Protection of privacy in efficient application of randomized response techniques

In estimating the proportion of people bearing a sensitive attribute A, say, in a given community, following Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, certain randomized response (RR) techniques are available for application. These are intended to ensure efficient and unbiased estimation protecting a respondent’s privacy when it touches a person’s socially stigmatizing feature like rash driving, tax evasion, induced abortion, testing HIV positive, etc. Lanke (Int Stat Rev 44:197–203, 1976), Leysieffer and Warner (J Am Stat Assoc 71:649–656, 1976), Anderson (Int Stat Rev 44:213–217, 1976, Scand J Stat 4:11–19, 1977) and Nayak (Commun Stat Theor Method 23:3303–3321, 1994) among others have discussed how maintenance of efficiency is in conflict with protection of privacy. In their RR-related activities the sample selection is traditionally by simple random sampling (SRS) with replacement (WR). In this paper, an extension of an essential similarity in case of general unequal probability sample selection even without replacement is reported. Large scale surveys overwhelmingly employ complex designs other than SRSWR. So extension of RR techniques to complex designs is essential and hence this paper principally refers to them. New jeopardy measures to protect revelation of secrecy presented here are needed as modifications of those in the literature covering SRSWR alone. Observing that multiple responses are feasible in addressing such a dichotomous situation especially with Kuk’s (Biometrika 77:436–438, 1990) and Christofides’ (Metrika 57:195–200, 2003) RR devices, an average of the response-specific jeopardizing measures is proposed. This measure which is device dependent, could be regarded as a technical characteristic of the device and it should be made known to the participants before they agree to use the randomization device. The views expressed are the authors’, not of the organizations they work for. Prof Chaudhuri’s research is partially supported by CSIR Grant No. 21(0539)/02/EMR-II.     

The Italian Labour Force Survey to estimate fertility

The own-children method (OCM) applied to the Italian Labour Force Survey (ILFS) is an alternative way to give information on fertility for the years before the survey. By deriving children information and the population at risk on the basis of parents’ characteristics, a large-scale dataset for fertility analysis in Italy becomes available, also to reconstruct event histories. The quality assessment provided by comparing the total fertility rate (TFR) calculated on ILFS with the official regional and national TFRs by ISTAT gives us usable outcomes.     

Influence of human immunodeficiency virus infection on neurological impairment: an analysis of longitudinal binary data with informative drop-out

A study to investigate the human immunodeficiency virus (HIV) status on the course of neurological impairment, conducted by the HIV Center at Columbia University, followed a cohort of HIV positive and negative gay men for 5 years and assessed the presence or absence of neurological impairment every 6 months. Almost half of the subjects dropped out before the end of the study for reasons that might have been related to the missing neurological data. We propose likelihood-based methods for analysing such binary longitudinal data under informative and non-informative drop-out. A transition model is assumed for the binary response, and several models for the drop-out processes are considered which are functions of the response variable (neurological impairment). The likelihood ratio test is used to compare models with informative and non-informative drop-out mechanisms. Using simulations, we investigate the percentage bias and mean-squared error (MSE) of the parameter estimates in the transition model under various assumptions for the drop-out. We find evidence for informative drop-out in the study, and we illustrate that the bias and MSE for the parameters of the transition model are not directly related to the observed drop-out or missing data rates. The effect of HIV status on the neurological impairment is found to be statistically significant under each of the models considered for the drop-out, although the regression coefficient may be biased in certain cases. The presence and relative magnitude of the bias depend on factors such as the probability of drop-out conditional on the presence of neurological impairment and the prevalence of neurological impairment in the population under study.     

Stochastic models for fractal processes

This paper considers the situation where a stochastic process may display both long-range dependence (LRD) and intermittency. The existence of such a process is established in Anh et al. (1999). Existing works have commonly paid attention either to LRD or intermittency quite separately. This paper offers a convenient framework to study both effects simultaneously. A method is given to estimate and separate the two effects. The wavelet theory plays an essential role in this procedure. Numerical experiments on fractional Brownian motion and multiplicative cascade processes confirm the power of the method.     

Efficacy of programmes for the unemployed: discrete time modelling of duration data from a matched-comparison study

An evaluation is described of two UK Government programmes for the long-term unemployed in Great Britain, Employment Training and Employment Action, using discrete time hazard modelling of event histories. The study design employed a closely matched comparison group and carefully chosen control variables to minimize the effect of selection bias on conclusions. The effect of unobserved heterogeneity is investigated by using some standard random effect model formulations.     

Study of a Markov model for a high-quality dependent process

For high-quality processes, non-conforming items are seldom observed and the traditional p (or np) charts are not suitable for monitoring the state of the process. A type of chart based on the count of cumulative conforming items has recently been introduced and it is especially useful for automatically collected one-at-a-time data. However, in such a case, it is common that the process characteristics become dependent as items produced one after another are inspected. In this paper, we study the problem of process monitoring when the process is of high quality and measurement values possess a certain serial dependence. The problem of assuming independence is examined and a Markov model for this type of process is studied, upon which suitable control procedures can be developed.     

Shrinkage Structure of Partial Least Squares

Partial least squares regression (PLS) is one method to estimate parameters in a linear model when predictor variables are nearly collinear. One way to characterize PLS is in terms of the scaling (shrinkage or expansion) along each eigenvector of the predictor correlation matrix. This characterization is useful in providing a link between PLS and other shrinkage estimators, such as principal components regression (PCR) and ridge regression (RR), thus facilitating a direct comparison of PLS with these methods. This paper gives a detailed analysis of the shrinkage structure of PLS, and several new results are presented regarding the nature and extent of shrinkage.