• Journal of the Korean Statistical Society
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• v.25 no.1
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• pp.25-37
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• 1996

In this paper, we propose regression estimators based on a partial replacement sampling scheme over two successive occasions and derive the minimum variances of them. PPSWR, RHC, $\pi$PS and PPSWOR schemes are considered to select unequal probability samples on two occasions. Simulation results over four populations are given for comparison of composite estimators and regression estimators.

• Journal of the Korean Statistical Society
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• v.33 no.1
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• pp.79-97
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• 2004

We propose a permutation approach to the classic Behrens-Fisher problem of comparing two means in the presence of unequal variances. It is motivated by the observation that a paired test is valid whether or not the variances are equal. Rather than using a single arbitrary pairing of the data, we average over all possible pairings. We do this in both a parametric and nonparametric setting. When the sample sizes are equal, the parametric version is equivalent to referral of the unpaired t-statistic to a t-table with half the usual degrees of freedom. The derivation provides an interesting representation of the unpaired t-statistic in terms of all possible pairwise t-statistics. The nonparametric version uses the same idea of considering all different pairings of data from the two groups, but applies it to a permutation test setting. Each pairing gives rise to a permutation distribution obtained by relabeling treatment and control within pairs. The totality of different mean differences across all possible pairings and relabelings forms the null distribution upon which the p-value is based. The conservatism of this procedure diminishes as the disparity in variances increases, disappearing completely when the ratio of the smaller to larger variance approaches 0. The nonparametric procedure behaves increasingly like a paired t-test as the sample sizes increase.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.553-566
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• 2003

In many cases, the measurement error variances may be functions of the unknown true values or related covariates. This paper considers design-based estimators of the parameters of these variance functions based on the within-unit sample variances. This paper devotes to: (1) define an error scale factor $\delta$; (2) develop estimators of the parameters of the linear measurement error variance function of the true values under large-sample and small-error conditions; (3) use propensity methods to adjust survey weights to account for possible selection effects at the replicate level. The proposed methods are applied to medical examination data from the U.S. Third National Health and Nutrition Examination Survey (NHANES III).

• 한국데이터정보과학회:학술대회논문집
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• 2003.05a
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• pp.1-14
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• 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)

• Journal of Korean Society for Quality Management
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• v.27 no.1
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• pp.101-110
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• 1999

Products are often evaluated on rating scales to measure and quantify their attributes of interest. In case that one wishes to compare multiple rating datasets simultaneously, there must be a standardized scale with which one can discriminate relative differences among corresponding scale means. In this regard, the concept of Thurstonian modeling applied to various discrimination tests including the triangular method has been recently being reconsidered. In this paper we extend previous researches on the triangular method and evaluate the effect of unequal variances and correlated variables upon the probability of correct response using Monte-Carlo simulation. We observed that the probability of correct response depends on dimensionality, variances, and correlation structure of stimulus sets. But it does not depend on the relative orientation in a multidimensional space.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.193-205
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• 1999

An approximate Bayes criterion for Behrens-Fisher problem (testing equality of means of two normal populations with unequal variances) is proposed and examined. Development of the criterion involves derivation of approximate Bayes factor using the imaginary training sample approachintroduced by Spiegelhalter and Smith (1982). The proposed criterion is designed to develop a Bayesian test criterion having a closed form, so that it provides an alternative test to those based upon asymptotic sampling theory (such as Welch's t test). For the suggested Bayes criterion, numerical study gives comparisons with a couple of asymptotic classical test criteria.

• Journal of Applied Reliability
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• v.2 no.2
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• pp.113-119
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• 2002

The estimation of mean lifetimes in presence of interval censoring with replacement procedure are examined when the distributions of lifetimes are exponential. It is assumed that, due to physical restrictions and/or economic constraints, the number of failures is investigated only at several inspection times during the lifetime test. The maximum likelihood estimator is found in an implicit form. The Cramer-Rao lower bounds of the estimates are found in places of variances and by simulations the properties of the estimates are examined.

• The Mathematical Education
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• v.45 no.2 s.113
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• pp.145-154
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• 2006

The main purpose of this study is to investigate the effect of departures from normality and equal variance on the two-sample test when the variances are unknown. We have found that type I error brought about a little bit change which is ignorable in relation to kurtosis. But the change of type I error was mainly based on the skewness of the parent population. In introductory statistics classes where data analysis includes techniques for detecting skewness of two populations, we recommend the two-sample t-test when maximal skewness of two populations is smalter than the value 4 when the variances seem equal. Furthermore, our simulations reveal that the two-sample t-test appears somewhat more robust than that of z-test if the assumption of equal variance is satisfied. In the case of unequal variance, the two-sample t-test appears somewhat more robust provided the t-statistic using Satterthwaite's approximate degrees of freedom.

• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.765-774
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• 2002

Suppose one is given a vector X of a finite set of quantities $X_i$ which are independent Poisson random variables. A null hypothesis $H_0$ about E(X) is to be tested against an alternative hypothesis $H_1$. A quantity $\sum\limits_{i}w_ix_i$ is to be computed and used for the test. The optimal values of $W_i$ are calculated for three cases: (1) signal to noise ratio is used in the test, (2) normal approximations with unequal variances to the Poisson distributions are used in the test, and (3) the Poisson distribution itself is used. The above three cases are considered to the situations that are without background noise and with background noise. A comparison is made of the optimal values of $W_i$ in the three cases for both situations.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.307-315
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• 2002

Suppose one is given a vector X of a finite set of quantities $X_i$ which are independent Poisson signals. A null hypothesis $H_0$ about E(X) is to be tested against an alternative hypothesis $H_1$. A quantity $$\sum\limits_{i}\omega_ix_i$$ is to be computed and used for the test. The optimal values of $\omega_i$ are calculated for three cases : (1) signal to noise ratio is used in the test, (2) normal approximations with unequal variances to the Poisson distributions are used in the test, and (3) the Poisson distribution it self is used. A comparison is made of the optimal values of $\omega_i$ in the three cases as parameter goes to infinity.