A. Arcos

University of Granada | UGR · Department Statistics and Operations Research

Randomized response (RR) techniques are widely used in research involving sensitive variables, such as drugs, violence or crime, especially when a population mean or prevalence must be estimated. However, they are not generally applied to examine relationships between a sensitive variable and other characteristics. This type of technique was initia...

Dual frame surveys are a device to reduce the costs derived from data collection in surveys and improve coverage for the whole target population. Since their introduction, in the 1960‘s, dual frame surveys have gained much attention and several estimators have been formulated based on a number of different approaches. In this work, we propose new d...

The use of probability-based panels that collect data via online or mixed-mode surveys has increased in the last few years as an answer to the growing concern with the quality of the data obtained with traditional survey modes. However, in order to adequately represent the general population, these tools must address the same sources of bias that a...

A sample selected from a single sampling frame may not represent adequatly the entire population. Multiple frame surveys are becoming increasingly used and popular among statistical agencies and private organizations, in particular in situations where several sampling frames may provide better coverage or can reduce sampling costs for estimating po...

Warner’s randomized response (RR) model is used to collect sensitive information for a broad range of surveys, but it possesses several limitations such as lack of reproducibility, higher costs and it is not feasible for mail questionnaires. To overcome such difficulties, nonrandomized response (NRR) surveys have been proposed. The proposed NRR sur...

This paper considers new techniques for complex surveys in the case of estimation of proportions when the variable of interest has ordinal outcomes. Ordinal modelassisted and ordinal model-calibrated estimators are introduced for class frequencies in a population, taking two different approaches. Theoretical properties and numerical methods are inv...

This article discusses the estimation of a population proportion, using the auxiliary information available, which is incorporated into the estimation procedure by a probit model fit. Three probit regression estimators are considered, using model-based and model-assisted approaches. The theoretical properties of the proposed estimators are derived...

This paper considers the problem of estimating a poverty measure, the Head Count Index, using the auxiliary information available, which is incorporated into the estimation procedure by calibration techniques. The proposed method does not directly use the auxiliary information provided by auxiliary variables related to the variable of interest in t...

Large scale surveys very often involve multi-stage sampling design, where the first-stage units are selected with varying probability sampling without replacement method and the second and subsequent stages units are selected with varying or equal probability sampling schemes. It is well known (vide Chaudhuri and Arnab (1982)) that for such samplin...

Surveys usually include questions where individuals must select one in a series of possible options that can be sorted. On the other hand, multiple frame surveys are becoming a widely used method to decrease bias due to undercoverage of the target population. In this work, we propose statistical techniques for handling ordinal data coming from a mu...

The rapid evolution of technology in last decades has allowed conducting studies for complex surveys. Over time, the software is used in all steps of the survey: survey design, data collection, statistical data edition, statistical analysis, and publication results. In this chapter we describe software that can be used in conducting surveys using r...

In this chapter, the problem of estimating a population mean with the help of the newly tuned model assisted estimation methodology is developed by assuming that the auxiliary information is available at the unit level in the population. The newly tuned model assisted estimator does an excellent job for small samples in the case of both the chi-squ...

In this chapter, we discuss the problem of estimation in survey sampling. The Statistical Jumbo Pumpkin Model (SJPM) is developed, which can produce very light to very heavy pumpkins, and is naturally correlated with their known circumferences. R code, used for generating the SJPM, is provided. A population of pumpkins is generated using the SJPM a...

In this chapter, we present the problem of estimating the finite population variance with the help of the newly tuned estimation methodology. The newly tuned model assisted estimator of finite population variance is studied under both the chi-squared and the dual-to-empirical log-likelihood (dell) functions. The R code for studying the reliability...

In this chapter, the problem of tuning the estimator of the correlation coefficient using empirical log-likelihood style techniques is considered. In practice, it is difficult to estimate the variance of the estimator of the correlation coefficient. However, the proposed newly tuned method leads to a very successful estimator of variance of the est...

In this chapter, we consider the tuning of the estimator of population total using probability proportional to size and without replacement (PPSWOR) sampling scheme. A new linear regression type estimator under PPSWOR sampling scheme is proposed. The proposed tuned estimator is free of second order inclusion probabilities and provides a simple and...

