• Journal of the Korean Data and Information Science Society
• /
• v.20 no.2
• /
• pp.251-260
• /
• 2009

In this study, we propose a new estimation method based on autocovariance for selecting optimal estimators of the regression coefficients in the simple linear regression model. Although this method does not seem to be intuitively attractive, these estimators are unbiased for the corresponding regression coefficients. When the exploratory variable takes the equally spaced values between 0 and 1, under mild conditions which are satisfied when errors follow an autoregressive moving average model, we show that these estimators have asymptotically the same distributions as the least squares estimators. Additionally, under the same conditions as before, we provide a self-contained proof that these estimators converge in probability to the corresponding regression coefficients.

• International Journal of Reliability and Applications
• /
• v.7 no.2
• /
• pp.187-201
• /
• 2006

In this paper, we derive recurrence relations for the single and product moments of progressively Type-II right censored order statistics from half logistic distribution. Next, we derive the maximum likelihood estimators (MLEs) of the location and scale parameters of the half logistic distribution. In addition, we use the setup proposed by Balakrishnan and Aggarwala (2000) to compute the approximate best linear unbiased estimates (ABLUEs) of the location and scale parameters. Finally, we point out a simulation study to compare between the efficiency of the techniques considered for the estimation.

• Proceedings of the KIEE Conference
• /
• 1998.07a
• /
• pp.396-398
• /
• 1998

Two estimators for the scale (${\delta}$) and shape (${\beta}$) parameters and percentiles of the Weibull distribution were compared. These estimators are maximum likelihood estimator (MLE) and the best linear unbiased estimator (BLUE). The performance of these estimators are compared by mean square error and studied in complete and type II censored samples of size 10 and 25. The overall performance of the MLE was similar to that of the BLUE.

• Journal of the Korean Statistical Society
• /
• v.22 no.2
• /
• pp.209-217
• /
• 1993

The multicollinearity problem in a multiple linear regression model may present deleterious effects on predictions. Thus, its is desirable to consider the optimal fractions with respect to the unbiased estimate of the mean squares errors of the predicted values. Interstingly, the optimal fractions can be also illuminated by the Bayesian inerpretation of the general James-Stein estimators.

• Journal of the Korean Statistical Society
• /
• v.36 no.1
• /
• pp.57-76
• /
• 2007

Kriging is a nonparametric regression method used in geostatistics for estimating curves and surfaces for spatial data. It may come as a surprise that the Kriging estimator, normally derived as the best linear unbiased estimator, is also the solution of a particular variational problem. Thus, Kriging estimators can also be interpreted as generalized smoothing splines where the roughness penalty is determined by the covariance function of a spatial process. We build off the early work by Silverman (1982, 1984) and the analysis by Cox (1983, 1984), Messer (1991), Messer and Goldstein (1993) and others and develop an equivalent kernel interpretation of geostatistical estimators. Given this connection we show how a given covariance function influences the bias and variance of the Kriging estimate as well as the mean squared prediction error. Some specific asymptotic results are given in one dimension for Matern covariances that have as their limit cubic smoothing splines.

• Communications for Statistical Applications and Methods
• /
• v.30 no.4
• /
• pp.403-410
• /
• 2023

Two-Phase sampling, which was first introduced by Neyman (1938), has various applications in different forms. Variance estimation for two-phase sampling has been an important research topic because conventional variance estimators used in most softwares are not working. In this paper, we considered a variance estimation for two-phase sampling in which stratified two-stage cluster sampling designs are used in both phases. By defining a conditionally unbiased estimator of an approximate variance estimator, which is calculable when all elements in the first phase sample are observed, we propose an explicit form of variance estimator of the double expanded estimator for a two-phase sample. A small simulation study shows the proposed variance estimator has a negligible bias with small variance. The suggested variance estimator is also applicable to other linear estimators of the population total or mean if appropriate residuals are defined.

• 한국데이터정보과학회:학술대회논문집
• /
• 2003.05a
• /
• pp.1-14
• /
• 2003

In man cases, the measurement error variances may be functions of the unknown true values or related covariate. In some cases, the measurement error variances increase in proportion to the value of predictor. This paper develops estimators of the parameters of a linear measurement error variance function under stratified multistage random sampling design and additional conditions. Also, this paper evaluates and compares the power of an asymptotically unbiased test with that of an asymptotically biased test. The proposed method are applied to blood sample measurements from the U.S. Third National Health and Nutrition Examination Survey(NHANES III)

• Communications for Statistical Applications and Methods
• /
• v.31 no.1
• /
• pp.155-178
• /
• 2024

Regression discontinuity (RD) design is one of the most widely used methods in causal inference for estimation of treatment effect when the treatment is created by a cutpoint from the covariate of interest. There has been little attention to RD design, although it provides a very useful tool for analysis of treatment effect for censored data. In this paper, we define the causal effect for survival function in RD design when the treatment is assigned deterministically by the covariate of interest. We propose estimators of this causal effect for survival data by using transformation, which leads unbiased estimator of the survival function with local linear regression. Simulation studies show the validity of our approach. We also illustrate our proposed method using the prostate, lung, colorectal and ovarian (PLCO) dataset.

• Journal of the Korean Data and Information Science Society
• /
• v.11 no.1
• /
• pp.111-126
• /
• 2000

Small area estimation is becoming important in survey sampling due to a growing demand for reliable small area statistics. In estimating means, totals, and other parameters for small areas of a finite population, samplie sizes for small areas are typically small because the overall sample size is usually determined to provide specific accuracy at a much higher level of aggregation than that of small area. The usual direct estimators that use the only information which is gotten from the sample in a given small area provide unreliable estimates. However, indirect estimators utilize the information from the areas related with a given small area, that is, borrow strength from other related areas, and so give more accurate estimates than direct estimators. In this paper we investigate small area estimation methods such as synthetic, composite and empirical best linear unbiased prediction estimator, and apply them to real domestic data which is from the Survey of Hotels and Restaurants in In-Chon as of 1996 and then evaluate the performance of these methods by measuring average squared errors. This evaluation shows that indirect estimators, which are small area estimation methods, are more efficient than direct estimator.

• Proceedings of the Korean Association for Survey Research Conference
• /
• 2000.06a
• /
• pp.57-73
• /
• 2000

Small area estimation is becoming important in survey sampling due to a growing demand for reliable small area statistics. In estimating means, totals, and other parameters for small areas of a finite population, samplie sizes for small areas are typically small because the overall sample size is usually determined to provide specific accuracy at a much higher level of aggregation than that of small area. The usual direct estimators that use the only information which is gotten from the sample in a given small area provide unreliable estimates. However, indirect estimators utilize the information from the areas related with a given small area, that is borrow strength from other related areas, and so give more accurate estimates than direct estimators. In this paper we investigate small area estimation methods such as synthetic, composite and empirical best linear unbiased prediction estimator, and apply them to real domestic data which is from the Survey of Hotels and Restaurants in In-Chon as of 1996 and then evaluate the performance of these methods by measuring average squared errors. This evaluation shows that indirect estimators, which are small area estimation methods, are more efficient direct estimator.