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Certain discrepancies in data sources for estimating the household consumption expenditure to derive Gross Domestic Product(GDP) of India are discussed in this paper. Simple implementable strategies are suggested to improve the estimation of GDP.

Sugden and Smith [2002. Exact linear unbiased estimation in survey sampling. J. Stat. Plann. Inf. 102, 25–38] and Rao [2002. Discussion of “Exact linear unbiased estimation in survey sampling”. J. Stat. Plann. Inf. 102, 39–40] suggested some useful techniques of deriving a linear unbiased estimator of a finite population total by modifying a given linear estimator. In this paper we suggest various generalizations of their results. In particular, we search for estimators satisfying the calibration property with respect to a related auxiliary variable and obtain some new calibrated unbiased ratio-type estimators for arbitrary sampling designs. We also explore a few properties of one of the estimators suggested in Sugden and Smith [2002. Exact linear unbiased estimation in survey sampling. J. Stat. Plann. Inf. 102, 25–38].

Consider a finite population of units (U1,U2,…,UN). On each unit Ui, variates of interest y and x are defined taking values Yi and Xi, respectively, i=1,2,…,N. In certain surveys, it is of interest to estimate the population ratio R=Y/X (or equivalently, Y / X ), whereY=∑1NYi and X=∑1NXi, based on a sample of size n selected according to a sampling design p(s). Under simple random sampling scheme, the usual choices for the estimation of R are (i) a (single) ratio of sample means given by R 1 = y / x or (ii) the mean of (n) ratios, viz. R n = ∑ 1 n (y i /x i )/n . It is well known that both R 1 and R n are biased for R. Using the extent of biases, we shall first discuss the role of R 1 and R n in the construction of unbiased ratio estimators. When y is considered as the study variate and x is an auxiliary variate related to y, the problem of estimation of the population mean Ȳ or the population total Y is dealt by constructing Y = R X or Y = R X . For the estimation of the population total Y, we shall consider a class of Symmetrized Des Raj (SDR) strategies and look for a choice of a model-optimum estimator when design-unbiasedness is not demanded, among those utilising ‘mean of ratios’ and ‘ratio of means’.

Summary This is a brief history of the evolution of official and academic Statistics in India which focuses mainly on the period 1930 to 1960 but traces its origins in antiquity and recent history. We also comment on how Statistics has continued to evolve since the 1960's. This is a history of both institutions and people, who built and shaped them, and of ideas. Resume Ceci est une coute histoire de l'evolution de la Statistique officielle et acadeemique en Inde. Nous retracons l'hisoire a patir des origines de l'antiquite jusqu'a l'histoire plus recente mais potons plus d'atention sur la peiode des annees 1930 a 1960. Ceci et lhistoire d'institutions, des gens qui les batirent et les formerent eet d'idees.

In this paper we study some order relations between the selection and the inclusion probabilities for PPSWOR Sampling Scheme. We also establish some interesting bounds on the inclusion probabilities in terms of the selection probabilities.

In the estimators t 3 , t 4 , t 5 of Mukerjee, Rao & Vijayan (1987), b yx and b yz are partial regression coefficients of y on x and z, respectively, based on the smaller sample. With the above interpretation of b yx and b yz in t 3 , t 4 , t 5 , all the calculations in Mukerjee at al.(1987) are correct. In this connection, we also wish to make it explicit that b xz in t 5 is an ordinary and not a partial regression coefficient. The 'corrected' MSEs of t 3 , t 4 , t 5 , as given in Ahmed (1998 Section 3) are computed assuming that our b yx and b yz are ordinary and not partial regression coefficients. Indeed, we had no intention of giving estimators using the corresponding ordinary regression coefficients which would lead to estimators inferior to those given by Kiregyera (1984). We accept responsibility for any notational confusion created by us and express regret to readers who have been confused by our notation. Finally, in consideration of the above, it may be noted that Tripathi & Ahmed's (1995) estimator t 0 , quoted also in Ahmed (1998), is no better than t 5 of Mukerjee at al.(1987).