This work proposes a general class of estimators for the population total of a sensitive variable using auxiliary information. Under a general randomized response model, the optimal estimator in this class is derived. Design-based properties of proposed estimators are obtained. A simulation study reflects the potential gains from the use of the pro...

The estimation of a finite population distribution function under a dual frame context is considered when auxiliary population information is available. Several procedures are defined and compared to various methods adapted from the literature. The asymptotic distribution of the proposed estimators is established, a brief simulation is implemented...

The calibration technique (Deville and Särndal, 1992) to estimate the finite distribution function has been studied in several papers. Calibration seeks for new weights close enough to sampling weights according to some distance function and that, at the same time, match benchmark constraints on available auxiliary information. The non smooth chara...

In this chapter, we consider the problem of tuning the estimators of population mean in stratified random sampling design, using both the chi-squared type and the dual-to-empirical log-likelihood (dell) type distance functions when the population mean of the auxiliary variable at the stratum level is available or known. The tuned estimators are sup...

In this chapter, we introduce the new concept of tuning design weights, which, in turn, leads to a computer friendly tuning methodology. The proposed methodology results in an estimator that is equivalent to the linear regression estimator of the population mean or total. The newly tuned estimation methodology is able to efficiently and effectively...

In this chapter, we introduce the idea of using multiauxiliary information for semi-tuning the estimators of population mean and finite population variance under simple random sampling. The use of multiauxiliary information for fully tuning estimators is addressed in the exercises. A new set of three tuning constraints is also introduced. These con...

In this chapter, the problem of estimating a population total using the concept of a multicharacter survey is addressed. The newly tuned multicharacter survey estimators that we introduce are studied for the probability proportional to size and with replacement sampling scheme. Simulation results with the relevant R code, are reported. The code is...

A New Concept for Tuning Design Weights in Survey Sampling: Jackknifing in Theory and Practice introduces the new concept of tuning design weights in survey sampling by combining three techniques: calibration, jackknifing, and (where needed) imputation. This new methodology suggests principles, around which survey statisticians can develop statisti...

A New Concept for Tuning Design Weights in Survey Sampling: Jackknifing in Theory and Practice introduces the new concept of tuning design weights in survey sampling by combining three techniques: calibration, jackknifing, and (where needed) imputation. This new methodology suggests principles, around which survey statisticians can develop statisti...

Randomized response (RR) techniques may be used to compile more reliable data, to protect the respondent’s confidentiality, and to avoid an unacceptable rate of nonresponse when the information requested is sensitive (e.g., concerning racism, drug use, abortion, delinquency, AIDS, or academic cheating). Standard RR methods are used primarily in sur...

The problem of variance estimation for two-phase sampling was considered by Särndal et al. (1992). Hidiroglou et al. (2009) studied the properties of the proposed estimators theoretically while Haziza et al. (2001) empirically studied the performances of the proposed estimators. In this paper a few alternative variance estimators have been proposed...

The rapid proliferation of cell phone use and the accompanying decline in landline service in recent years have resulted in substantial potential for coverage bias in landline random-digit-dial telephone surveys, which has led to the implementation of dual-frame designs that incorporate both landline and cell phone samples. Consequently, researcher...

Data from complex survey designs require special consideration with regard to estimation of finite population parameters and corresponding variance estimation procedures, as a consequence of significant departures from the simple random sampling assumption. In the past decade a number of statistical software packages have been developed to facilita...

Nonparametric regression has become largely used for estimating the regression function in a wide range of fields. We consider the problem of estimating the population total in dual frame surveys. A model-assisted estimator, that can handle continuous covariates is proposed. Asymptotic properties of the proposed method are provided under certain re...

This paper considers the problem of estimating the population proportion of a categorical variable using the calibration framework. Different situations are explored according to the level of auxiliary information available and the theoretical properties are investigated. A new class of estimator based upon the proposed calibration estimators is al...

Survey statisticians make use of auxiliary information to improve estimates, for example in calibration estimation, introduced in Deville and Särndal (1992), which is used to obtain new weights that are close to the basic design weights and that, at the same time, comply with benchmark constraints on the auxiliary information available. Rueda et al...

