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Recent studies have shown that an adaptive T 2 chart with double sampling and variable sampling interval D S V S I T 2 chart shows a good performance in detecting small to moderate shifts in the me...

Count data arising in various fields of applications are often under‐reported. Ignoring undercount naturally leads to biased estimators and inaccurate confidence intervals. In the presence of undercount, in this paper, we develop likelihood‐based methodologies for estimation of mean using validation data. The asymptotic distributions of the competing estimators of the mean are derived. The impact of ignoring undercount on the coverage and length of the confidence intervals is investigated using extensive numerical studies. Finally an analysis of heat mortality data is presented.

In many applications, the quality of a process is characterized by the functional relationship between a response variable and one or more explanatory variables. This functional relationship is ref...

This manuscript presents the process for estimating the mean number of individuals having rare sensitive characteristic when population units are heterogeneous with and without prior information on the supplementary (unrelated rare non-sensitive) characteristic. The rare stigmatized parameter is estimated using an ameliorated two-stage randomized response model under stratified sampling and stratified double sampling schemes. The properties of the suggested estimators have been discussed under random, proportional and optimal allocations of sample from different strata. The proposed estimators perform better over some contemporary competent estimators for similar situations which have been shown through empirical studies.

The present article deals with the estimation of mean number of respondents who possess a rare sensitive character in presence of known and unknown proportion of a rare unrelated non-sensitive attribute by using the Poisson probability distribution in stratified random sampling as well as in stratified random double sampling. The variance of rare sensitive character is also derived under proportional and optimal allocation methods in stratified random sampling when stratum sizes are known and unknown. The properties of the suggested estimation procedures have been deeply examined. The proposed model is found to be dominant over Lee et al. [Estimation of a rare sensitive attribute in a stratified sample using Poisson distribution. Statistics. 2013;47:575–589] model. Numerical illustrations are presented to support the theoretical results. Results are analysed and suitable recommendations are put forward to the survey practitioners.

Ratio-product-ratio estimators with two parameters in double sampling under non-response are considered along with their properties. Practical conditions are obtained in which the suggested estimators are more proficient than other existing estimators. An example is given.

A disease prevalence can be estimated by classifying subjects according to whether they have the disease. When gold-standard tests are too expensive to be applied to all subjects, partially validated data can be obtained by double-sampling in which all individuals are classified by a fallible classifier, and some of individuals are validated by the gold-standard classifier. However, it could happen in practice that such infallible classifier does not available. In this article, we consider two models in which both classifiers are fallible and propose four asymptotic test procedures for comparing disease prevalence in two groups. Corresponding sample size formulae and validated ratio given the total sample sizes are also derived and evaluated. Simulation results show that (i) Score test performs well and the corresponding sample size formula is also accurate in terms of the empirical power and size in two models; (ii) the Wald test based on the variance estimator with parameters estimated under the null hypothesis outperforms the others even under small sample sizes in Model II, and the sample size estimated by this test is also accurate; (iii) the estimated validated ratios based on all tests are accurate. The malarial data are used to illustrate the proposed methodologies.

Semi-competing risks data arise when two types of events, non-terminal and terminal, may be observed. When the terminal event occurs first, it censors the non-terminal event. Otherwise the terminal event is observable after the occurrence of the non-terminal event. In practice, it can be hard to ascertain all terminal event information after the non-terminal event. Yu and Yiannoutsos [(2015), ‘Marginal and Conditional Distribution Estimation from Double-Sampled Semi-Competing Risks Data’, Scandinavian Journal of Statistics, 42, 87–103] considered a setting when the terminal event is ascertained via double sampling from only a subset of patients who experienced the non-terminal event. They discussed estimation for marginal and conditional distributions under this double sampled semi-competing risk data framework. We propose a more efficient estimation method in the same setting by fully utilising the non-terminal event information. The efficiency gain can be substantial as observed in our simulatio...

The implementation of an adaptive cluster sampling design often becomes logistically challenging because variation in the final sampling effort introduces uncertainty in survey planning. To overcome this drawback, an inexpensive and easy to measure auxiliary variable could be used in a two-phase survey strategy, called adaptive cluster double sampling (Felix-Medina and Thompson in Biometrika 91:877–891, 2004). In this paper, a two-phase sampling strategy is proposed which combines the idea of adaptive cluster double sampling with the principle of post-stratification. In the first-phase an adaptive cluster sample is selected by means of an inexpensive auxiliary variable. Networks from the first phase sampling are then post-stratified according to their size. In the second-phase, the network structure is used to select a subsample of units by means of stratified random sampling. The proposed sampling strategy employs stratification without requiring an a priori delineation of the strata. Indeed, the strata sizes are estimated in the course of the two-phase sampling process. Therefore, it is suitable for situations where stratification is suspected to be efficient but strata cannot be easily delineated in advance. In this framework, a new type of estimator for the population mean which mimics the stratified sampling mean estimator and an estimator of the sampling variance are proposed. The results of a simulation study confirm, as expected, that the use of post-stratification leads to gain in precision for the estimator. The proposed sampling strategy is applied for targeting an epiphytic lichen community Lobarion pulmonariae in a forest area of the Northern Apennines (N-Italy), characterized by several species of conservation concern.

