Comparing the empirical powers of several independence tests in generalized FGM family

Zargar, M.,Jabbari, H.,Amini, M. The Korean Statistical Society 2016 Communications for statistical applications and me Vol.23 No.3

The powers of some tests for independence hypothesis against positive (negative) quadrant dependence in generalized Farlie-Gumbel-Morgenstern distribution are compared graphically by simulation. Some of these tests are usual linear rank tests of independence. Two other possible rank tests of independence are locally most powerful rank test and a powerful nonparametric test based on the $Cram{\acute{e}}r-von$ Mises statistic. We also evaluate the empirical power of the class of distribution-free tests proposed by Kochar and Gupta (1987) based on the asymptotic distribution of a U-statistic and the test statistic proposed by $G{\ddot{u}}ven$ and Kotz (2008) in generalized Farlie-Gumbel-Morgenstern distribution. Tests of independence are also compared for sample sizes n = 20, 30, 50, empirically. Finally, we apply two examples to illustrate the results.

On Detecting Multiple Outliers in Gamma Samples

황은영,조영석,김동희 한국자료분석학회 2017 Journal of the Korean Data Analysis Society Vol.19 No.5

In this paper, we suggest the test statistic for detecting multiple outliers in gamma distribution and derive its probability density function using characteristic function. Since the probability density function of the proposed function is very complicative, from simulation study, we present the critical values of the proposed test statistics to detect outliers easily. We also compare the powers of the proposed test statistic with other comparative statistics, Dixon (1950)’s statistic, Nooghabi et al. (2010)‘s statistic, Kumar, Lalitha (2012)’s statistic, Kim, Kim (2015)’s statistic. Throughout the simulation studies, we show that our proposed test statistic has good powers among other statistics. In particular we can inspect that the powers of our proposed test statistics are relatively good when the number of outliers, k, is greater than or equal to 2. As we know, an exponential distribution is a special case of a gamma distribution, therefore the results in this paper are applicable to an exponential distribution.

전략적 인적자원관리(SHRM) 연구에 있어서 적합성 검증에 관한 방법론적 연구

장충석 대한경영학회 2002 大韓經營學會誌 Vol.15 No.4

This Study aims to explore the concept of fit and its statistical correspondence. The concept of fit has an important building block for theory construction in several areas of research. However, a major problem is the lack of corresponding schemes by which fit has been tested. A lack of correspondence between the concept and its mathematical formulation weakness the link between theory building and theory testing, which may be a major reason for inconsistent research result. This paper has been developed along the following premises: (a) fit is central to both theoretical discussions and empirical research in strategic human resources management; (b) the role of fit in strategic human resources management has been severely handicapped by the absence of appropriate links between the concept and theory testing; and (c) although the operationalization of fit has been discussed generally, this research in particular or the many testing issues that are central to liking concepts with empirical tests. Fit, as a general concept, is central to the study of strategic human resources management. Yet, theory in this area must be extended th clarify the specific meaning of fit as used in various settings, to develop strong links between verbalizations and statistical testing schemes, and to test relationships by using multiple comparable statistical schemes wherever feasible. Toward this end, six concepts of fit within strategic human resources management have been discussed. For each perspective, available statistical schemes highlighted the isomorphic nature of the link between the theory and the testing scheme, and it was demonstrated that the statistical methods are not freely interchangeable without confounding the underlying theoretical meaning of fit.

Neyman-Pearson 검정과 Fisher 검정에 의한 비모수 통계의 고찰

최성운 대한안전경영과학회 2008 대한안전경영과학회 학술대회논문집 Vol.2008 No.04

This paper reviews nonparametric statistics by Neyman-Pearson test and Fisher test. Nonparametric statistics deal with the small sample with distribution-free assumption in multi-product and small-volume production. Two tests for various nonparametric statistic methods such as sign test, Wilcoxon test, Mann-Whitney test, Kruskal-Wallis test, Mood test, Friedman test and run test are also presented with the steps for testing hypotheses and test of significance.