We first consider Neyman's optimum allocation of sample size to strata in the light of available auxiliary information for which a suitable random permutation model is assumed. For a special case of this model the allocation of the sample size reduces to the same as when a certain superpopulation regression model is assumed. Motivated by this, more generally, we discuss some optimality results under random permutation models and compare them with the corresponding results when a superpopulation regression model is assumed.

In this paper, we shall study an alternative method of deriving Neyman's Optimum allocation of sample size to strata for simple random sampling which is intuitive and simple. In order to obtain this allocation, the within stratum standard deviations of the study variate are required which are unknown and hence are substituted by known quantities. We shall discuss the effects of deviations from the optimum allocation and other related problems.

In this note we observe that Brewer's (1979) result concerning the asymptotically design unbiased strategy which has minimum expected variance under a super population model can be established in a more general setting.

Bansal and Singh (1985) have developed an alternative estimator for the probability proportional to size with replacement sampling scheme when certain characteristics under study are poorly correlated with the selection probabilities. We suggest, in this paper, a more intuitive and meaningful estimator and study its efficiency compared with other related estimators.

The problem of estimating the variance of the ratio estimator for theMidzuno-Sen sampling scheme is further studied in this paper. Sufficient conditions are derived for which the suggested variance estimator is always positive definite.

The method of ratio estimation for estimating the population mean Ȳ of a characteristic y when we have auxillary information on a characteristic x highly correlated with y, consists in getting an estimator of the population ratio R = Ȳ/X and then multiplying this estimator by the known population mean X. Though efficient, ratio estimators are in general biased and in this article we review some of the unbiased ratio estimators and discuss a method of constructing them. Next we present the Jackknife technique for reducing bias and show how the generalized Jackknife could be interpreted by the same method.

Cassel (1977) discussed the correspondence between the Horvitz-Thompson strategy and the stratefied random sampling strategy for a special case of the general superpopulation model. We consider a more general model and discuss the correspondence between these strategies in a more formal way.

In this paper we shall consider the problem of judging how good an actual compromise allocation is compared to Neyman's optimum allocation for the case of stratified random sampling by obtaining a bound to the ratio of the corresponding variances. A solution to a more general version of the problem considered by COCHRAN (1977) and RAO (1983) has been obtained and the results have been empirically demonstrated.

Using the criterion of minimum expected variance and the Horvitz-Thompson estimator, we study various πPS (πi, the probability of inclusion of the ith unit, Proportional to Size) strategies and make a comparison between these strategies under a general super population model. This discussion further motivates the search for a class of designs which are best suited for the use of the Horvitz-Thompson estimator. A new class of such designs is obtained.

In an earlier paper [Rao 1966] an exact expression for the variance of the ratio estimator under theMidzuno-Sen sampling scheme is obtained and here we study some of the interesting properties of the coefficients involved in this expression which depend on the auxiliary information. Use of these coefficients is made of in finding out an exact expression for the Bias and Mean Square Error of the ratio estimator under Simple Random Sampling With-Out Replacement (SRSWOR) scheme.

For the sampling scheme ofMidzuno [3] andSen [4], which provides unbiased ratio estimators an expression for the variance of the estimator does not seem to be available in literature. An expression for the same is derived in this note.

Summary In this review paper, the problem of optimum allocation of sample size to strata is examined in the light of a priori distributions. We first consider Neyman's optimum allocation in the case of the Simple Random Sampling (SRS) scheme and review the results concerning the justification for the assumption that the unknown proportionate values of within stratum variances ca's can be replaced by the known proportionate values of aVc's which are the corresponding within stratum variances based on the auxiliary information. We next review the problem of optimum stratification with proportional and optimum allocations in the case of SRS in the light of a priori distributions and discuss the role of arranging the auxiliary variate in increasing order for stratification. We then turn our attention to varying probability sampling schemes and present a review of the results based on a study discussing whether a stratified ,rPS (PPS) strategy with various non-optimal allocations is likely to be worth while in practice.