Journal ArticleDOI

# The Effect of Increasing Sample Size on the Precision of an Estimator

01 Oct 1967-The American Statistician-Vol. 21, Iss: 4, pp 26
TL;DR: In this article, it is shown that by Schwarz's inequality for any two vectors, any convex function h(y) = \/y of a single real variable y can be replaced by a convex functions h(x, y) = x, y to obtain (1).
Abstract: of n real variables x1,x2,.. .xn, and use the fact that g (E(Xi), E (X2). I. . E (Xn) ) _< E(g(X-,X,,X. * .,X,,) ). to obtain (1) . Similarly consider the convex function h(y) = \/y of a single real variable y, use the fact n that h (E (Y)) E (h (Y) ), and replace Y by E X,2 to j 1 obtain (2). There is however a more elementary method for proving (1) and (2), which does not depend on the concept of convexity. It is as follows: By Schwarz's inequality for any two vectors
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01 Jan 2008
TL;DR: In this article, the authors proposed a method to investigate differences of driving at a tactical level between different categories of drivers and found a significant correlation between their sensation seeking score and their mean speed on motorway.
Abstract: We propose a method to investigate differences of driving at a tactical level, between different categories of drivers We analysed the naturalistic driving performance of 19 French drivers using an instrumented vehicle We assessed their sensation seeking scores with the Zuckerman questionnaire We observed a significant correlation between their sensation seeking score and their mean speed on motorway We set up a method to model their tactical behaviour and investigate possible correlation between their sensation seeking score and their tendency to perform certain types of behaviour We applied it to the study of lane changes on motorways We could model two categories of lane changes but we show that they were not correlated with the sensation seeking score Despite this negative first result, we are proposing an innovative approach for this kind of study

2 citations

Journal ArticleDOI
TL;DR: In this paper, the problem of extending a given sampling design, when additional resources are available, is considered and some existing methods of improving an initial sampling strategy, so that the use of the additional resources is justified, are critically reviewed.
Journal ArticleDOI
TL;DR: The general impression quoted by Ajgaonkar is known to be true in some cases like sampling from an infinite theoretical population and when the sampling is done with replacement from a finite population, with the same set of probabilities of selection used for the different draws.
Abstract: The general impression quoted by Ajgaonkar is known to be true in some cases like sampling from an infinite theoretical population and when the sampling is done with replacement from a finite population, with the same set of probabilities of selection used for the different draws, to estimate the population mean in each case. In this case the sample values Xl, X2, . . . . Xn are independent and identically distributed random variables so that
##### References
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Journal ArticleDOI
TL;DR: In this paper, two sampling schemes are discussed in connection with the problem of determining optimum selection probabilities according to the information available in a supplementary variable, which is a general technique for the treatment of samples drawn without replacement from finite universes when unequal selection probabilities are used.
Abstract: This paper presents a general technique for the treatment of samples drawn without replacement from finite universes when unequal selection probabilities are used. Two sampling schemes are discussed in connection with the problem of determining optimum selection probabilities according to the information available in a supplementary variable. Admittedly, these two schemes have limited application. They should prove useful, however, for the first stage of sampling with multi-stage designs, since both permit unbiased estimation of the sampling variance without resorting to additional assumptions. * Journal Paper No. J2139 of the Iowa Agricultural Experiment Station, Ames, Iowa, Project 1005. Presented to the Institute of Mathematical Statistics, March 17, 1951.

3,990 citations

### "The Effect of Increasing Sample Siz..." refers methods in this paper

• ...Consider the sampling procedure introduced by Hansen and Hurwitz [2] and generalized by Horvitz and Thompson [3] and Midzuno [4] wherein the population elements are drawn without replacement with varying probabilities of selection at each draw....

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Journal ArticleDOI

565 citations

### "The Effect of Increasing Sample Siz..." refers background or methods in this paper

• ...Consider the sampling procedure introduced by Hansen and Hurwitz [2] and generalized by Horvitz and Thompson [3] and Midzuno [4] wherein the population elements are drawn without replacement with varying probabilities of selection at each draw....

[...]

• ...It is the well recognized fact that in sampling with varying probabilities, the probabilities are determined so as to incorporate the supplementary information into the sampling procedure and thus reducing considerably the sampling variance of the estimator, as noted by Hansen and Hurwitz [2]....

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Journal ArticleDOI

194 citations

### "The Effect of Increasing Sample Siz..." refers background or methods in this paper

• ...Considered below is a particular specification of general sampling procedure underlying this principle, which is attributed to Midzuno [4]....

[...]

• ...Consider the sampling procedure introduced by Hansen and Hurwitz [2] and generalized by Horvitz and Thompson [3] and Midzuno [4] wherein the population elements are drawn without replacement with varying probabilities of selection at each draw....

[...]

Journal ArticleDOI
TL;DR: In this article, several unbiased estimators for the variances of the estimators are obtained. But the results obtained for unistage sampling in the first part of the paper are extended to multistage designs in the second part.
Abstract: The problem considered is estimation of the total value of a character for a finite population from a sample when the units are selected with varying probabilities without replacement. Several unbiased estimators are proposed. Exact expressions and unbiased estimators for the variances of the estimators are obtained. Certain properties of Yates and Grundy's estimator of variance are proved. Examples are included to study the relative performance of the various estimators. The results obtained for unistage sampling in the first part of the paper are extended to multistage designs in the second part.

94 citations

### "The Effect of Increasing Sample Siz..." refers background in this paper

• ...Here it is pertinent to point out that the estimator t' was first suggested by Sukhatme [5] for a sample of size two and subsequently by Des Raj [1] for a linear combination of n unbiased estimators....

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