Giancarlo Diana

Cross-validation methods in principal component analysis: A comparison

In principal component analysis (PCA), it is crucial to know how many principal components (PCs) should be retained in order to account for most of the data variability. A class of “objective” rules for finding this quantity is the class of cross-validation (CV) methods. In this work we compare three CV techniques showing how the performance of these methods depends on the covariance matrix structure. Finally we propose a rule for the choice of the “best” CV method and give an application to real data.

New scrambled response models for estimating the mean of a sensitive quantitative character

Moving from the scrambling mechanism recently suggested by Saha [25], three scrambled randomized response (SRR) models are introduced with the intent to realize a right trade-off between efficiency and privacy protection. The models perturb the true response on the sensitive variable by resorting to the multiplicative and additive approaches in different ways. Some analytical and numerical comparisons of efficiency are performed to set up the conditions under which improvements upon Sahas model can be obtained and to quantify the efficiency gain. The use of auxiliary information is also discussed in a class of estimators for the sensitive mean under a generic randomization scheme. The class includes also the three proposed SRR models. Finally, some graphical comparisons are carried out from the double perspective of the accuracy in the estimates and respondents’ privacy protection.

An improved class of estimators for the population mean

Starting from the Rao (Commun Stat Theory Methods 20:3325–3340, 1991) regression estimator, we propose a class of estimators for the unknown mean of a survey variable when auxiliary information is available. The bias and the mean square error of the estimators belonging to the class are obtained and the expressions for the optimum parameters minimizing the asymptotic mean square error are given in closed form. A simple condition allowing us to improve the classical regression estimator is worked out. Finally, in order to compare the performance of some estimators with the regression one, a simulation study is carried out when some population parameters are supposed to be unknown.

Improved Estimators of the Population Mean for Missing Data

Motivated by a recent work by Kadilar and Cingi (2008), we proposed three regression-type estimators to overcome the problem of missing data for a study variable. The estimators make optimal use of the available auxiliary information. We show that, given the same amount of information, these estimators are simpler and more efficient than those proposed by Kadilar and Cingi. A numerical illustration, performed on three different populations, highlights the efficiency gain from using our proposal. Finally, a suggestion is made regarding the optimal use of auxiliary information in sampling practice.

A calibration-based approach to sensitive data: a simulation study

In this paper, we discuss the use of auxiliary information to estimate the population mean of a sensitive variable when data are perturbed by means of three scrambled response devices, namely the additive, the multiplicative and the mixed model. Emphasis is given to the calibration approach, and the behavior of different estimators is investigated through simulated and real data. It is shown that the use of auxiliary information can considerably improve the efficiency of the estimates without jeopardizing respondent privacy.

Optimal estimation for finite population mean in two-phase sampling

Using two-phase sampling scheme, we propose a general class of estimators for finite population mean. This class depends on the sample means and variances of two auxiliary variables. The minimum variance bound for any estimator in the class is provided (up to terms of ordern−1). It is also proved that there exists at least a chain regression type estimator which reaches this minimum. Finally, it is shown that other proposed estimators can reach the minimum variance bound, i.e. the optimal estimator is not unique.

A Clustering Method for Categorical Ordinal Data

Often, categorical ordinal data are clustered using a well-defined similarity measure for this kind of data and then using a clustering algorithm not specifically developed for them. The aim of this article is to introduce a new clustering method suitably planned for ordinal data. Objects are grouped using a multinomial model, a cluster tree and a pruning strategy. Two types of pruning are analyzed through simulations. The proposed method allows to overcome two typical problems of cluster analysis: the choice of the number of groups and the scale invariance.

Hansen and Hurwitz estimator with scrambled response on the second call

In this paper we propose a modified version of the estimator of Hansen and Hurwitz [12] in the case of quantitative sensitive variable and consider a randomization mechanism on the second call that provides privacy protection to the respondents to get truthful information. We use variance of the modified estimator as a tool to measure privacy protection and it is observed that the higher is the variance, the lower is the efficiency but the higher is the privacy protection. To overcome this efficiency loss, we consider a linear regression estimator using known non-sensitive auxiliary information. With consideration of four scrambled models, we try to make a trade-off between efficiency and privacy protection. To show this compromise, analytical and numerical comparisons are obtained.

Scrambled Response Models Based on Auxiliary Variables

We discuss the problem of obtaining reliable data on a sensitive quantitative variable without jeopardizing respondent privacy. The information is obtained by asking respondents to perturb the response through a scrambling mechanism. A general device allowing for the use of multi-auxiliary variables is illustrated as well as a class of estimators for the unknown mean of a sensitive variable. A number of scrambled response models are shown and others discussed in terms of the efficiency of the estimates and the privacy guaranteed to respondents.

Finite Population Variance Estimation in Presence of Measurement Errors

In this article, we propose a class of estimators for the population variance of a quantity of interest. The estimators in the class use auxiliary information to improve efficiency, and we suppose that measurement errors are present both in the study and auxiliary variate. We take into account such problem using a regression approach. We show that the class proposed is quite flexible and general, allowing to consider many kinds of information as auxiliary one. Comparisons within estimators in the class are studied theoretically and through simulations.