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Design of On-line Process Control with Variable Measurement Interval
Park, Changsoon The Korean Statistical Society 2000 Journal of the Korean Statistical Society Vol.29 No.3
A mixed model with a white noise process and an IMA(0,1,1) process is considered as a process model. It is assumed that the process is a white noise in the absence of a special cause and the process changes to an IMA(0,1,1) due to a special cause. One useful scheme in measuring the process level is to use the variable measurement interval (VMI) between measurement times according to the value of the previous chart statistic. The advantage of the VMI scheme is to measure the process level infrequently when in control to save the measurement cost and to measure frequently when out of control to save the off-target cost. This paper considers the VMI scheme in order to detect changes in the process model from a white noise to an IMA(0,1,1). The VMI scheme is shown to be effective compared to the standard fixed measurement interval (FMI) scheme in both statistical and economic contexts.
STATISTICS PRESENT, NEAR FUTURE, AND BEYOND
Johnson, Richard A. The Korean Statistical Society 2001 Communications for statistical applications and me Vol.8 No.-
We berlin with a brief review of some important advances made in statistical theory over the last decade. The choice of topics is decidedly influenced by personal interests. Based on this review, we then propose some possible scenarios about the future of statistics.
Statistical Bias and Inflated Variance in the Genehunter Nonparametric Linkage Test Statistic
Song, Hae-Hiang,Choi, Eun-Kyeong The Korean Statistical Society 2009 Communications for statistical applications and me Vol.16 No.2
Evidence of linkage is expressed as a decreasing trend of the squared trait difference of two siblings with increasing identical by descent scores. In contrast to successes in the application of a parametric approach of Haseman-Elston regression, notably low powers are demonstrated in the nonparametric linkage analysis methods for complex traits and diseases with sib-pairs data. We report that the Genehunter nonparametric linkage statistic is biased and furthermore the variance formula that they used is an inflated one, and this is one reason for a low performance. Thus, we propose bias-corrected nonparametric linkage statistics. Simulation studies comparing our proposed nonparametric test statistics versus the existing test statistics suggest that the bias-corrected new nonparametric test statistics are more powerful and attains efficiencies close to that of Haseman-Elston regression.
On the comparison of cumulative hazard functions
Park, Sangun,Ha, Seung Ah The Korean Statistical Society 2019 Communications for statistical applications and me Vol.26 No.6
This paper proposes two distance measures between two cumulative hazard functions that can be obtained by comparing their difference and ratio, respectively. Then we estimate the measures and present goodness of t test statistics. Since the proposed test statistics are expressed in terms of the cumulative hazard functions, we can easily give more weights on earlier (or later) departures in cumulative hazards if we like to place an emphasis on earlier (or later) departures. We also show that these test statistics present comparable performances with other well-known test statistics based on the empirical distribution function for an exponential null distribution. The proposed test statistic is an omnibus test which is applicable to other lots of distributions than an exponential distribution.
Zooming Statistics: Inference across scales
Hannig, Jan,Marron, J.S.,Riedi, R.H. The Korean Statistical Society 2001 Journal of the Korean Statistical Society Vol.30 No.2
New statistical methods are ended to analyzed data in a multi-scale way. Some multi-scale extensions of stand methods, including novel visualization using dynamic graphics are proposed. These tools are used to explore non-standard structure in internet traffic data.
Non-identifiability and testability of missing mechanisms in incomplete two-way contingency tables
Park, Yousung,Oh, Seung Mo,Kwon, Tae Yeon The Korean Statistical Society 2021 Communications for statistical applications and me Vol.28 No.3
We showed that any missing mechanism is reproduced by EMAR or MNAR with equal fit for observed likelihood if there are non-negative solutions of maximum likelihood equations. This is a generalization of Molenberghs et al. (2008) and Jeon et al. (2019). Nonetheless, as MCAR becomes a nested model of MNAR, a natural question is whether or not MNAR and MCAR are testable by using the well-known three statistics, LR (Likelihood ratio), Wald, and Score test statistics. Through simulation studies, we compared these three statistics. We investigated to what extent the boundary solution affect tesing MCAR against MNAR, which is the only testable pair of missing mechanisms based on observed likelihood. We showed that all three statistics are useful as long as the boundary proximity is far from 1.
Kim, S.H,Kim, T.S. The Korean Statistical Society 1998 Communications for statistical applications and me Vol.5 No.3
For a random sample of size n from general linear model, $Y_i= heta(X_i)+varepsilon_i,;let Y_{in}$ denote the ith oder statistics of the Y sample values. The X-value associated with $Y_{in}$ is denoted by $X_{[in]}$ and is called the concomitant of ith order statistics. The estimator of the location of a maximum of a regression function, $ heta$($\chi$), was proposed by (equation omitted) and was found the convergence rate of it under certain weak assumptions on $ heta$. We will discuss the asymptotic distributions of both $ heta(X_{〔n-r+1〕}$) and (equation omitted) when r is fixed as nolongrightarrow$\infty$(i.e. extreme case) on the basis of the theorem of the concomitants of order statistics. And the will investigate the asymptotic behavior of Max{$\theta$( $X_{〔n-r+1:n〕/}$ ), . , $\theta$( $X_{〔n:n〕}$)}as an estimator for the peak of a regression function.
A Study on Cell Influences to Chi-square Statistic in Contingency Tables
Kim, Hong-Gie The Korean Statistical Society 1998 Communications for statistical applications and me Vol.5 No.1
Once a contingency table is constructed, the first interest will be the hypotheses of either homogeneity or independence depending on the sampling scheme. The most widely used test statistic in practice is the classical Pearson's $\chi^2$ statistic. When the null hypothesis is rejected, another natural interest becomes which cell contributed to the rejection of the null hypothesis more than others. For this purpose, so called cell $\chi^2$ components are investigated. In this paper, the influence function of a cell to the $\chi^2$ statistic is derived, which can be used for the same purpose. This function measures the effect of each cell to the $\chi$$^2$ statistic. A numerical example is given to demonstrate the role of the new function.
Influence Measures for a Test Statistic on Independence of Two Random Vectors
Jung Kang-Mo The Korean Statistical Society 2005 Communications for statistical applications and me Vol.12 No.3
In statistical diagnostics a large number of influence measures have been proposed for identifying outliers and influential observations. However it seems to be few accounts of the influence diagnostics on test statistics. We study influence analysis on the likelihood ratio test statistic whether the two sets of variables are uncorrelated with one another or not. The influence of observations is measured using the case-deletion approach, the influence function. We compared the proposed influence measures through two illustrative examples.
Test procedures for the mean and variance simultaneously under normality
Park, Hyo-Il The Korean Statistical Society 2016 Communications for statistical applications and me Vol.23 No.6
In this study, we propose several simultaneous tests to detect the difference between means and variances for the two-sample problem when the underlying distribution is normal. For this, we apply the likelihood ratio principle and propose a likelihood ratio test. We then consider a union-intersection test after identifying the likelihood statistic, a product of two individual likelihood statistics, to test the individual sub-null hypotheses. By noting that the union-intersection test can be considered a simultaneous test with combination function, also we propose simultaneous tests with combination functions to combine individual tests for each sub-null hypothesis. We apply the permutation principle to obtain the null distributions. We then provide an example to illustrate our proposed procedure and compare the efficiency among the proposed tests through a simulation study. We discuss some interesting features related to the simultaneous test as concluding remarks. Finally we show the expression of the likelihood ratio statistic with a product of two individual likelihood ratio statistics.