• 제목/요약/키워드: Statistical Hypothesis Test

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A tutorial on generalizing the default Bayesian t-test via posterior sampling and encompassing priors

  • Faulkenberry, Thomas J.
    • Communications for Statistical Applications and Methods
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    • 제26권2호
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    • pp.217-238
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    • 2019
  • With the advent of so-called "default" Bayesian hypothesis tests, scientists in applied fields have gained access to a powerful and principled method for testing hypotheses. However, such default tests usually come with a compromise, requiring the analyst to accept a one-size-fits-all approach to hypothesis testing. Further, such tests may not have the flexibility to test problems the scientist really cares about. In this tutorial, I demonstrate a flexible approach to generalizing one specific default test (the JZS t-test) (Rouder et al., Psychonomic Bulletin & Review, 16, 225-237, 2009) that is becoming increasingly popular in the social and behavioral sciences. The approach uses two results, the Savage-Dickey density ratio (Dickey and Lientz, 1980) and the technique of encompassing priors (Klugkist et al., Statistica Neerlandica, 59, 57-69, 2005) in combination with MCMC sampling via an easy-to-use probabilistic modeling package for R called Greta. Through a comprehensive mathematical description of the techniques as well as illustrative examples, the reader is presented with a general, flexible workflow that can be extended to solve problems relevant to his or her own work.

Testing Hypothesis for the Logistic Model with Estimated Parameters : Modified Tables of Cirticla Values for K-S Type Statistic

  • Hwang, Chung-Sun
    • Journal of the Korean Statistical Society
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    • 제13권1호
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    • pp.48-56
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    • 1984
  • This paper considers one-sample and two-sample test for the logistic function by means of Kolmororov-Smirnov type statistics. The standard tables used for the Kolmogorov-Smirnov test are valid only when the function is completely specified; but they are not valid if the parameters of function are estimated from the sample. This note presents modified tables for the Kolmogorov-Sminov type staistic. These tables can be used to test the hypothesis that a sample comes from a logistic function when shape parameter $(\alpha)$ and location parameter $(\beta)$ must be estimated from the sample by the method of maximum likelihood. Monte Carlo method is employed to calculate the criticla values of the test. The tables of the critical values are provided.

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A Nonparametric Bootstrap Test and Estimation for Change

  • Kim, Jae-Hee
    • Communications for Statistical Applications and Methods
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    • 제14권2호
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    • pp.443-457
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    • 2007
  • This paper deals with the problem of testing the existence of change in mean and estimating the change-point using nonparametric bootstrap technique. A test statistic using Gombay and Horvath (1990)'s functional form is applied to derive a test statistic and nonparametric change-point estimator with bootstrapping idea. Achieved significance level of the test is calculated for the proposed test to show the evidence against the null hypothesis. MSE and percentiles of the bootstrap change-point estimators are given to show the distribution of the proposed estimator in simulation.

An Adaptive Test for Ordered Interqartile Ranges among Several Distributions

  • Park, Chul-Gyu
    • Journal of the Korean Statistical Society
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    • 제30권1호
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    • pp.63-76
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    • 2001
  • An adaptive estimation and testing method is proposed for comparing dispersions among several ordered groups. Based upon the large sampling theory for nonparametric quartile estimators, we derive the order restricted estimators and construct a simple test statistic. This test statistic has a mixture of several chi-square distributions as its asymptotic null distribution. The proposed test is illustratively applied to survival time data for the patients with carcinoma of the oropharynx.

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Non-Conservatism of Bonferroni-Adjusted Test

  • Jeon, Cyeong-Bae;Lee, Sung-Duck
    • Communications for Statistical Applications and Methods
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    • 제8권1호
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    • pp.219-227
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    • 2001
  • Another approach (multi-parameter measurement method) of interlaboratory studies of test methods is presented. When the unrestricted normal likelihood for the fixed latent variable model is unbounded, we propose a me쇙 of restricting the parameter space by formulating realistic alternative hypothesis under which the likelihood is bounded. A simulation study verified the claim of conservatism of level of significance based on assumptions about central chi-square distributed test statistics and on Bonferroni approximations. We showed a randomization approach that furnished empirical significance levels would be better than a Bonferroni adjustment.