The methodology of randomized response has advanced considerably in recent years. Nevertheless, to date all the proposed estimators with randomized response techniques have been based on the hypothesis of the availability of a unique and complete list of units forming the target population to be used as a sampling frame. In this paper, we present a...

We consider estimation techniques from dual frame surveys in the case of estimation of proportions when the variable of interest has multinomial outcomes. We propose to describe the joint distribution of the class indicators by a multinomial logistic model. Logistic generalized regression estimators and model calibration estimators are introduced f...

In the present investigation, we consider the problem of estimating a population total using the well known Rao, Hartley and Cochran (J R Stat Soc Ser B 24:482–491, 1962), say RHC scheme, in the presence of dubious random nonresponse. The proposed estimator is compared to the usual estimators of the population total in the presence of random nonres...

New design-based ratio and difference estimators of the distribution function are defined by minimizing the mean square error of a class of estimators. Proposed estimators do not assume a superpopulation model between the variable of interest and the auxiliary variable. Results derived from simulation studies indicate that proposed estimators can b...

We consider the problem of finite population mean estimation with mixed data types. A model-assisted estimator based on nonparametric regression is proposed, which can handle discrete and continuous data and incorporates the sampling design in a natural manner. The proposed method shares the design-based properties of the kernel-based model-assiste...

This paper considers the problem of estimating a finite population proportion when there are missing values. The prediction approach is used to define a new estimator that presents desirable efficiency properties. Simulation studies are considered to evaluate the performance of the proposed estimator via empirical relative bias and empirical relati...

The methodology of randomised response (RR) has advanced considerably in recent years. Nevertheless, most research in this area has addressed the estimation of qualitative variables, and relatively little attention has been paid to the study of quantitative ones. Furthermore, most studies concern only simple random sampling. In this paper, we prese...

Survey statisticians make use of the available auxiliary information to improve estimates. One important example is given by calibration estimation, that seeks for new weights that are close (in some sense) to the basic design weights and that, at the same time, match benchmark constraints on available auxiliary information. Recently, multiple fram...

Social surveys generally assume that a sample of units (students, individuals, employees,…) is observed by two-stage selection from a finite population, which is grouped into clusters (schools, household, companies,…). This design involves sampling from two different populations: the population of schools or primary stage units and the population o...

The most common form of data for socio-economic studies comes from survey sampling. Often the designs of such surveys are complex and use stratification as a method for selecting sample units. A parametric regression model is widely employed for the analysis of such survey data. However the use of a parametric model to represent the relationship be...

This paper discusses the estimation of a population proportion in the presence of missing data and using auxiliary information at the estimation stage. A general class of estimators, which make efficient use of the available information, are proposed. Some theoretical properties of the proposed estimators are analyzed, and they allow us to find the...

The problem of the estimation of a population proportion using auxiliary information has been recently studied by Rueda et al. (Estimators and confidence intervals for the proportion using binary auxiliary information with applications to pharmaceutical studies, J. Biopharmaceut. Statist. 21 (2011), pp. 526–554), which proposed several ratio estima...

The calibration approach to estimating the finite population distribution function was proposed by Rueda et al. (J. Stat. Plan. Inference 137(2):435–448, 2007). The proposed estimator is built by means of constraints that require the use of a set of fixed values. Assuming a linear regression working model, Rueda et al. (Metrika 71:33–44, 2010) cons...

In this work we have collected estimators of the population proportion through the use of auxiliary information under simple random sampling. We analyzed the main properties of these estimators. Theorethical properties suggest that the estimators with use of auxiliary information can outperform alternative methods, and the results derived from a Mo...

Various microbial polymers, namely xanthan gum, gellan gum, pullulan gum and jamilan, were tested as a suitable encapsulating material for Lactobacillus plantarum CRL 1815 and Lactobacillus rhamnosus ATCC 53103. Resulting capsules were also studied for their pH and simulated gastrointestinal conditions tolerance. The morphology of the microcapsules...

Regression type estimators of a population proportion under a general sampling design and using auxiliary information are obtained. Confidence intervals based on various methods, involving auxiliary information, are also derived. An application of the proposed methods is illustrated by estimating the proportion of lakes at risk of acidification, ba...

