Search

Partitioning objects into closely related groups that have different states allows to understand the underlying structure in the data set treated. Different kinds of similarity measure with clustering algorithms are commonly used to find an optimal clustering or closely akin to original clustering. Using shrinkage-based and rank-based correlation coefficients, which are known to be robust, the recovery level of six chosen clustering algorithms is evaluated using Rand’s C values. The recovery levels using weighted likelihood estimate of correlation coefficient are obtained and compared to the results from using those correlation coefficients in applying agglomerative clustering algorithms.

Principal coordinate analysis is a more powerful technique than principal component analysis to ensure identification on groups of objects if some conditions are satisfied. The results of using principal coordinates prior to cluster analysis were investigated. Three different methods of standardization were examined and compared with no standardization using both principal coordinates and principal components. The retrieval abilities of the known agglomerative clustering algorithms were improved by using principal coordinates. The results of applying principal coordinates based on the correlation coefficient instead of Euclidean distance prior to clustering algorithms were less sensitive to changes in noise.

To implement the privacy problem with the Moors (J. Amer. Statist. Assoc. 66 (1971) 627) model, Mangat et al. (Commun. Statist. Theory Methods 26(3) (1997) 243) and Singh et al. (J. Statist. Plann. Inference 83 (2000) 243) presented several strategies as an alternative to Moors model, but their models may lose a large portion of data information and require a high cost to obtain confidentiality of the respondents. Our proposed model has the advantage of simplicity over the previous models while protecting confidentiality. We extend the proposed model to stratified sampling.

The randomized response technique is an effective survey method designed to elicit sensitive information while ensuring the privacy of the respondents. In this article, we present some new results on the randomization response model in situations wherein one or two response variables are assumed to follow a multinomial distribution. For a single sensitive question, we use the well-known Hopkins randomization device to derive estimates, both under the assumption of truthful and untruthful responses, and present a technique for making pairwise comparisons. When there are two sensitive questions of interest, we derive a Pearson product moment correlation estimator based on the multinomial model assumption. This estimator may be used to quantify the linear relationship between two variables when multinomial response data are observed according to a randomized-response protocol.

Two different formulations on the moments of Rand's C appear incompatible. The mean and variance of Rand's C statistic given by Fowlkes and Mallows (J. Amer Statist. Assoc. 78 (1983) 553) are special cases of the mean and variance of C given by DuBien and Warde (ASA proceedings of the social statistics section (1981) 309).

Clustering algorithms with different similarity measures are commonly used to find an optimal clustering or close to original clustering. The recovery level of using Euclidean distance and distances transformed from correlation coefficients is evaluated and compared using Rand's (1971) C statistic. The C values present how the resultant clustering is close to the original clustering. In simulation study, the recovery level is improved by applying the correlation coefficients between objects. Using the data set from Spellman et al. (1998), the recovery levels with different similarity measures are also presented. In general, the recovery level of true clusters was increased by using the correlation coefficients.

This paper proposes a new stratified randomized response model based on Warner's (J. Amer. Statist. Assoc. 60 (1965) 63) model that has an optimal allocation and large gain in precision. It also presents a drawback of the Hong et al. (Korean J. Appl. Statist. 7 (1994) 141) model under their proportional sampling assumption. It is shown that the proposed model is more efficient than the Hong et al. (Korean J. Appl. Statist. 7 (1994) 141) stratified randomized response model. Additionally, it is shown that the estimator based on the proposed method is more efficient than the Warner (J. Amer. Statist. Assoc. 60 (1965) 63), the Mangat and Singh (Biometrika 77 (1990) 439) and the Mangat (J. Roy. Statist. SQC. Ser. B 56 (1) (1994) 93) estimators under the conditions presented in both the case of completely truthful reporting and that of not completely truthful reporting by the respondents.

A first-order corrected test statistic for analyzing frequency data when the data are obtained from a two-stage sampling scheme is presented in this paper. The data are summarized in a cross-classified table in such a way that the cell values are not necessarily a count. Comparisons are made with the Wald statistic, Pearson statistic, other modified Pearson statistics, and a proposed first-order corrected test for comparing vectors of proportion. The proposed test shows that a convenient approximation to the Wald test statistic is to construct a modification of the Pearson tupe statistic based on the pre-adjusted table cell values. Simulated data are used to examine the behavior of the first-order statistic under the two-stage sampling scheme.

This article delineates the important considerations in any extensive, systematic comparison of clustering methods, and then it presents an empirical investigation of the effect of correlated variables on the “retrieval” ability of a particular class of agglomerative clustering methods. The empirical investigation re- sulted in two major observations; namely, that there are many agglomerative clustering methods, which have never been applied, that are “better” than any of the commonly used agglomerative clus- tering methods, and that correlated variables affect the “retrieval” ability of different agglomerative clustering methods differ- ently.

When examining the simple linear regression model, we may know a priori that the slope parameter is constrained to lie in an interval (finite or semi-infinite). In this article, we examine the behavior and properties of the Bayesian posterior mean, median and mode as estimators of the slope parameter, both when σ2 is known and unknown.

This article presents an algebraic analysis of agglomerative clustering method algorithms, which results in a graphic portrayal of these algorithms and a classification scheme for these algorithms based on the degree of distortion perpetrated on the object space by the algorithms in each group. Cet article presente une analyse algebrique des methodes algorithmiques de groupement agglomere qui debouche sur une representation graphique et une methode de classification de ces algorithmes, basee sur le degre de distortion perpetree sur l'espace object par les algorithmes dans chaque groupe.