A Combined Product Estimator in Sample Survey

For the estimation of the population mean in stratified random sampling a ‘Combined Product Estimator’ is proposed which is more efficient than the ‘Combined Ratio’ and ‘Separate Ratio’ estimators. Also, the proposed estimator have exact expressions for bias and mean square error. An empirical illustration is given to compare the efficiencies of different estimators.     

A Class of Ratio-Cum-Product-Type Estimator

The problem of estimating the population mean using an auxiliary information has been dealt with in literature quite extensively. Ratio, product, linear regression and ratio-type estimators are well known. A class of ratio-cum-product-type estimator is proposed in this paper. Its bias and variance to the first order of approximation are obtained. For an appropriate weight ‘a’ and good range of α-values, it is found that the proposed estimator is superior than a set of estimators (i.e., sample mean, usual ratio and product estimators, SRIVASTAVA's (1967) estimator, CHAKRABARTY's (1979) estimator and a product-type estimator) which are, in fact, the particular cases of it. At optimum value of α, the proposed estimator is as efficient as linear regression estimator.     

A Product-Type Estimator in Double Sampling

The use of ratio and product estimators, using auxiliary information, for estimating the mean of a finite population is well known. The efficiency of ratio estimator or product estimator is high depending on whether the auxiliary character is highly positively or negatively coorelated with the main character of interest. This paper proposes a product-type estimator which is more efficient than the usual ratio and product estimators in practical situations. We consider the case of double sampling from which the single sampling results may easily be derived.     

A Class of Ratio Cum Product-Type Estimator in Double Sampling

A class of ratio cum product-type estimator is proposed in case of double sampling in the present paper. Its bias and variance to the first order of approximation are obtained. For an appropriate weight ‘a’ and a good range of α-values, it is found that the proposed estimator is more efficient than the set of estimator viz., simple mean estimator, usual ratio and product estimators, SRIVASTAVA 's estimator (1967), CHAKARBARTY 's estimator and product-type estimator, which are in fact the particular cases of it. The proposed estimator is as efficient as linear regression estimator in double sampling at optimum value of α.     

On Combination of Ratio and PPS Estimators

AGARWAL and KUMAR (1980) proposed an estimator, combining ratio and pps estimators of population mean and proved that the proposed estimator would always be better (in minimum mean square error sense) than the pps estimator or the ratio estimator under pps sampling scheme for optimum value of constant k (parameter). The optimum value of k is rarely known in practice, hence the alternative is to replace k from the sample-values. In this paper, an estimator depending on estimated optimum value of k based on sample-values, under pps sampling scheme is proposed and studied.     

An Efficient Regression Type Estimator in Survey Sampling

For the estimation of population mean in simple random sampling, an efficient regression-type estimator is proposed which is more efficient than the conventional regression estimator and hence than mean per unit estimator, ratio and product estimators and many other estimators proposed by various authors. Some numerical examples are included for illustration.     

A random effects model for multivariate failure time data from multicenter clinical trials

A random effects model for analyzing multivariate failure time data is proposed. The work is motivated by the need for assessing the mean treatment effect in a multicenter clinical trial study, assuming that the centers are a random sample from an underlying population. An estimating equation for the mean hazard ratio parameter is proposed. The proposed estimator is shown to be consistent and asymptotically normally distributed. A variance estimator, based on large sample theory, is proposed. Simulation results indicate that the proposed estimator performs well in finite samples. The proposed variance estimator effectively corrects the bias of the naive variance estimator, which assumes independence of individuals within a group. The methodology is illustrated with a clinical trial data set from the Studies of Left Ventricular Dysfunction. This shows that the variability of the treatment effect is higher than found by means of simpler models.     

The Chain Ratio Estimator and Regression Estimator with Linear Combination of Two Auxiliary Variables

In sample surveys, it is usual to make use of auxiliary information to increase the precision of the estimators. We propose a new chain ratio estimator and regression estimator of a finite population mean using linear combination of two auxiliary variables and obtain the mean squared error (MSE) equations for the proposed estimators. We find theoretical conditions that make proposed estimators more efficient than the traditional multivariate ratio estimator and the regression estimator using information of two auxiliary variables.     

Use of known Coefficients of Variation in the Estimation of the Common mean of two Normal Populations

The problem of estimating the common mean of two normal populations N(?, a1?2) and N(?, a2?2) where the coefficients of variation of two populations respectively, are known constants, on the basis of two independent random samples, one from each population, is considered. The minimum mean square estimator is proposed. It is also shown that the proposed estimator is Best Asymptotic Normal (BAN) estimator. It is pointed out that the result can be generalized to k population problem. It is remarked that the same method works, also for the problem of estimating the common standard deviation of k normal populations when coefficients of variation are known.     

Estimating Ratio of Proportions Using Auxiliary Information

The problem of estimation of ratio of population proportions is considered and a difference-type estimator is proposed using auxiliary information. The bias and mean squared error of the proposed estimator is found and compared to the usual estimator and also to WYNN'S (1976) type estimator. An example is included for illustration.     

