• Communications for Statistical Applications and Methods
• /
• v.10 no.2
• /
• pp.277-289
• /
• 2003

We propose modified exact inferential methods in logistic regression model. Exact conditional distribution in logistic regression model is often highly discrete, and ordinary exact inference in logistic regression is conservative, because of the discreteness of the distribution. For the exact inference in logistic regression model we utilize the modified P-value. The modified P-value can not exceed the ordinary P-value, so the test of size $\alpha$ based on the modified P-value is less conservative. The modified exact confidence interval maintains at least a fixed confidence level but tends to be much narrower. The approach inverts results of a test with a modified P-value utilizing the test statistic and table probabilities in logistic regression model.

• The Korean Journal of Applied Statistics
• /
• v.15 no.1
• /
• pp.187-199
• /
• 2002

When the sample size is small, exact tests are often employed because the asymptotic distribution of the test statistic is in doubt. The advantage of exact tests is that it is guaranteed to bound the type I error probability to the nominal level. In this paper we review the methods of constructing exact tests, the algorithm and commercial software. We also examine the difference between exact p-values obtained from exact tests and true p-values obtained from the true underlying distribution.

• The Korean Journal of Applied Statistics
• /
• v.26 no.4
• /
• pp.595-610
• /
• 2013

Testing of order-restricted alternative hypothesis in $2{\times}k$ contingency tables can be applied to various fields of medicine, sociology, and business administration. Most testing methods have been developed based on a large sample theory. In the case of a small sample size or unbalanced sample size, the Type I error rate of the testing method (based on a large sample theory) is very different from the target point of 5%. In this paper, the exact testing method is introduced in regards to the testing of an order-restricted alternative hypothesis in categorical data (particularly if a small sample size or extreme unbalanced data). Power and exact p-value are calculated, respectively.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.487-494
• /
• 2016

Let p be an odd prime and c be a fixed integer with (c, p) = 1. For each integer a with $1{\leq}a{\leq}p-1$, it is clear that there exists one and only one b with $0{\leq}b{\leq}p-1$ such that $ab{\equiv}c$ mod p. Let N(c, p) denote the number of all solutions of the congruence equation $ab{\equiv}c$ mod p for $1{\leq}a$, $b{{\leq}}p-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b{\bar{b}}{\equiv}1$ mod p. The main purpose of this paper is using the mean value theorem of Dirichlet L-functions and the properties of Gauss sums to study the computational problem of one kind mean value function related to $E(c,p)=N(c,p)-{\frac{1}{2}}{\phi}(p)$, and give its an exact computational formula.

• Journal of applied mathematics & informatics
• /
• v.27 no.1_2
• /
• pp.441-452
• /
• 2009

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

• Journal of Korean Society of Transportation
• /
• v.27 no.1
• /
• pp.107-114
• /
• 2009

Human walking is essential and important mean of transportation. Pedestrian safety is recently important because accidents often happen while walking. This research is showing that Walking-environmental factors have effect on safety while walking. At first, exact 15 factors and conduct survey in the preceding research. After that, exact 4 important factors through factor analysis. At result of Multiple regression analysis, null hypothesis has proved to be true by satisfying therms which is F-value 9.211 and P-value 0.000. and come to the conclusion that walking-environmental factors influence pedestrian safety. 4 important factors can be listed by below. Pedestrian-road characteristic, landscape characteristic, commercial characteristic, walking characteristics by following influence. Especially, landscape characteristic and pedestrian-road characteristic can be vital factors.

• Communications for Statistical Applications and Methods
• /
• v.24 no.6
• /
• pp.663-671
• /
• 2017

Some genetic association tests include an unidentifiable nuisance parameter under the null hypothesis of no association. When the mode of inheritance (MOI) is not specified in a case-control design, the Cochran-Armitage (CA) trend test contains an unidentifiable nuisance parameter. The transmission disequilibrium test (TDT) in a family-based association study that includes the unaffected also contains an unidentifiable nuisance parameter. The hypothesis tests that include an unidentifiable nuisance parameter are typically performed by taking a supremum of the CA tests or TDT over reasonable values of the parameter. The p-values of the supremum test statistics cannot be obtained by a normal or chi-square distribution. A common method is to use a Davies's upper bound of the p-value instead of an exact asymptotic p-value. In this paper, we provide a unified sine-cosine process expression of the CA trend test that does not specify the MOI and the TDT that includes the unaffected. We also present a closed form expression of the exact asymptotic formulas to calculate the p-values of the supremum tests when the score function can be written as a linear form in an unidentifiable parameter. We illustrate how to use the derived formulas using a pharmacogenetics case-control dataset and an attention deficit hyperactivity disorder family-based example.

• Journal of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.267-298
• /
• 1999

A geometric construction of an exact algebraic formula for graded partition functions, of which a special one is the classical unrestricted partition function p(n), from a diophantine point of view is presented. Moreover, the involved process allows us to compute the value of a graded partition function in an inductive manner with a geometrically built-in self-error-checking ability at each step for correctness of the computed values of the partition function under consideration.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.3
• /
• pp.611-622
• /
• 2023

The main purpose of this paper is to study the hybrid mean value problem involving generalized Dedekind sums, generalized Hardy sums and Kloosterman sums. Some exact computational formulas are given by using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function. A result of W. Peng and T. P. Zhang [12] is extended. The new results avoid the restriction that q is a prime.

• The Korean Journal of Applied Statistics
• /
• v.22 no.4
• /
• pp.781-792
• /
• 2009

At an early stage of genomic investigations, a small sample of microarrays is used in gene expression experiments to identify small subsets of candidate genes for a further accurate investigation. Unlike the statistical analysis methods for a large sample of microarrays, an appropriate statistical method for identifying small subsets is a randomization test that provides exact P values. These exact P values from a randomization test for a small sample of microarrays are discrete. The possible existence of differentially expressed genes in the sample of a full set of genes can be tested for the null hypothesis of a uniform distribution. Subsets of smaller P values are of prime interest for a further accurate investigation and identifying these outlier cells from a multinomial distribution of P values is possible by M test of Fuchs et al. (1980). Above all, the genome-wide gene expressions in microarrays are correlated, but the majority of statistical analysis methods in the microarray analysis are based on an independence assumption of genes and ignore the possibly correlated expression levels. We investigated with simulation studies the effect that correlated gene expression levels could have on the randomization test results and M test results, and found that the effects are often not ignorable.