• Journal of the Korean Data and Information Science Society
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• v.21 no.6
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• pp.1171-1180
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• 2010

It is well known that the asymptotic convergence rates of nonparametric regression estimator gets worse as the dimension of covariates gets larger. One possible way to overcome this problem is reducing the dimension of covariates by using single index models. Two coefficient estimation methods in single index models are introduced. One is semiparametric least square estimation method, which tries to find approximate solution by using iterative computation. The other one is weighted average derivative estimation method, which is non-iterative method. Both of these methods offer the parametric convergence rate to normal distribution. However, practical comparison of these two methods has not been done yet. In this article, we compare these methods by examining the variances of estimators in various models.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.51 no.5
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• pp.386-395
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• 2006

The core questions for determining nitrogen topdress rate (Npi) at panicle initiation stage (PIS) are 'how much nitrogen accumulation during the reproductive stage (PNup) is required for the target rice yield or protein content depending on the growth and nitrogen nutrition status at PIS?' and 'how can we diagnose the growth and nitrogen nutrition status easily at real time basis?'. To address these questions, two years experiments from 2001 to 2002 were done under various rates of basal, tillering, and panicle nitrogen fertilizer by employing a rice cultivar, Hwaseongbyeo. The response of grain yield and milled-rice protein content was quantified in relation to RVIgreen (green ratio vegetation index) and SPAD reading measured around PIS as indirect estimators for growth and nitrogen nutrition status, the regression models were formulated to predict PNup based on the growth and nitrogen nutrition status and Npi at PIS. Grain yield showed quadratic response to PNup, RVIgreen around PIS, and SPAD reading around PIS. The regression models to predict grain yield had a high determination coefficient of above 0.95. PNup for the maximum grain yield was estimated to be 9 to 13.5 kgN/10a within the range of RVIgreen around PIS of this experiment. decreasing with increasing RVIgreen and also to be 10 to 11 kgN/10a regardless of SPAD readings around PIS. At these PNup's the protein content of milled rice was estimated to rise above 9% that might degrade eating quality seriously Milled-rice protein content showed curve-linear increase with the increase of PNup, RVIgreen around PIS, and SPAD reading around PIS. The regression models to predict protein content had a high determination coefficient of above 0.91. PNup to control the milled-rice protein content below 7% was estimated as 6 to 8 kgN/10a within the range of RVIgreen and SPAD reading of this experiment, showing much lower values than those for the maximum grain yield. The recovery of the Npi applied at PIS ranged from 53 to 83%, increasing with the increased growth amount while decreasing with the increasing Npi. The natural nitrogen supply from PIS to harvest ranged from 2.5 to 4 kg/10a, showing quadratic relationship with the shoot dry weight or shoot nitrogen content at PIS. The regression models to estimate PNup was formulated using Npi and anyone of RVIgreen, shoot dry weight, and shoot nitrogen content at PIS as predictor variables. These models showed good fitness with determination coefficients of 0.86 to 0.95 The prescription method based on the above models predicting grain yield, protein content and PNup and its constraints were discussed.

• The Korean Journal of Applied Statistics
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• v.10 no.1
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• pp.69-84
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• 1997

We consider a linear calibration problem, $y_i = $$\alpha + \beta (x_i - x_0) + \epsilon_i$, $i=1, 2, {\cdot}{\cdot},n$ $y_f = \alpha + \beta (x_f - x_0) + \epsilon, $ where we observe $(x_i, y_i)$'s for the controlled calibration experiments and later we make inference about $x_f$ from a new observation $y_f$. The objective of the calibration design problem is to find the optimal design $x = (x_i, \cdots, x_n$ that gives the best estimates for $x_f$. We compare Kim(1989)'s Bayesian design which minimizes the expected value of the posterior variance of $x_f$ and some optimal designs from literature. Kim suggested the Bayesian optimal design based on the analysis of the characteristics of the expected loss function and numerical must be equal to the prior mean and that the sum of squares be as large as possible. The designs to be compared are (1) Buonaccorsi(1986)'s AV optimal design that minimizes the average asymptotic variance of the classical estimators, (2) D-optimal and A-optimal design for the linear regression model that optimize some functions of $M(x) = \sum x_i x_i'$, and (3) Hunter & Lamboy (1981)'s reference design from their paper. In order to compare the designs which are optimal in some sense, we consider two criteria. First, we compare them by the expected posterior variance criterion and secondly, we perform the Monte Carlo simulation to obtain the HPD intervals and compare the lengths of them. If the prior mean of $x_f$ is at the center of the finite design interval, then the Bayesian, AV optimal, D-optimal and A-optimal designs are indentical and they are equally weighted end-point design. However if the prior mean is not at the center, then they are not expected to be identical.In this case, we demonstrate that the almost Bayesian-optimal design was slightly better than the approximate AV optimal design. We also investigate the effects of the prior variance of the parameters and solution for the case when the number of experiments is odd.