In this paper, we consider the problem of estimation of population mean of a study variable by making use of first-phase sample mean and first-phase sample median of the auxiliary variable at the estimation stage. The proposed new estimator of the population mean is compared to the sample mean estimator, ratio estimator and the difference type estimator for the fixed cost of the survey by using the concept of two-phase sampling. The magnitude of the relative efficiency of the proposed new estimator has been investigated through simulation study.

This paper discusses the problem of estimation of finite population mean in double sampling for stratification. In fact, ratio and product type exponential estimators of population mean are proposed in double sampling for stratification. The biases and mean squared errors of proposed estimators are obtained upto the first degree of approximation. The proposed estimators have been compared with usual unbiased estimator, ratio and product estimators in double sampling for stratification. To judge the performance of the proposed estimators an empirical study has been carried out.

This paper considers the problem of estimating the product of two population means using the information on multi-auxiliary characters with double sampling the non-respondents. Classes of estimators are proposed for estimating P under two different situations [discussed by Rao (1986, 90)] using known population mean of multi-auxiliary characters. Further, this problem has been extended to the case when population means of the auxiliary characters are unknown and they are estimated on the basis of a larger first phase sample. In this situation, a class of two phase sampling estimators for estimating P is suggested using multi-auxiliary characters with unknown population means in the presence of non-response. The expressions of bias and mean square error of all the proposed estimators are derived and their properties are studied. An empirical study using real data sets is given to justify the theoretical considerations.

This paper presents exponential ratio and product estimators for estimating finite population mean using auxiliary information in double sampling and analyzes their properties. These estimators are compared for their precision with simple mean per unit, usual double sampling ratio and product estimators. An empirical study is also carried out to judge the merits of the suggested estimators.

This paper defines a general procedure for estimating the population mean of the study variate based on double sampling for stratification in presence of multi-auxiliary information. Classes of combined and separate estimators have been suggested and their properties are studied under large sample approximation. A class of unstratified double sampling estimators is also proposed with its properties. Asymptotic optimum estimators in the classes are identified with their approximate variance formulae. Further the proposed classes of estimators are compared with the corresponding class of estimators based on un-stratified double sampling. All findings are encouraging and support the soundness of the proposed procedure for mean estimation.

Double-sampling designs are commonly used in real applications when it is infeasible to collect exact measurements on all variables of interest. Two samples, a primary sample on proxy measures and a validation subsample on exact measures, are available in these designs. We assume that the validation sample is drawn from the primary sample by the Bernoulli sampling with equal selection probability. An empirical likelihood based approach is proposed to estimate the parameters of interest. By allowing the number of constraints to grow as the sample size goes to infinity, the resulting maximum empirical likelihood estimator is asymptotically normal and its limiting variance–covariance matrix reaches the semiparametric efficiency bound. Moreover, the Wilks-type result of convergence to chi-squared distribution for the empirical likelihood ratio based test is established. Some simulation studies are carried out to assess the finite sample performances of the new approach.

In this paper, we consider the Birnbaum–Saunders distribution as a life model to develop various acceptance sampling schemes based on the truncated life tests. We develop the double sampling plan and determine the design parameters satisfying both the producer's and consumer's risks simultaneously for the specified reliability levels in terms of the mean ratio to the specified life. We also propose a group sampling plan and determine the parameters by the above-mentioned two-point method. Tables are constructed for the proposed sampling plans and results are explained with examples.

Sampling plans are a useful tool to decide whether large-size lots should be accepted or rejected. In this paper we introduce double sampling plans by variables for a normally distributed characteristic with known standard deviation and two-sided specification limits. These plans fulfill the classical two-points-condition on the operating characteristic (OC) and feature minimal maximal average sample number (ASN).

In this article, we introduce minimum divergence estimators of parameters of a binary response model when data are subject to false-positive misclassification and obtained using a double-sampling plan. Under this set up, the problem of goodness-of-fit is considered and divergence-based confidence intervals (CIs) for a population proportion parameter are derived. A simulation experiment is carried out to compare the coverage probabilities of the new CIs. An application to real data is also given.