Standard jackknife confidence intervals for a quantile Q y (β) are usually preferred to confidence intervals based on analytical variance estimators due to their operational simplicity. However, the standard jackknife confidence intervals can give undesirable coverage probabilities for small samples sizes and large or small values of β. In this pap...

Estimation of a proportion is commonly used in areas such as medicine, biopharmaceutical experiments, etc. Estimation of a proportion using auxiliary information has not been investigated in the literature. Ratio estimators of the population proportion and two-sided confidence intervals based upon auxiliary information are derived in this paper. Re...

The estimation of quantiles in the presence of auxiliary information is discussed. Calibration and poststratification techniques provide simple and practical procedures for incorporating auxiliary information into the estimation of distribution functions, which can offer some useful gains in efficiency. The estimator proposed combines these techniq...

In this paper we are going to describe a proposal of working methodology for the subject Statistics Sampling, compulsory for the future graduates in Statistics. This methodology is based on a semipresential teaching which can combine virtual lessons with traditional lessons both in English and Spanish.

The Spanish University is involved in an update process to adapt their degrees to the “European higher education area”. This paper describes the adaptation of the department of Statistics and Operational Research by means of the Moodle Virtual Learning Platform. After one year, the Virtual Learning approach has improve the academic results of the p...

Nonparametric regression has only recently been employed in the estimation of finite population parameters in a model-assisted framework. This paper proposes a new calibration estimator for the distribution function using nonparametric methods to obtain the fitted values on which to calibrate. The proposed estimator is a genuine distribution functi...

Selenium (Se) is an antioxidant element that protects against cellular damage by reactive oxygen species. Therefore, total serum Se concentration may reflect protection during the development of cirrhosis, an oxidative stress-related disease. We hypothesized that serum Se levels are diminished in cirrhotic patients due to their enhanced oxidative s...

The calibration method has been widely discussed in the recent literature on survey sampling, and calibration estimators are routinely computed by many survey organizations. The calibration technique was introduced in [12] to estimate linear parameters as mean or total. Recently, some authors have applied the calibration technique to estimate the f...

In this study we address the problem of the mean estimation of the IBEX-35 index stock quotes in the presence of change points. We rely on nonparametric regression methods for detecting and estimating changes points, and for estimating the discontinuous regression function. Model-assisted and model-based estimators and their jump-preserving counter...

The estimation of the finite population mean in successive occasions is investigated with calibration estimators in this article. We propose several estimators based on calibration techniques with arbitrary sampling design in each of the occasions. Asymptotic variance formulaes are derived for the proposed estimators. The properties of these estima...

The successive sampling is a known technique that can be used in longitudinal surveys to estimate population parameters and measurements of difference or change of a study variable. The paper discusses the estimation of quantiles for the current occasion based on sampling in two successive occasions and using p-auxiliary variables obtained of the p...

We consider the inference on quantiles, Q y (β), with jackknife techniques, in finite populations of a variable, Y, using the quantile information on an auxiliary variable, X. Jackknife techniques are applied to estimate quantiles and the behaviour of these estimators is analyzed. Their properties are studied for simple random sampling. We also exa...

Missing data due to nonresponse, though undesirable, is a reality of any survey. In this paper we consider a situation in which, at a given time, observations are missing for one of the several auxiliary characteristics; thus the ‘missing’ phenomenon occurs for the characteristics separately but not simultaneously. A new method, making use of all t...

A practical problem related to the estimation of quantiles in double sampling with arbitrary sampling designs in each of the two phases is investigated. In practice, this scheme is commonly used for official surveys, in which quantile estimation is often required when the investigation deals with variables such as income or expenditure. A class of...

We address the problem of selecting between two (available) auxiliary variables for computing optimal quantile estimators in finite population survey sampling. The assumed asymptotic perspective allow us to derive optimal conditions for auxiliary variables when a wide class of estimators is considered, under an arbitrary sampling design. For a simp...

One of the most difficult problems confronting investigators who analyze data from surveys is how treat missing data. Many statistical procedures can not be used immediately if any values are missing. This paper considers the problem of estimating the population mean using auxiliary information when some observations on the sample are missing and t...