• Korean Journal of Soil Science and Fertilizer
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• v.13 no.1
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• pp.21-32
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• 1980

Linear models, with and without site variables, have been investigated in order to develop an alternative methodology for determining optimal fertilizer levels. The resultant models are : (1) Model I is an ordinary quadratic response function formed by combining the simple response function estimated at each site in block diagonal form, and has parameters [${\gamma}^{(1)}_{m{\ell}}$], for m=1, 2, ${\cdots}$, n sites and degrees of polynomial, ${\ell}$=0, 1, 2. (2) Mode II is a multiple regression model with a set of site variables (including an intercept) repeated for each fertilizer level and the linear and quadratic terms of the fertilizer variables arranged in block diagonal form as in Model I. The parameters are equal to [${\beta}_h\;{\gamma}^{(2)}_{m{\ell}}$] for h=0, 1, 2, ${\cdots}$, k site variable, m=1, 2, ${\cdots}$ and ${\ell}$=1, 2. (3) Model III is a classical response surface model, I. e., a common quadratic polynomial model for the fertilizer variables augmented with site variables and interactions between site variables and the linear fertilizer terms. The parameters are equal to [${\beta}_h\;{\gamma}_{\ell}\;{\theta}_h$], for h=0, 1, ${\cdots}$, k, ${\ell}$=1, 2, and h'=1, 2, ${\cdots}$, k. (4) Model IV has the same basic structure as Mode I, but estimation procedure involves two stages. In stage 1, yields for each fertilizer level are regressed on the site variables and the resulting predicted yields for each site are then regressed on the fertilizer variables in stage 2. Each model has been evaluated under the assumption that Model III is the postulated true response function. Under this assumption, Models I, II and IV give biased estimators of the linear fertilizer response parameter which depend on the interaction between site variables and applied fertilizer variables. When the interaction is significant, Model III is the most efficient for calculation of optimal fertilizer level. It has been found that Model IV is always more efficient than Models I and II, with efficiency depending on the magnitude of ${\lambda}m$, the mth diagonal element of X (X' X)' X' where X is the site variable matrix. When the site variable by linear fertilizer interaction parameters are zero or when the estimated interactions are not important, it is demonstrated that Model IV can be a reasonable alternative model for calculation of optimal fertilizer level. The efficiencies of the models are compared us ing data from 256 fertilizer trials on rice conducted in Korea. Although Model III is usually preferred, the empirical results from the data analysis support the feasibility of using Model IV in practice when the estimated interaction term between measured soil organic matter and applied nitrogen is not important.

• The Korean Journal of Financial Management
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• v.26 no.4
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• pp.191-234
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• 2009

This study examined on the volatility feedback hypothesis through the use of threshold GARCH-in-Mean (GJR-GARCH-M) model developed by Glosten, Jaganathan, and Runkle (1993) in the stock markets of 14 emerging countries during the period of January, 1996 to May, 2009. On this study, I found successful evidences which can support the volatility feedback hypothesis through the following three estimation procedures. First, I found relatively strong positive relationship between the expected market risk premiums and their conditional standard deviations from the GARCH-M model in the basis of daily return on each representative stock market index, which is appropriate to investors' risk-averse preferences. Second, I can also identify the significant asymmetric time-varying volatility originated from the investors' differentiated reactions toward the unexpected market shocks by applying the GJR-GARCH-M model and further find the lasting positive risk aversion coefficient estimators. Third, I derived the negative signs of the regression coefficient of unpredicted volatility on the stock market return by re-applying the GJR-GARCH-M model after I controlled the positive effect of predicted volatility through including the conditional standard deviations from the previous GARCH-M model estimation as an independent explanatory variable in the re-applied new GJR-GARCH-M model. With these consecutive results, the volatility feedback effect was successfully tested to be effective also in the various emerging stock markets, although the leverage hypothesis turned out to be insufficient to be applied to another source of explaining the negative relationship between the unexpected volatility and the ex-post stock market return in the emerging countries in general.

