Compromised imputation in survey sampling

In this paper, a compromised imputation procedure has been suggested. The estimator of mean obtained from compromised imputation remains better than the estimators obtained from ratio method of imputation and mean method of imputation. An idea to form “Warm Deck Method” of imputation has also been suggested. Received: July 1998     

Qualitative sampling in a multi-method survey

Because method triangulation is able to reduce disadvantages of one method by using another one, it has been demanded in social science for many years. Nevertheless, it is seldom applied in practical research. To show the importance of multi-method-research for improving the results of social science investigation, one possibility of method triangulation and its execution is presented. Out of a representative youth survey about sexual behavior and AIDS-prevention with 1500 German respondents a sample of 15–20 respondents for depth-interviews is extracted by combining clusteranalysis and random-sampling. The aim of that multi-method procedure is to get more detailed information about subgroup specific topics and problems. At first the paper shows the necessity of method triangulation and its application in our survey. After that the procedure and the results of the clusteranalysis are presented. In the last chapter the sampling and its results are discribed and discussed.     

A conditional minimax approach in survey sampling

Summary Applying the usual minimax criterion in finite sampling theory yields complicated solutions except the parameter space has certain invariance properties. A conditional minimax criterion is suggested. After a sample is selected it is reasonable to seek an estimator that has good properties (e.g. minimaxity) for that sample. Explicit solutions are given in the case where the parameter space is described by quadratic forms.     

Model assisted survey sampling strategy in two phases

Postulating a super-population regression model connecting a size variable, a cheaply measurable variable and an expensively observable variable of interest, an asymptotically optimal double sampling strategy to estimate the survey population total of the third variable is specified. To render it practicable, unknown model-parameters in the optimal estimator are replaced by appropriate statistics. The resulting generalized regression estimator is then shown to have a model-cum-asymptotic design based expected square error equal to that of the asymptotically optimum estimator itself. An estimator for design variance of the estimator is also proposed.     

Loss functions and admissible estimators in survey sampling

Summary Consider simple random sampling (without replacement) of a fixed size and lett ₀ be the sample mean, i.e. the arithmetic mean of all variate values observed in the sample. The class {t ₀: real} of estimators for the population mean (i.e. The arithmetic mean of all variate values) then surely is of interest.We discuss different types of variates, in particular variates with positive values only. For these variates the usual square error loss gives rise to a strange class of admissible estimators. An other type of loss functions seems far more appropriate. For this (logarithmic) type, t ₀ is admissible iff =1. We prove that there exists no other type of loss functions with the property that the unbiased estimatort ₀ is the only admissible element of the class {t ₀: >0}.

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Zusammenfassung Bei fest vorgegebenem Stichprobenumfang werde uneingeschränkt zufällig ausgewählt (ohne Zurücklegen);t ₀ bezeichne das Stichprobenmittel, d.h. das arithmetische Mittel aller Stichprobenbeobachtungen des Untersuchungsmerkmals. Von besonderen Interesse ist dann zweifellos die Klasse {t ₀: reell} von Schätzfunktionen für das Gesamtmittel, d.h. für das arithmetische Mittel aller Ausprägungen des Untersuchungsmerkmals.Wir betrachten verschiedene Typen von Untersuchungsmerkmalen, insbesondere Merkmale, die nur positive Ausprägungen besitzen. Für diese Merkmale führt die Verwendung der üblichen quadratischen verlustfunktion zu einer sehr merkwürdigen Klasse zulässiger Schätzfunktionen. Ein anderer Typ von Verlustfunktionen erscheint weit eher angebracht. Für diesen (logarithmischen) Typ ist t ₀ genaudann zulässig, wenn =1 gilt. Wir beweisen, daß für keinen anderen Typ von Verlustfunktionent ₀ das einzige zulässige Element der Klasse {t ₀:>0} ist.

     

Asymptotic expansion of the minimax value in survey sampling

Summary Suppose that a real numbery _u is associated with each unitu of a populationU and that the functiony:u →y _u onU is known to be an element of the parameter space Θ. The statistician has to select a samples ⊂U ofn units and to employy _u;u ∈s to estimate the arithmetic mean of ally _u,u ∈U. The performance of such a strategy is assessed by its mean square error or, more simply, by the supremum of the mean square error. This supremum cannot be determined exactly for the parameter space of Scott/Smith (1975). We propose, therefore, an asymptotic approximation; this approximation is based on the assumption, that the sample sizen is fixed and that linear estimators have to be used.     