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A Wald Test for a Unit Root Based on the Symmetric Estimator

  • Jong Hyup Lee;Dong Wan SHin
    • Communications for Statistical Applications and Methods
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    • 제4권3호
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    • pp.677-683
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    • 1997
  • For an AR(1) model with intercept $y_t=\mu+\rho{y_{t-1}}+e_t$, a test for random walk hypothesis $H_0:(\mu, \rho)=(0, 1)$is proposed, which is based on the symmetric estimator. In the vicinity of the null, the test in shown to be more powerful than the test of Dickey and Fuller(1981) based on the ordinary least squares estimator.

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Testing the Randomness of the Coefficients In First Order Autoregressive Processes

  • Park, Sangwoo;Lee, Sangyeol;Sun Y. Hwang
    • Journal of the Korean Statistical Society
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    • 제27권2호
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    • pp.189-195
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    • 1998
  • In this paper, we are concerned with the problem of testing the randomness of the coefficients in a first order autoregressive model. A consistent test based on prediction error is suggested. It is shown that under the null hypothesis, the test statistic is asymptotically normal.

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국부 확률을 이용한 데이터 분류에 관한 연구 (A Study on Data Clustering Method Using Local Probability)

  • 손창호;최원호;이재국
    • 제어로봇시스템학회논문지
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    • 제13권1호
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    • pp.46-51
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    • 2007
  • In this paper, we propose a new data clustering method using local probability and hypothesis theory. To cluster the test data set we analyze the local area of the test data set using local probability distribution and decide the candidate class of the data set using mean standard deviation and variance etc. To decide each class of the test data, statistical hypothesis theory is applied to the decided candidate class of the test data set. For evaluating, the proposed classification method is compared to the conventional fuzzy c-mean method, k-means algorithm and Discriminator analysis algorithm. The simulation results show more accuracy than results of fuzzy c-mean method, k-means algorithm and Discriminator analysis algorithm.

지수분표에 있어서 최우수 처리의 판별을 위한 우도비 검정 (The likelihood ratio test for detecting the best treatment among several exponential populations)

  • 황형태
    • 응용통계연구
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    • 제8권1호
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    • pp.151-157
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    • 1995
  • 다수의 지수분포에 있어서 최우수 처리를 판별하는 방법을 가설검정의 형식으로 연구하였다. 최우수 처리의 판별을 위해 적절한 가설을 설정하고, 주어진 유의수준을 만족시키는 우도비 검정 방법을 유도하였으며, 관심영역에서의 최소 검정력을 계산함으로써 실제 표본 설계가 가능하도록 하였다.

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국내 사례로 살펴보는 국방체계 개발의 신뢰성을 높이기 위한 시험평가 방안 (Effective Test and Evaluation Approaches for Reliable Defense Systems Development examined through Domestic Defense Cases)

  • 서경민;이찬영;방경운;이동철;최우영;김탁곤
    • 대한조선학회논문집
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    • 제53권2호
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    • pp.127-134
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    • 2016
  • This paper presents practical issues for test and evaluation(T&E) methods to develop defense systems. Our argument is motivated by several domestic defense cases and the cases lead us to discuss two main factors for reliable defense systems development: 1) statistical approaches and 2) technical schemes. Specifically, statistical approaches enable to provide credible interpretations about T&E results in the decision-making process. With practical T&E results of the “Red Shark” torpedo, we performed statistical hypothesis tests and suggest a minimum sample size to accept the hypothesis. Next, technical schemes have more direct effects on improving reliability of developed defense systems and we shortly introduce tools development for systems verification that is required to integrate several sub-systems, e.g., combat, sensor, weapon, and communication systems, within a defense system. We additionally summary some domain cases using modeling and simulation techniques for successful T&E. In closing, we expect that the paper shows empirical investigation and lessons learned with these two practical issues, which provides a guide those who desire to make decisions about reliable defense systems development.