KOSPI시장에서 대용시장지수의 효율성 검증

구본열 ( Bon Yul Koo ),남윤명 ( Yun Myung Nam ),유수연 ( Su Yeon Ryu ),김병기 ( Pyung Kee Kim ) 한국금융공학회 2015 금융공학연구 Vol.14 No.3

대용시장지수에 대한 사전적 효율성에 대한 연구는 연구접근의 방법의 차이에 따라 크게 두 분류로 나누어 질 수 있는데, Ross(1980)에 의한 무위험자산이 존재하는 경우의 효율성 검증과 Shanken(1985)에 의한 무위험자산이 존재하지 않을 경우인 제로베타(zero-beta)모형에 의한 효율성 검증이다. 그런데 이에 대한 국내의 연구는 대부분 1990년대에 이루어졌고, 구본열-남윤명-김병기(2010)는 비교적 최근에 검증을 실시하였으나 KOSDAQ시장을 중심으로 효율성을 검증하였다. 따라서 한국경제 및 환경의 변화에 따라 KOSPI시장에 대한 효율성을 최근의 자료를 이용하여 새롭게 검증하는 것은 큰 의의가 있다고 하겠다. 이에 본 연구는 KOSPI시장에서 무위험자산이 존재하는 경우에는 Ross(1980)의X2 통계치에 의한 대용시장지수의 효율성 검증과 무위험자산이 존재하지 않을 경우에는 Shanken(1985)의 F 통계치에 의한 효율성 검증을 시행하고자 하였다. 효율성 검증을 위하여 채택된 대용시장지수들은 KOSPI지수, KRX100지수와 EW지수이다. 실증적 연구결과, Ross(1980)에 의한 효율성 검증에서 KOSPI지수와 KRX100지수는 대용시장지수가 효율적이라는 귀무가설을 기각하였다. 그러나 EW지수는 대용시장지수가 효율적이라는 귀무가설을 기각하지 못하였으며 EW지수의 평균수익률도 GMVP의 수익률보다 크기 때문에 효율적 프론티어상의 효율성이 성립하였다. 그리고 Shanken(1985)에 의한 효율성 검증에서 KOSPI지수, KRX100지수와 EW지수 모두 대용시장지수가 효율적이라는 귀무가설을 기각하지 못하였다. 그러나 KOSPI지수와 KRX100지수의 평균수익률은 GMVP의 평균수익률보다 작기 때문에 효율적 프론티어상에 있는가에 대한 효율성 검증이라기보다 단순히 평균-분산 프론티어상의 효율적이라는 것에 불과하였다. 그러나 EW지수의 평균수익률은 GMVP의 수익률보다 크기때문에 효율적 프론티어상의 효율성이 성립하였다. 결론적으로, KOSPI지수와 KRX100지수는 GMVP의 평균수익률보다 낮아 효율성 측정에 문제가 있기 때문에 성과측정지수나 CAPM의 실증적 연구시에 대용시장지수로 사용할 경우, 연구결론이 오도될 위험이 있어 EW지수의 사용이 보다 바람직한 것으로 판단된다. Whether a proxy market index is ex-ante efficient is a basic question of investment analysis. Thus, the test of efficiency has been a significant interest to financial economics since the Markowitz``s seminal work. To test the efficiency of a proxy market index, we use two types of test methods. First, in case there is a riskless asset, we employ Ross``s(1980) method which derives the analytical solution for the likelihood ratio test(LRT). The method derives the exact forms of the maximum likelihood estimators and the LRT statistic. Secondly, in case where there is no riskless asset, we employ Shanken``s(1985) method which derives a cross-sectional regression of the GLS estimators and the Hotelling``s T2 statistic. Using the two methods, we test the hypotheses to find out whether three proxy market indexes in KOSPI Stock Market are ex-ante efficient. The three proxy market indexes are KOSPI Index, KRX100 Index and Equally-weighted Index. To carry out the efficiency test, the stocks with monthly returns are grouped into ten portfolios on the basis of beta-size. Each portfolio contains the same number of stocks with the length of T=168(months) from January, 2001 to December, 2014. The X2 statistics for Ross``s(1980) test and F statistics for Shanken``s(1985) test are computed with significant values α=0.05. We find that, in Ross``s X2 test, the null hypothesis that such market indexes as KOSPI Index and KRX100 Index are efficient is rejected. However, the null hypothesis that Equally-weighted Index is efficient is not rejected. We also find that, in Shanken``s F test, the null hypothesis that all three indexes are efficient in terms of the proxy market index is not rejected. But, as both KOSPI Index``s and KRX100 Index``s expected returns are lower than GMVP``s expected return, these two indexes are efficient only on the mean-variance frontier, not on the efficient frontier. In contrast, as the expected return of Equally-weighted Index is higher than that of GMVP, Equally-weighted Index is truly efficient on the viewpoint of efficient frontier. In sum, the results suggest that Equally-weighted Index is a better proxy market index than KOSPI Index and KRX100 Index in the KOSPI stock market.