Influence diagnostic in survey sampling: Estimating the conditional bias

The conditional bias has been proposed by Moreno Rebollo et al. (1999) as an influence diagnostic in survey sampling, when the inference is based on the randomization distribution generated by a random sampling. The conditional bias is a population parameter. So, from an applied point of view, it must be estimated. In this paper, we propose an estimator of the conditional bias and we study conditions that guarantee its unbiasedness. The results are applied in a Simple Random Sampling and in a Proportional Probability Aggregated Size Sampling, when the ratio estimator is used. Received October 2000     

Estimation of a proportion in survey sampling using the logratio approach

The estimation of a mean of a proportion is a frequent task in statistical survey analysis, and often such ratios are estimated from compositions such as income components, wage components, tax components, etc. In practice, the weighted arithmetic mean is regularly used to estimate the center of the data. However, this estimator is not appropriate if the ratios are estimated from compositions, because the sample space of compositional data is the simplex and not the usual Euclidean space. We demonstrate that the weighted geometric mean is useful for this purpose. Even for different sampling designs, the weighted geometric mean shows excellent behavior.     

Estimation of finite population variance using random non-response in survey sampling

In this paper, an estimator of finite population variance proposed by Isaki (1983) is studied under the two different situations of random non-response suggested by Tracy and Osahan (1994). A distribution is proposed for the number of sampling units on which information could not be obtained due to random non-response. The estimators for the mean square errors of the proposed strategies are also suggested. This paper was written while both authors were members of the Dept. of Econometrics, Monash University, Clayton 3168, Australia. This paper was presented on SISC—1996, Sydney, Australia. The opinions and results discussed in this paper are of authors and not necessarily of their institutes.     

Estimation of ratio of population means in survey sampling when some observations are missing

This paper considers the estimation of the ratio of population means when some observations are missing. Four estimators are presented and their bias and mean square error properties are studied. Received: June 1998     

On a use of stratified sampling in optimal estimation

Summary Postulating an intra-class correlation structure for a finite population vector of variate — values optimal stratified and unstratified strategies for estimating the total are identified and relative efficiencies noted. Higher efficiency of stratified over unstratified sampling is demonstrated for usual estimators in ppswr case, in particular. In the uncorrelated case appropriately chosen two-stage strategies are observed to fare at par with optimal stratified ones.     

On the relative precision of several allocations in stratified sampling

MOORS (1973) gave lower bounds for the relative precision of different allocations compared to Neyman allocation in stratified sampling. These results are extended here to the relative precision with respect to optimal allocation. A result of COCHRAN (1977) is generalized.     

浅论工程地质勘查

文章主要通过对北京大学第三医院改扩建门急诊医技楼与运动医学楼护坡、降水及土方开挖工程项目来具体说明工程地质勘查的重要性。     

On the efficiency of systematic sampling in ratio and product estimation

Summary In this paper the possibility of gain in efficiency in systematic sampling as compared to simple random sampling has been considered when a ratio or product estimator is used to improve upon the conventional unbiased estimator. The expression for the variance of the estimators are derived for multistage design where systematic selection is used at the ultimate-stage with any probability scheme at the previous stages. In particular the results for the uni-stage systematic sampling and for two-stage sampling with systematic selection at the second-stage have been obtained in section 3.     

On two properties of an unequal probability sampling scheme

Summary For an inclusion probability proportional to size (IPPS) sampling scheme recently proposed by Saxena, Singh and Srivastava (1986), it is shown that under certain simple verifiable conditions (1) the Horvitz-Thompson (1952) estimator based on it has a smaller variance than the variance of the Hansen-Hurwitz (1943) estimator based on probability proportional to size (PPS) sampling with replacement (WR) both involving the same size-measures and the expected sample size in the former being equal to the number of draws in the latter and (2) the Yates-Grundy (1953) estimator for the variance of the Horvitz-Thompson estimator based on this IPPS scheme is uniformly non-negative.     

On the application of the Minkowski-Farkas theorem to sampling designs

In the paper, we consider the following problem: Let {π_k} be a sequence satisfying 0π_kΣ1 (k=1,…, N) and π=n.Tben, is there an unordered sampling design such that, for each k=1,…N, the inclusion probability of unit k is equal to π? It is shown that it can be solved by the straightforward application of the Minkowski-Farkas theorem.     

On kernel nonparametric regression designed for complex survey data

In this article, we consider nonparametric regression analysis between two variables when data are sampled through a complex survey. While nonparametric regression analysis has been widely used with data that may be assumed to be generated from independently and identically distributed (iid) random variables, the methods and asymptotic analyses established for iid data need to be extended in the framework of complex survey designs. Local polynomial regression estimators are studied, which include as particular cases design-based versions of the Nadaraya–Watson estimator and of the local linear regression estimator. In this paper, special emphasis is given to the local linear regression estimator. Our estimators incorporate both the sampling weights and the kernel weights. We derive the asymptotic mean squared error (MSE) of the kernel estimators using a combined inference framework, and as a corollary consistency of the estimators is deduced. Selection of a bandwidth is necessary for the resulting estimators; an optimal bandwidth can be determined, according to the MSE criterion in the combined mode of inference. Simulation experiments are conducted to illustrate the proposed methodology and an application with the Canadian survey of labour and income dynamics is presented.