A common approach to the design of an acceptance sampling plan is to require that the operating characteristic (OC) curve should pass through two designated points that would fix the curve in accordance with a desired degree of discrimination. This paper presents a search procedure for the selection of double sampling inspection plans of type DSP - (0, 1) for specified two points on the OC curve, namely acceptance quality limit, producer's risk, limiting quality and consumer's risk. Selection of the plans is discussed for both the cases of fraction non-conforming and the number of non-conformities per unit.

Fallible classification scheme is known to produce inconsistent relative frequency estimates from a polychotomous variable. These estimates however can be improved upon by the use of a sub-sample that results in a square table. In this research we highlight the method of improvement.

Summary We analyse a combination of errant count data subject to under-reported counts and inerrant count data to estimate multiple Poisson rates and reporting probabilities of cervical cancer for four European countries. Our analysis uses a Bayesian hierarchical model. Using a simulation study, we demonstrate the efficacy of our new simultaneous inference method and compare the utility of our method with an empirical Bayes approach developed by Fader and Hardie (J. Appl. Statist., 2000).

The paper proposes a class of dual to ratio estimators for estimating the mean of finite population, for double sampling.

We propose a double sampling scheme with two classifiers to address the problem of optimal sample size when misclassification among binomial observations is observed. The classifiers vary with respect to the classifying cost and precision. Furthermore, since the data are unknown, an additional constraint is set on the probability of observing ``undesirable'' data. The method is developed following the Bayesian point of view.

Double sampling scheme is used when cheap auxiliary variables may be measured to improve the estimation of a finite population parameter. Several estimators for population mean, ratio of means and variance are available, when two dependent samples are drawn. However, there are few proposals for the case of independent samples. In this paper both cases of dependent and independent samples are dealt with. A general approach for estimating a finite population parameter is given, showing that all the proposed estimators are particular cases of the same general class. The minimum variance bound for any estimator in this class is provided (at the first order of approximation). Furthermore, an optimal estimator which reaches this minimum is found.

This paper proposes a general class of estimators for estimating the median in double sampling. The position estimator, stratification estimator and regression type estimator attain the minimum variance of the general class of estimators. The optimum values of the first-phase and second-phase sample sizes are also obtained for the fixed cost and the fixed variance cases. An empirical study examines the performance of the double sampling strategies for median estimation. Finally, an extension of the methods of Chen & Qin (1993) and Kuk & Mak (1994) is considered for the double sampling strategy.

We provide a method for finding the optimal double sampling plan for estimating the mean value of a continuous outcome. It is assumed that the fallible and true outcome data are related by a simple linear regression model. The design parameters are the total sample size, N, and the number of doubly sampled units n. We show that under certain conditions the efficiency gains, relative to standard sampling plans are considerable.

In this paper, a new sampling scheme called the 'conditional double sampling scheme' (CDSS) has been proposed. A compact table is presented for the selection of a CDSS indexed by various combinations of entry parameters. Advantages of the CDSS over the single sampling scheme have been discussed. The basis for the construction of the table is given.

This paper presents a design for skip-lot sampling inspection plans with the double-sampling plan as the reference plan, so as to reduce the sample size and produce more efficient plans in return for the same sampling effort. The efficiency of the proposed plan compared with that of the conventional double-sampling plan is also discussed. The need for smaller acceptance numbers under the plan is highlighted. Methods of selecting the plan indexed by the acceptable quality level and limiting quality level, and by the acceptable quality level and average outgoing quality level are also presented.

The method of double sampling in experiments has been recently rediscovered by Pepe (Biometrika 79 (1992), 355–365) and Pepe et al. (J. Statist. Plann. Inference 42 (1994), 137–160). However, a partially semi-parametric analysis method is employed, motivated by fears of misspecification of parts of the model and the belief that these parts are of little substantive interest. This paper points out the often substantial loss of information involved in the use of the method as compared with parametric analysis. It also argues that a broader review of the literature relevant to double sampling suggests that all of the model is usually of substantive interest and that the fears and consequences of misspecification are exaggerated.

A new sampling inspection system involving normal and tightened plans is presented. Performance measures are developed. The average sample number of the newly developed system is compared with those of existing plans. Procedures are indicated an tables are constructed for designing the system indexed by various combinations of parameters.

Designing double sampling plan requires identification of sample sizes and acceptance numbers. In this paper a genetic algorithm has been designed for the selection of optimal acceptance numbers and sample sizes for the specified producer’s risk and consumer’s risk. Implementation of the algorithm has been illustrated numerically for different choices of quantities involved in a double sampling plan &nbsp

The Theory of double sampling as proposed by Neyman (1938) and subsequently used for successive sampling by Jesson (1942), Yates (1960), Patterson (1950), Eckler (1955), Kuldroff (1963) and Tikkiwal (1960, 1967) has been explored to develop a general estimator which can be used for estimation of parameters such as mean, ratio or double ratio. A simple case of sampling on two occasions has only been considered but the logic can easily be extended for more than two occasions. The results show that the generalised estimator will be very useful for the applied statisticians.