최근 10년간(2000-2009) 사상체질의학회지 게재논문의 통계분석방법에 대한 연구

박기현,김상혁,김홍기,이시우,Park, Ki-Hyun,Kim, Sang-Hyuk,Kim, Hong-Gie,Lee, Si-Woo 사상체질의학회 2010 사상체질의학회지 Vol.22 No.4

1. Objectives The purpose of this study is to assess the statistical methods used in the Journal of Sasang Constitutional Medicine and to identify the types of errors in the statistical analysis. 2. Methods We have reviewed quantitative articles published in the Journal of Sasang Constitutional Medicine from 2000 to 2009. Except for the case report, a total of 505 articles was reviewed by year. We focused on the methods of statistics in these articles. We have analysed the number of thesis used the statistical methods, the number of the statistical methods, the types of the statistical methods, and the errors of the statistical methods with the object of 202 thesis used the statistical method. 3. Results 1. Of the 370 articles, 202 used inferential statistics. 2. The most dominant was the thesis with one type of the statistical method forming 61.9% (125 thesis) of the total. 3. The ANOVA was the statistic of choice overall (40.1%), followed by the t-test (35.6%). 4. By examining the errors of the statistical methods, there were 49 thesis with errors among 81 thesis using ANOVA, 25 thesis among 72 thesis using t-test, and 18 over 62 thesis using chi-squared test. 4. Conclusions We have found various mistakes or misuses in the applications of statistical methodologies in the articles published in the Journal of Sasang Constitutional Medicine. It is necessary to present the cases of inappropriate statistical methods in order to improve the quality of academic researches. So long as Sasang constitutional medicine uses the statistical methods, researchers should fully examine and be aware of the statistical methods which they wish to use through other research articles, and statistic publications.

Goodness of fit test for Rayleigh distribution with censored observations

Vaisakh K. M.,Xavier Thomas,Sreedevi E. P. 한국통계학회 2023 Journal of the Korean Statistical Society Vol.52 No.4

We develop new goodness of fit tests for Rayleigh distribution based on fixed point characterization. We use U-Statistic theory to derive the test statistics. First we develop a test for complete data and then discuss, how the right censored observations can be incorporated in the testing procedure. The asymptotic properties of the test statistic in both uncensored and censored cases are studied in detail. Extensive Monte Carlo simulation studies are carried out to validate the performance of the proposed tests. We illustrate the procedures using real data sets. We also provide, a goodness of fit test for the standard Rayleigh distribution based on jackknife empirical likelihood.