This work proposes a general class of estimators for a finite population quantile using auxiliary information. This information is provided by the population means of auxiliary variables. The optimum estimator in this class is derived. This result is supported with a numerical example.

The estimation of quantiles in two-phase sampling with arbitrary sampling design in each of the two phases is investigated. Several ratio and exponentiation type estimators that provide the optimum estimate of a quantile based on an optimum exponent α are proposed. Properties of these estimators are studied under large sample size approximation and...

The paper proposes a new calibration estimator for the distribution function of the study variable. This estimator is a distribution function unlike others estimators that use auxiliary information. Comparisons are made with existing estimators in two simulation studies.

In this paper, we propose an estimator for the population mean when some observations on the study and auxiliary variables are missing from the sample. The proposed estimator is valid for any unequal probability sampling design, and is based upon the pseudo empirical likelihood method. The proposed estimator is compared with other estimators in a s...

We propose a calibrated estimator of the quantiles of sample survey data and discuss the asymptotic theory behind it. This estimator is defined for any sampling design and uses the information available on J auxiliary variables. A simulation study based on a real population is used to compare the estimator with various methods proposed previously.

This paper considers the construction of bootstrap confidence intervals for estimating finite population quantiles. The intervals involve estimators which make use of the auxiliary information provided by an available auxiliary variable. The proposed bootstrap confidence intervals are validated under theoretical (asymptotic) and empirical points of...

This paper proposes some estimators for the finite population mean when observations on some units (on either the auxiliary variable or the main variable) are missing. The optimum estimator in the proposed class is derived. Asymptotic properties of optimum estimator are studied. A brief simulation study shows goods properties for moderate sample si...

The problem of estimating the population mean using calibration estimators when some observations on the study and auxiliary characteristics are missing from the sample, is considered. Some new classes of estimators are proposed for any sampling design. These new classes employ to all observation (incomplete cases too) in the estimation without usi...

We address the problem of estimating the finite population mean in survey sampling, by exploiting any available auxiliary information in order to increase the precision of classical estimators. The idea is to use any population quantiles of the available auxiliary variables which are known in many real situation from census, administrative files, e...

This paper deals with the estimation, under sampling in two successive occasions, of a finite population quantile. For this sampling design a class of estimators is proposed whose the ratio and difference estimators are particular cases. Asymptotic variance formulae are derived for the proposed estimators, and the optimal matching fraction is discu...

Difference type estimators use auxiliary information based on an auxiliary parameter (specifically the parameter of interest), associated with the auxiliary variable. In practice, however, several parameters for auxiliary variables are available. This paper discusses how such estimators can be modified to improve the usual methods if information re...

One of the most difficult problems confronting investigators who analyze data from surveys is how to treat missing data. Many statistical procedures cannot be used immediately if any values are missing. Imputation of missing data before starting statistical analysis is then necessary. This paper proposes imputation methods of the mean based on indi...

A difference estimator using an auxiliary variable x is defined to estimate the finite population variance Sy2 of the study character y. Classical difference type estimators use auxiliary information based on a single auxiliary parameter, specifically the parameter of interest, associated with the auxiliary variable. In practice, however, several p...

The problem of quantile estimation using quantiles Qx(α) in which the order of the auxiliary variable is different from that of the main variable to be estimated, Qy(β), is considered. Certain new estimators for the β-quantile have been proposed for any sampling design. The effect of this modification on the standard estimators, ratio, position, st...

This paper presents a technique for improving the ratio method of estimation for finite population quantiles. The performance of this estimator with respect to others is studied theoretically and empirically, for a wide variety of real and artificial populations, and includes simple random sampling and sampling proportional to an auxiliary variable...

This paper deals with the inference of finite populations quantiles by using auxiliary information. The population information considered on the proposed estimatiors is a population quantile of the auxiliary variable with the same order as that of the quantile of the main variable to be estimated. A simulation study based on three real finite popul...

This paper proposes the use of multi-auxiliary information using quantiles and ratio and difference type estimators of the finite population distribution function to derive confidence intervals for medians. A simulation study based on three real populations compares its behaviour to that of standard methods.