• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.237-249
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• 1999

It has been issued that the irreconcilability of the classical test for a point null and standard Bayesian formulation for testing such a point null. The infimum of the posterior probability of the null hypothesis is used as measure of evidence against the null hypothesis in Bayesian approach; here the infimum is over the family of priors on the alternative hypotheses which includes all density that are a priori reasonable. For iid observations from a multivariate normal distribution in $\textit{p}$ dimensions with an unknown mean and a covariance matrix propotional to the Identity we consider the difference and the Wolfowitz distance of the distributions of the P-value and the lower bound of the posterior probability over the family of all normal priors. The Wolfowitz distance is interpreted as the average difference of the quantiles of the two distrbutions.

• Communications for Statistical Applications and Methods
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• v.21 no.1
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• pp.11-22
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• 2014

In this study, we propose a simultaneous test procedure based on the individual - values for each sub-null hypothesis with several well-known combining functions. We then compare the efficiency of our procedure with existing tests by obtaining empirical powers through a simulation study. Finally, we discuss some interesting features related to simultaneous test and point out a misconduct for the simulation study published in the previous work.

• Journal of the Korean Data and Information Science Society
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• v.12 no.1
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• pp.135-142
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• 2001

A multivariate statistic based on interdirection is proposed for detecting dependence among many vectors. The asymptotic distribution of the proposed statistic is derived under the null hypothesis of independence. Also we find the asymptotic distribution under the alternatives contiguous to the null hypothesis, which is needed for later use of computing relative efficiencies.

• The Korean Journal of Applied Statistics
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• v.23 no.6
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• pp.1115-1124
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• 2010

Normal approximation methods under the null hypothesis of no difference are frequently used to test the two independent proportions in non-inferiority trials. However, these tests are not appropriate under the null hypothesis of non-zero difference. We review the likelihood score methods proposed by Miettinen and Nurminen, Farrington and Manning, and Gart and Nam and compare the performance of these tests. The simulation study shows that the likelihood score tests under the null hypothesis of non-zero difference have better performance at a Type I error and power than usual normal approximation methods.

• Communications for Statistical Applications and Methods
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• v.17 no.2
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• pp.241-253
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• 2010

As standard unit root tests are empirically proved to fail to reject the null hypothesis of a unit root for many economic and business time series, it is doubtful that most of those series are informative about the existence of a unit root or that those tests are powerful against relevant alternative hypotheses. This study attempts to perform tests of the null hypothesis of stationarity as well as tests of the null hypothesis of a unit root using the time series data of housing prices in the major metropolitan areas. The results of the additional analyses such as lead-lag, cross-correlation and impulse response for testing the statistical interrelationships between the prices are generally found to be consistent.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.289-298
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• 1998

We investigate the distribution of likelihood ratio test(LRT) of null hypothesis a sample is from single gamma with unknown shape and scale against the alternative hypothesis a sample is from a mixture of two gammas, each with unknown scale and unknown (but equal) scale. To obtain stable maximum likelihood estimates(MLE) of a mixture of two gamma distributions, the EM(Dempster, Laird, and Robin(1977))and Modified Newton(Jensen and Johansen(1991)) algorithms were implemented. Based on EM, we made a simple structure likelihood equation for each parameter and could obtain stable solution by Modified Newton Algorithms. Simulation study was conducted to investigate the distribution of LRT for sample size n = 25, 50, 75, 100, 50, 200, 300, 400, 500 with 2500 replications. To determine the small sample distribution of LRT, I considered the model of a gamma distribution with shape parameter equal to 1 + f(n) and scale parameter equal to 2. The simulation results indicate that the null distribution is essentially invariant to the value of the shape parameter. Modeling of the null distribution indicates that it is well approximated by a gamma distribution with shape parameter equal to the quantity $0.927+1.18/\sqrt{n}$ and scale parameter equal to 2.16.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.153-165
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• 2003

This paper considers the likelihood ratio test statistic based on nonlinear regression quantiles estimators in order to test of hypothesis about the regression parameter $\theta_o$ and derives asymptotic distribution of proposed test statistic under the null hypothesis and a sequence of local alternative hypothesis. The paper also investigates asymptotic relative efficiency of the proposed test to the test based on the least squares estimators or the least absolute deviation estimators and gives some examples to illustrate the application of the main result.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.10
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• pp.523-530
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• 2020

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.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.141-148
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• 2020

We consider estimating the proportion of true null hypotheses in multiple testing problems. A traditional multiple testing rate, family-wise error rate is too conservative and old to control type I error in multiple testing setups; however, false discovery rate (FDR) has received significant attention in many research areas such as GWAS data, FMRI data, and signal processing. Identify differentially expressed genes in microarray studies involves estimating the proportion of true null hypotheses in FDR procedures. However, we need to account for unknown dependence structures among genes in microarray data in order to estimate the proportion of true null hypothesis since the genuine dependence structure of microarray data is unknown. We compare various procedures in simulation data and real microarray data. We consider a hidden Markov model for simulated data with dependency. Cai procedure (2007) and a sliding linear model procedure (2011) have a relatively smaller bias and standard errors, being more proper for estimating the proportion of true null hypotheses in simulated data under various setups. Real data analysis shows that 5 estimation procedures among 9 procedures have almost similar values of the estimated proportion of true null hypotheses in microarray data.

• Journal of the Korean Statistical Society
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• v.23 no.1
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• pp.199-206
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• 1994

Sometimes a researcher with a view of conventional significance testing rejects his/her hypothesis, even through it could have not been rejected with a smaller sample. This can be a logical dilemma for a researcher who wants to "prove" a hypothesis rather than to show discrepancy from a null hypothesis. In this study, a new testing paradigm called equivalence testing via confidence interval will be developed so that it is suitable for the purpose of statistical proof.cal proof.