The Existence of Random Walk in the Philippine Stock Market: Evidence from Unit Root and Variance-Ratio Tests

CAMBA, Abraham C. Jr.,CAMBA, Aileen L. Korea Distribution Science Association 2020 The Journal of Asian Finance, Economics and Busine Vol.7 No.10

The efficient market hypothesis explains the random walk hypothesis suggesting that stock prices are independent of each other, hence, it is impossible to earn abnormal profits. The positive effect of a well-functioning and highly efficient stock market on the performance of an economy motivated the Philippine Stock Exchange to pursue massive modernization initiatives. This research provides evidence of the existence of random walk in the Philippine stock market employing the Augmented Dickey-Fuller (1981) and Phillips-Perron (1988) unit root tests, the Lo-MacKinlay's (1988) conventional variance ratio test, and Chow-Denning's (1993) simple multiple variance ratio test. Results of the ADF and PP unit root tests confirm the necessary condition for a random walk. The Chow-Denning (1993) maximum /z/ statistic and the Wald test statistic as in Richardson and Smith (1991) for the joint hypotheses and the Lo and MacKinlay (1988) individual statistics variance ratio test generally accepted the null hypothesis of a random walk. That is, the unit root and variance ratio tests consistently indicate that the null hypothesis of random walk cannot be rejected. The existence of a random walk in weak-form efficiency can be attributed to market liquidity as a result of continuous development and modernization of the Philippine equity market.

Impedance-based health monitoring and mechanical testing of structures

Palomino, Lizeth Vargas,de Moura, Jose Dos Reis Vieira Jr.,Tsuruta, Karina Mayumi,Rade, Domingos Alves,Steffen, Valder Jr. Techno-Press 2011 Smart Structures and Systems, An International Jou Vol.7 No.1

The mechanical properties obtained from mechanical tests, such as tensile, buckling, impact and fatigue tests, are largely applied to several materials and are used today for preliminary studies for the investigation of a desired element in a structure and prediction of its behavior in use. This contribution focus on two widely used different tests: tensile and fatigue tests. Small PZT (Lead Titanate Zirconate) patches are bonded on the surface of test samples for impedance-based health monitoring purposes. Together with these two tests, the electromechanical impedance technique was performed by using aluminum test samples similar to those used in the aeronautical industry. The results obtained both from tensile and fatigue tests were compared with the impedance signatures. Finally, statistical meta-models were built to investigate the possibility of determining the state of the structure from the impedance signatures.