• The Korean Journal of Applied Statistics
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• v.37 no.2
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• pp.225-237
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• 2024

In the analysis of competing risks data, some of covariates may not be fully observed for some subjects. In such cases, excluding subjects with missing covariate values from the analysis may result in biased estimates and loss of efficiency. In this paper, we studied multiple imputation and the augmented inverse probability weighting method for regression parameter estimation in the cause-specific proportional hazards model with missing covariates. The performance of estimators obtained from multiple imputation and the augmented inverse probability weighting method is evaluated by simulation studies, which show that those methods perform well. Multiple imputation and the augmented inverse probability weighting method were applied to investigate significant risk factors for the risk of death from breast cancer and from other causes for breast cancer data with missing values for tumor size obtained from the Prostate, Lung, Colorectal, and Ovarian Cancer Screen Trial Study. Under the cause-specific proportional hazards model, the methods show that race, marital status, stage, grade, and tumor size are significant risk factors for breast cancer mortality, and stage has the greatest effect on increasing the risk of breast cancer death. Age at diagnosis and tumor size have significant effects on increasing the risk of other-cause death.

• KDI Journal of Economic Policy
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• v.12 no.2
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• pp.3-49
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• 1990

This paper analyzes U.S. demand for imports from Asian NIEs and Japan, utilizing the Almost Ideal Demand System (AIDS) developed by Deaton and Muellbauer, with an emphasis on the effect of changes in the exchange rate. The empirical model assumes a two-stage budgeting process in which the first stage represents the allocation of total U.S. demand among three groups: the Asian NIEs and Japan, six Western developed countries, and the U.S. domestic non-tradables and import competing sector. The second stage represents the allocation of total U.S. imports from the Asian NIEs and Japan among them, by country. According to the AIDS model, the share equation for the Asia NIEs and Japan in U.S. nominal GNP is estimated as a single equation for the first stage. The share equations for those five countries in total U.S. imports are estimated as a system with the general demand restrictions of homogeneity, symmetry and adding-up, together with polynomially distributed lag restrictions. The negativity condition is also satisfied for all cases. The overall results of these complicated estimations, using quarterly data from the first quarter of 1972 to the fourth quarter of 1989, are quite promising in terms of the significance of individual estimators and other statistics. The conclusions drawn from the estimation results and the derived demand elasticities can be summarized as follows: First, the exports of each Asian NIE to the U.S. are competitive with (substitutes for) Japan's exports, while complementary to the exports of fellow NIEs, with the exception of the competitive relation between Hong Kong and Singapore. Second, the exports of each Asian NIE and of Japan to the U.S. are competitive with those of Western developed countries' to the U.S, while they are complementary to the U.S.' non-tradables and import-competing sector. Third, as far as both the first and second stages of budgeting are coneidered, the imports from each Asian NIE and Japan are luxuries in total U.S. consumption. However, when only the second budgeting stage is considered, the imports from Japan and Singapore are luxuries in U.S. imports from the NIEs and Japan, while those of Korea, Taiwan and Hong Kong are necessities. Fourth, the above results may be evidenced more concretely in their implied exchange rate effects. It appears that, in general, a change in the yen-dollar exchange rate will have at least as great an impact, on an NIE's share and volume of exports to the U.S. though in the opposite direction, as a change in the exchange rate of the NIE's own currency $vis-{\grave{a}}-vis$ the dollar. Asian NIEs, therefore, should counteract yen-dollar movements in order to stabilize their exports to the U.S.. More specifically, Korea should depreciate the value of the won relative to the dollar by approximately the same proportion as the depreciation rate of the yen $vis-{\grave{a}}-vis$ the dollar, in order to maintain the volume of Korean exports to the U.S.. In the worst case scenario, Korea should devalue the won by three times the maguitude of the yen's depreciation rate, in order to keep market share in the aforementioned five countries' total exports to the U.S.. Finally, this study provides additional information which may support empirical findings on the competitive relations among the Asian NIEs and Japan. The correlation matrices among the strutures of those five countries' exports to the U.S.. during the 1970s and 1980s were estimated, with the export structure constructed as the shares of each of the 29 industrial sectors' exports as defined by the 3 digit KSIC in total exports to the U.S. from each individual country. In general, the correlation between each of the four Asian NIEs and Japan, and that between Hong Kong and Singapore, are all far below .5, while the ones among the Asian NIEs themselves (except for the one between Hong Kong and Singapore) all greatly exceed .5. If there exists a tendency on the part of the U.S. to import goods in each specific sector from different countries in a relatively constant proportion, the export structures of those countries will probably exhibit a high correlation. To take this hypothesis to the extreme, if the U.S. maintained an absolutely fixed ratio between its imports from any two countries for each of the 29 sectors, the correlation between the export structures of these two countries would be perfect. Therefore, since any two goods purchased in a fixed proportion could be classified as close complements, a high correlation between export structures will imply a complementary relationship between them. Conversely, low correlation would imply a competitive relationship. According to this interpretation, the pattern formed by the correlation coefficients among the five countries' export structures to the U.S. are consistent with the empirical findings of the regression analysis.