A simple method of analyzing the MIL-STD-105D double sampling plans by ‘normalizing the OC curve’ is presented. Among a set of competing double sampling plans, procedures are given to select a particular plan when costs are unknown. Necessary tables are constructed and examples given.

A table is presented for the construction and selection of tightened-normal-tightened sampling scheme of type TNT-(n1, n2;c). Efficiency of TNT-(n1, n2;c) scheme over conventional single and double sampling plans is discussed.

Procedures and tables for the selection of conditional double sampling plans for various entry parameters are given. A search procedure is also developed to determine the parameters of the plans when two points on the operating characteristic curve are specified.

Manufacturers and government agencies frequently use acceptance sampling to decide whether a lot from a supplier or exporting country should be accepted or rejected. International standards on acceptance sampling provide sampling plans for specific circumstances. The aim of this package is to provide an easy-to-use interface to visualize single, double or multiple sampling plans. In addition, methods have been provided to enable the user to assess sampling plans against pre-specified levels of performance, as measured by the probability of acceptance for a given level of quality in the lot.

Catch curve analysis provides a simple method for estimating the abundance and the fishing mortality rate of a stock of exploited fish. The age composition of a catch of fish is the key ingredient of catch curve analysis. However, estimation of the age composition of the catch is rarely of interest in its own right. Rather, a double sampling design is used to economize the estimation of the age composition of the catch for the purposes of estimating abundance and vital rates of the fishery. This paper provides a framework for obtaining the most precise estimates of abundance and the fishing mortality rate for a fixed budget with respect to the second phase subsampling strategy of the double sampling design. Also, methods are given describing how to optimize the survey design when there is nonsampling error due to age misclassification.

Tables have been prepared for the construction and selection of multiple dependent (deferred) state (MDS) sampling plans of type MDS-(c1,c2). These plans are compared with conventional sampling plans (such as single and double sampling) and it is shown that MDS-type plans require a smaller sample size. A special feature of the MDS-(0,1) plan is highlighted and its design procedure is indicated.

In order to resolve the difficulties involved in inference from a sample of categorical data obtained by using a fallible classifying mechanism (usually inexpensive), we consider, as in Tenenbein (1970, 1971, 1972), the utilization of an additional sample. The second sample is subjected to a simultaneous cross-classification of its elements by the fallible mechanism and by some true (usually expensive) classifying mechanism. The setup is general; i.e., the discussion can be applied to any multidimensional cross-classified data obtained by unrestricted random sampling. Two methodologies are presented: (i) a combined maximum likelihood (ML) and least squares (LS) approach and (ii) a complete-LS approach. Both methodologies are illustrated using real data.

We propose an estimator for the number of sources, N, which transmit signals according to a Poisson process with a common rate g. This estimation problem was originated by Starr and pursued by Vardi. Our procedure is a 'double sampling' one and has the advantage that it can be used when it is unknown. DOUBLE SAMPLING; FINITE POPULATIONS; POISSON PROCESS; TRANSMISSION SOURCES

The effect of the inspector's accuracy on types I and II errors on Dependent and Deferred double sampling plans by Baker et al. (1978) and Chain-deferred inspection plans by Osanaiye (1983) which utilise the surrounding lot information on sentencing a lot is examined. The proportion of production that is wrongly accepted or rejected by each of the plans are also examined drawing particular attention to the effect of making resorts. A linear trend in process quality is assumed. The Chain-deferred plan in general has more tendency to reject defective items more than any of the other plans irrespective of the magnitude of the inspector's error. Although it has slightly higher tendency to reject good items, this is not very significant compared with the other plan as can be seen in the results.

SUMMARY This paper considers the estimation of the subgroup means of a response variable when the individuals in a random sample are allocated to the subgroups or classes by a fallible device. A double sampling scheme under which we determine also the true classes of the individuals in a subsample is utilized. A simple distributional-free estimator is proposed and the associated large-sample properties are also derived. The proposed estimator is also demonstrated by simulation studies to be more efficient than Selen's estimator (1986).

An examination is made of the effectiveness of the Chandrasekar-Deming technique for estimating the number of vital events using both the registration (continuous recording) of events and a periodic retrospective survey. It is shown that, under a general model for response errors, the technique may produce estimates that are considerably biased downwards. A comparison is made with a number of other estimators. The possibility of improving results through double sampling is explored.