because higher order of autoregressive model is necessary to account for long memory, however, it can also induce estimation instability as the number of parameter increases. To resolve this issue, we propose outlier detection methods based on the VHAR structure. We also adapt the robust estimation method to estimate VHAR coefficients more efficiently. Our simulation results show that our proposed method performs well in detecting outliers in multivariate long memory time series. Empirical analysis with stock index shows RVHAR model finds additional outliers that existing model does not detect.

• The Korean Journal of Applied Statistics
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• v.19 no.3
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• pp.421-430
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• 2006

In sample survey sample designs are performed by geographically-based domain such as countries, states and metropolitan areas. However mostly statistics of interests are smaller domain than sample designed domain. Then sample sizes are typically small or even zero within the domain of interest. Shin and Lee(2003) mentioned Spatial Autoregressive(SAR) model in small area estimation model-based method and show the effectiveness by MSE. In this study, Bayesian Auto-Poisson Model is applied in model-based small area estimation method and compare the results with SAR model using MSE ME and bias check diagnosis using regression line. In this paper Survey of Disability, Aging and Cares(SDAC) data are used for simulation studies.

• The Korean Journal of Applied Statistics
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• v.29 no.3
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• pp.471-485
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• 2016

Least squares (LS) regression is a classic method for regression that is optimal under assumptions of regression and usual observations. However, the presence of unusual data in the LS method leads to seriously distorted estimates. Therefore, various robust estimation methods are proposed to circumvent the limitations of traditional LS regression. Among these, there are M-estimators based on maximum likelihood estimation (MLE), L-estimators based on linear combinations of order statistics and R-estimators based on a linear combinations of the ordered residuals. In this paper, robust regression estimators with high breakdown point and/or with high efficiency are compared under several simulated situations. The paper analyses and compares distributions of estimates as well as relative efficiencies calculated from mean squared errors (MSE) in the simulation study. We conclude that MM-estimators or GR-estimators are a good choice for the real data application.

• Journal of the Korean Data and Information Science Society
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• v.28 no.4
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• pp.733-742
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• 2017

There are many areas of applications where Gumbel distribution are employed such as environmental sciences, system reliability and hydrology. The goodness-of-fit test for Gumbel distribution is very important in environmental sciences, system reliability and hydrology data analysis. Therefore, we propose the two test statistics to test goodness-of-fit for the Gumbel distribution based on the generalized Lorenz curve. We compare the new test statistic with the Anderson - Darling test, Cramer - vonMises test, and modified Anderson - Darling test in terms of the power of the test through by Monte Carlo method. As a result, the new test statistics are more powerful than the other test statistics. Also, we propose new graphic method to goodness-of-fit test for the Gumbel distribution based on the generalized Lorenz curve.

• Communications for Statistical Applications and Methods
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• v.17 no.3
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• pp.337-347
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• 2010

Most sample surveys are designed to estimate reliable statistics for the whole population and for some large subpopulations. However, the research for small area estimation have been increasing in recent years because users demand to reliable estimates for smaller subpopulations like small areas or specific domains. In Korea, the Economically Active Population Survey(EAPS) is the main household survey that produces monthly unemployment rates for nationwide and 16 large areas (7 metropolitans and 9 provinces) in Korea. For county level estimation, direct estimators are not reliable because of the small sample sizes. We consider small area estimation of the county level unemployment ratesfrom the sample observations in EAPS. To do this, we use an area level model to "borrow strength" from the auxiliary information, such as administrative data and census data. The proposed method is based on the assumption of normality of the model errors in the area level model. The proposed method is compared with the other alternatives in terms of the estimated mean squared errors.

• Communications for Statistical Applications and Methods
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• v.19 no.4
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• pp.619-628
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• 2012

Noise reduction is an important issue in the field of image processing because image noise lowers the quality of the original pure image. The basic difficulty is that the noise and the signal are not easily distinguished. Simple smoothing is the most basic and important procedure to effectively remove the noise; however, the weakness is that the feature area is simultaneously blurred. In this research, we use ways to measure the degree of noise with respect to the degree of image features and propose a Bayesian noise reduction method based on MAP (maximum a posteriori). Simulation results show that the proposed adaptive noise reduction algorithm using Bayesian MAP provides good performance regardless of the level of noise variance.