• The Korean Journal of Applied Statistics
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• v.29 no.1
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• pp.157-169
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• 2016

We compare four methods to estimate a regression coefficient under linear regression models with serially correlated errors. We assume that regression errors are generated with nonlinear autoregressive models. The four methods are: ordinary least square estimator, general least square estimator, parametric regression error correction method, and nonparametric regression error correction method. We also discuss some properties of nonlinear autoregressive models by presenting numerical studies with typical examples. Our numerical study suggests that no method dominates; however, the nonparametric regression error correction method works quite well.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1753-1767
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• 2008

Consider the nonparametric regression model $Y_{ni}\;=\;g(x_{ni})+{\epsilon}_{ni}$ ($1\;{\leq}\;i\;{\leq}\;n$), where g($\cdot$) is an unknown regression function, $x_{ni}$ are known fixed design points, and the correlated errors {${\epsilon}_{ni}$, $1\;{\leq}\;i\;{\leq}\;n$} have the same distribution as {$V_i$, $1\;{\leq}\;i\;{\leq}\;n$}, here $V_t\;=\;{\sum}^{\infty}_{j=-{\infty}}\;{\psi}_je_{t-j}$ with ${\sum}^{\infty}_{j=-{\infty}}\;|{\psi}_j|$ < $\infty$ and {$e_t$} are negatively associated random variables. Under appropriate conditions, we derive a Berry-Esseen type bound for the estimator of g($\cdot$). As corollary, by choice of the weights, the Berry-Esseen type bound can attain O($n^{-1/4}({\log}\;n)^{3/4}$).

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.31-38
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• 2003

A simple method is proposed to detect the number of change points and test the location and size of multiple change points with jump discontinuities in an otherwise smooth regression model. The proposed estimators are based on a local linear regression fit by the comparison of left and right one-side kernel smoother. Our proposed methodology is explained and applied to real data and simulated data.

• The Korean Journal of Applied Statistics
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• v.21 no.1
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• pp.19-33
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• 2008

Linear regression method, proposed by Haseman and Elston(1972), for detecting linkage to a quantitative trait of sib pairs is a linkage testing method for a single locus and a single trait. However, multivariate methods for detecting linkage are needed, when information from each of several traits that are affected by the same major gene are available on each individual. Amos et al. (1990) extended the regression method of Haseman and Elston(1972) to incorporate observations of two or more traits by estimating the principal component linear function that results in the strongest correlation between the squared pair differences in the trait measurements and identity by descent at a marker locus. But, it is impossible to control the probability of type I errors with this method at present, since the exact distribution of the statistic that they use is yet unknown. In this paper, we propose a multivariate nonparametric trend test for detecting linkage to multiple traits. We compared with a simulation study the efficiencies of multivariate nonparametric trend test with those of the method developed by Amos et al. (1990) for quantitative traits data. For multivariate nonparametric trend test, the results of the simulation study reveal that the Type I error rates are close to the predetermined significance levels, and have in general high powers.

• Communications for Statistical Applications and Methods
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• v.19 no.6
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• pp.809-817
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• 2012

We propose a semiparametric inference for a generalized varying coefficient partially linear model(VCPLM) for negative binomial data. The VCPLM is useful to model real data in that varying coefficients are a special type of interaction between explanatory variables and partially linear models fit both parametric and nonparametric terms. The negative binomial distribution often arise in modelling count data which usually are overdispersed. The varying coefficient function estimators and regression parameters in generalized VCPLM are obtained by formulating a penalized likelihood through smoothing splines for negative binomial data when the shape parameter is known. The performance of the proposed method is then evaluated by simulations.

• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.85-92
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• 2003

We consider the partially linear model E(Y) : X$^{t}$ $\beta$＋η(Z) when the X's are measured with additive error. The semiparametric likelihood estimation ignoring the measurement error gives inconsistent estimator for both $\beta$ and η(.). In this paper we suggest the SIMEX estimator for f to correct the bias induced by measurement error, and explore its properties. We show that the rational linear extrapolant is proper in extrapolation step in the sense that the SIMEX method under this extrapolant gives consistent estimator It is also shown that the SIMEX estimator is asymptotically equivalent to the semiparametric version of the usual parametric correction for attenuation suggested by Liang et al. (1999) A simulation study is given to compare two variance estimating methods for SIMEX estimator.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.385-407
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• 2010

To study the relationship between the levels of chemical pollutants and the number of daily total hospital admissions for respiratory diseases and to find the effect of temperature/relative humidity on the admission number, Wong et al. [17] introduced the varying-coefficient single-index model (VCSIM). As pointed out, it is a popular multivariate nonparametric fitting technique. However, the tests of the model have not been very well developed. In this paper, based on the estimators obtained by the local linear technique, the average method and the one-step back-fitting technique in the VCSIM, the generalized likelihood ratio (GLR) tests for varying-coefficient parts on the VCSIM are established. Under the null hypotheses the new proposed GLR tests follow the $\chi^2$-distribution asymptotically with scale constant and degree of freedom independent of the nuisance parameters, known as Wilks phenomenon. Simulations are conducted to evaluate the test procedure empirically. A real example is used to illustrate the performance of the testing approach.

• The Korean Journal of Applied Statistics
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• v.34 no.6
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• pp.923-936
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• 2021

A large number of non-responses are occurring in the sample survey, and various methods have been developed to deal with them appropriately. In particular, the bias caused by non-ignorable non-response greatly reduces the accuracy of estimation and makes non-response processing difficult. Recently, Chung and Shin (2017, 2020) proposed an estimator that improves the accuracy of estimation using parametric super-population model and response rate model. In this study, we suggested a bias corrected non-response mean estimator using a nonparametric function generalizing the form of a parametric super-population model. We confirmed the superiority of the proposed estimator through simulation studies.

• Communications for Statistical Applications and Methods
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• v.16 no.4
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• pp.713-722
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• 2009

The estimation of odds ratio and corresponding confidence intervals for case-control data have been done by traditional generalized linear models which assumed that the logarithm of odds ratio is linearly related to risk factors. We adapt a lower-dimensional approximation of Gu and Kim (2002) to provide a faster computation in nonparametric method for the estimation of odds ratio by allowing flexibility of the estimating function and its Bayesian confidence interval under the Bayes model for the lower-dimensional approximations. Simulation studies showed that taking larger samples with the lower-dimensional approximations help to improve the smoothing spline estimates of odds ratio in this settings. The proposed method can be used to analyze case-control data in medical studies.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2003.09a
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• pp.20-27
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• 2003

The nonparametric method was employed to obtain detailed broadband attenuation characteristics of horizontal Fourier spectra without generally assigned constraint that derived path terms be zeros at a reference distance. Instead, path terms fer a reference distance were obtained based on the physical phenomenon that the seismic phase is stable over the hypocentral distance range from 200km to 400km so that the Q-values evaluated at several distances inside that region should be the same. The inverted path terms show three distinct linear regions roughly divided by hypocentral distances at 65km and 115km. Also complex behavior at the near distance range below 100km was revealed which can not be properly fitted by combination of single $Q_{0}$ $f^{η}$ model and any geometrical spreading models.s.