체계적 비통계적 표본감사에 관한 연구

배원용,박성배 韓國公認會計士會 2007 회계·세무와 감사 연구 Vol.46 No.-

현대 회계감사에 있어서 중요한 특징은 내부통제제도의 의존과 시사의 활용이라고 할 수 있다. 시사(test)란 모집단 전체 중 일부만을 감사하고 그 결과를 모집단 전체의 결과로 추정하는 것을 의미한다. 시사에 의한 감사기법 즉 표본감사는 회계감사 목적의 변천과 밀접한 관계를 맺고 있다. 부정이나 허위의 적발을 주목적으로 하는 초창기에는 전수조사를 행하여 왔으나 경제규모가 확대되고 신용사회가 발달함에 따라 회계감사의 목적도 부정적발의 목적에서 재무제표의 적정성 판정을 위한 것으로 변화되면서 경험적 시사(비통계적표본감사)와 통계적 표본감사로 발전하여 왔다. 여기서 비통계적 표본감사란 통계이론에 근거하지 않고 감사인의 경험과 주관적 판단에 따라 표본의 크기, 표본추출 및 평가가 이루어지는 방법으로 일명 경험적 표본감사라 일컫는다. 이 방법은 동일한 상황 또는 동일한 대상에 대하여 감사인들이 서로 다른 시사방법을 적용함으로 인하여 서로 상이한 감사결론을 내릴 수 있기 때문에 비통계적 표본감사는 비판을 받아 왔다. 즉 감사 중 표본선택에 문제가 생겼을 때 왜 그러한 표본만을 조사하였느냐 하는 질문을 받았을 때 그 표본이 과학적(통계적)표본이 아니기 때문에 근거를 제시하기가 어려운 것이 사실이다. 그렇다면 통계적 표본감사를 실시하면 될 것이 아니냐하는 답이 나오지만 실무상 통계적 표본감사가 시간상의 제약과 적용상의 어려움으로 실제 몇몇 대형 회계법인을 제외하고는 실시하지 못하고 있는 실정이다. 그러므로 본 논문에서는 이러한 애로를 해소하기 위하여 많은 감사인 들이 감사 실무에서 적용하고 있는 표본감사기법에 대한 실태를 파악하여 새로운 표본감사 모형개발의 기본 자료를 세우는데 그 목적이 있다. This study carried out three objects: analysis of application in practices statistical audit sampling, which is also called the "S/S", technique for external auditors, understanding of necessity and application possibility of new model development, and development of model of S/S techniques based on the efficiency of a development level of model that could be applied in the practice empirically. Library method by the relevant literatures and precedent study in addition to empirical research by questionnaires applied to achieve this study purpose. Question investigation distributed 400 questionnaires to Seoul and six big cities auditors and reclaimed 217. In order to seek application possibility of analysis of variance (ANOVA), parametric procedures, collected questionnaires verification of normal distribution executed Kolmogorov-Smirnov test for goodness of fit and of equivalent variance test executed Scheffe's variance test were used. As a result, the data did not illustrate normal distribution and equivalent variance for all items. Therefore, application of parametric procedures was considered irrelevant. As a result of executed chi square of non-parametric procedures, frequency analysis, and ratio analysis new model was presented. Also, before hypothesis test, all items were used for reliability verification used in variable measuring according to Cronbach's alpha test. There are important results of the research and suggestion. First, auditors still prefer the non-statistical audit sampling called the “N/S”, techniques in regard to application research on practices. Including individual audit team, all the auditors generally used non-statistical sampling techniques. However, big four CPA firms used probability Proportional to size Sampling (PPS) in field of S/S techniques. Necessity of systematic education was clearly noticed because the education for S/S technique was consisted of education by CPA firm and audit practices. The motive of using S/S techniques were audit technique's objectiveness that protects a auditor from litigious matter and gives information of precedent study. However, the reason why people don't use S/S techniques is lack of statistical knowledge, blur judgment, and containing inefficiency. Second point was that auditors found necessity of education previous to obligatory application, which many auditors opposed to, in regard to research of cognition degree investigation of model development. Auditors perceived the necessity of new model development and are willing to apply relevant audit techniques if the techniques are developed. In development of model, auditors wanted technical mixture ratio rate of statistical techniques to be 25.5% of non-statistical factor. Third, S/S technique was considered a better way to examine the efficiency of the technique than N/S technique. Even though the type of business does not affect importantly the audit technique, the S/S technique shows better efficiency when auditors audit the companies with few transactions that involve large amount of money, and having total asset scale exceeds fifty billion wons. Fourth, as a result of hypothesis test, there were significant differences in all the fields except for motive of using technique, reasons for not using S/S technique, opposed obligatory application, and judgemental technique. Moreover, it was proven that S/S technique is more efficient technique than N/S technique in the decision of sample's size, selection of a sample, and evaluation of a sample. Fifth, based on points made above, S/S technique's constant ratio in addition to non-statistical factors presents new model of audit sampling. However, there are few limitations in this study and solutions to these problems are listed. First, because research objects were only external auditors in order to compare the efficiency among the techniques, this study's objective relevance is doubtful. Therefore, this study needs to expand the scope of research objects to all the auditors including internal auditors. Second, suggestion is development of computer software that enables application of development model in practices. Third, in order to testify the efficiency of the new model in practices, additional empirical simulation is necessary because the suggested development model is only conceived hypothetically. Fourth, because the model is never made previously, addition of detailed study about types of business, size of company, and transaction type to the application in practices will make more advanced and precious model than precedent one.