二次等距抽样

本文提出了一种二次等距抽样方法,并提出了总体平均值的一个估计量：拼配部分的比型估计与轮换部分的样本均值的加权平均。当样本量较大时,求出了估计量的方差及最优轮换比．并对特殊情形进行了讨论和数值比较．     

Improved Generalized Ratio-Cum-Product Estimation

In this paper, a generalized ratio-cum-product estimator for estimating the ratio (product) of two population means using auxiliary information on two other variables is given of which the estimators by SINGH (1969) and SHAH and SHAH (1978) are particular cases. The estimator is regeneralized when the covariance between two auxiliary variables is known.     

On Use of Distinct Respondents in Randomized Response Surveys

It is well known for direct response surveys (DR), where the responses are obtained from the respondents directly, that the sample mean, based on distinct units of a simple random sample selected with replacement (SRSWR) method, is more efficient than the sample mean based on all the units including repetition. In this paper, it is shown that a linear unbiased estimator based on distinct units is inadmissible for estimating a finite population mean when the sample is selected by an arbitrary with replacement (WR) sampling scheme and the responses are obtained independently by some RR technique. Efficiencies for a few linear unbiased estimators are compared under SRSWR sampling.     

Time‐shift experiments and patterns of adaptation across time and space

Time‐shift experiments provide measures of the mean fitness of a population in environments of different points in time. Here, we show how to use this type of data to decompose mean fitness into (1) the effect of the environment in which the population is transplanted, (2) the effect of the genetic composition of the population and (3) ‘temporal adaptation’, which measures how the population fits the environment at that time. We derive analytical results for the pattern of ‘temporal adaptation’ and show that it is in general maximal in the recent past. The link between ‘temporal adaptation’ and ‘local adaptation’ is discussed, and we show when patterns of adaptation in time and space are expected to be similar. Finally, we illustrate the potential use of this approach using a data set measuring the adaptation of HIV to the immune response of several recently infected patients.     

A New Exponential Ratio-Type Estimator with Linear Combination of Two Auxiliary Variables

In sample surveys, it is usual to make use of auxiliary information to increase the precision of estimators. We propose a new exponential ratio-type estimator of a finite population mean using linear combination of two auxiliary variables and obtain mean square error (MSE) equation for proposed estimator. We find theoretical conditions that make proposed estimator more efficient than traditional multivariate ratio estimator using information of two auxiliary variables, the estimator of Bahl and Tuteja and the estimator proposed by Abu-Dayeh et al. In addition, we support these theoretical results with the aid of two numerical examples.     

A General Class of Ratio‐Type Estimators Under Super‐Population Model

The problem of constructing classes of estimators for population mean has been widely discussed by various authors under design approach in sample surveys. An attempt by Upadhyaya , Singh , and Vos (1985) has been made to combine the usual mean and ratio estimator with suitable weights in order to define a general class of estimators. This paper is an attempt to study properties of the same estimator under super‐population model. Optimum weights have also been proposed. Results have been supported with some numerical examples.     

Three‐dimensional post‐glacial expansion and diversification of an exploited oceanic fish

Vertical divergence in marine organisms is being increasingly documented, yet much remains to be carried out to understand the role of depth in the context of phylogeographic reconstruction and the identification of management units. An ideal study system to address this issue is the beaked redfish, Sebastes mentella – one of four species of ‘redfish’ occurring in the North Atlantic – which is known for a widely distributed ‘shallow‐pelagic’ oceanic type inhabiting waters between 250 and 550 m, and a more localized ‘deep‐pelagic’ population dwelling between 550 and 800 m, in the oceanic habitat of the Irminger Sea. Here, we investigate the extent of population structure in relation to both depth and geographic spread of oceanic beaked redfish throughout most of its distribution range. By sequencing the mitochondrial control region of 261 redfish collected over a decadal interval, and combining 160 rhodopsin coding nuclear sequences and previously genotyped microsatellite data, we map the existence of two strongly divergent evolutionary lineages with significantly different distribution patterns and historical demography, and whose genetic variance is mostly explained by depth. Combined genetic data, analysed via independent approaches, are consistent with a Late Pleistocene lineage split, where segregation by depth probably resulted from the interplay of climatic and oceanographic processes with life history and behavioural traits. The ongoing process of diversification in North Atlantic S. mentella may serve as an ‘hourglass’ to understand speciation and adaptive radiation in Sebastes and in other marine taxa distributed across a depth gradient.     

Use of prior information in simple random sampling

Is is assumed that the population mean, to be estimated, is less than or equal to a known constant. An estimator is suggested which takes into account this information to advantage. It is also suggested that stratification coupled with the modified estimator can be best suited in such situations.     

Improvement Over Transformed Auxiliary Variable in Estimating the Finite Population Mean

For estimating the finite population mean of the study variable y, we propose a ratio‐type estimator which gives an improvement over estimators given by Upadhyaya and Singh (1999), Sisodia and Dwivedi (1981), and Singh and Kakran (1993). These estimators are compared by observing the bias and mean square error (MSE). In this empirical study, the suggested estimator under the optimal condition is found to be more efficient than the estimators mentioned above.     

A Note on the Estimation of the Population Mean in Stratified Random Sampling Using Two Auxiliary Variables

In this paper, a two‐phase sampling estimator for a stratified population mean using two auxiliary variables x and z is considered when the stratum mean of x is unknown but that of z is known. The suggested estimator under its optimal condition is found to be more efficient than the one using only x.