Weighted Distributions Arising Out of Methods of Ascertainment: What Population Does a Sample Represent?

Rao, C. Radhakrishna

doi:10.1007/978-1-4613-8560-8_24

Cited by 128 publications

(61 citation statements)

References 23 publications

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“…We refer to Rao (1977, 1978) and to Rao (1985) for a survey of statistical applications of weighted distributions, especially to the analysis of data relating to human populations and ecology. Gupta and Keating (1986) obtained relations for reliability measures of the length-biased distribution and some characterization results.…”

Section: Accepted M Manuscriptmentioning

confidence: 99%

On a representation of weighted distributions

Bartoszewicz

2009

Statistics & Probability Letters

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Please cite this article as: Bartoszewicz, J., On a representation of weighted distributions. Statistics and Probability Letters (2009Letters ( ), doi:10.1016Letters ( /j.spl.2009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT On a representation of weighted distributions

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Section: Accepted M Manuscriptmentioning

confidence: 99%

On a representation of weighted distributions

Bartoszewicz

2009

Statistics & Probability Letters

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“…Some recent papers by Dear and Begg (1992), Iyengar and Greenhouse (1988), and Hedges (1992) describe several methods of modeling the p-values using the concept of weighted distributions developed by Rao (1965Rao ( , 1985 and Patil and Rao (1977). It is suggested by Light and Pillemer (1984) that publication bias can be detected by plotting 'sample size against the effect size', which is called a funnel plot.…”

Section: Correcting For Publication Bias (The File Drawer Problem)mentioning

confidence: 99%

Combining information from different sources to estimate a common effect and use of multiple measurements for ecological assessment

Rao

2004

Environmetrics

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“…We find that the set of X that is chosen is robust to wide variations in P c around the (known) population mean of P i , E(P(X)). Our estimation method corrects for the overrepresentation of the experimental control group (D ϭ 1) relative to the eligible nonparticipants (D ϭ 0) in the available data using ideas developed in the analysis of weighted distributions by Rao (14,15). A universal finding in our research using a variety of covariates is the failure of the common support condition.…”

Section: Failure Of a Common Support Condition: A Major Component Of mentioning

confidence: 99%

Sources of selection bias in evaluating social programs: An interpretation of conventional measures and evidence on the effectiveness of matching as a program evaluation method

Heckman

Ichimura

Smith

et al. 1996

Proc. Natl. Acad. Sci. U.S.A.

145

109

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This paper decomposes the conventional measure of selection bias in observational studies into three components. The first two components are due to differences in the distributions of characteristics between participant and nonparticipant (comparison) group members: the first arises from differences in the supports, and the second from differences in densities over the region of common support. The third component arises from selection bias precisely defined. Using data from a recent social experiment, we find that the component due to selection bias, precisely defined, is smaller than the first two components. However, selection bias still represents a substantial fraction of the experimental impact estimate. The empirical performance of matching methods of program evaluation is also examined. We find that matching based on the propensity score eliminates some but not all of the measured selection bias, with the remaining bias still a substantial fraction of the estimated impact. We find that the support of the distribution of propensity scores for the comparison group is typically only a small portion of the support for the participant group. For values outside the common support, it is impossible to reliably estimate the effect of program participation using matching methods. If the impact of participation depends on the propensity score, as we find in our data, the failure of the common support condition severely limits matching compared with random assignment as an evaluation estimator. This paper uses data from a large-scale social experiment conducted on a prototypical job training program to decompose conventional measures of selection bias into a component corresponding to selection bias, precisely defined, and into components arising from failure of a common support condition and failure to weight the data appropriately. We demonstrate that a substantial fraction of the conventional measure of selection bias is not due to selection, precisely defined, and we conjecture that this is a general finding. We find that the conventional measure of selection bias is misleading. We also provide mixed evidence on the effectiveness of the matching methods widely used for evaluating programs. The selection bias remaining after matching is a substantial percentageoften over 100%-of the experimentally estimated impact of program participation.Our analysis is based on the Roy (1) model of potential outcomes, which is identical to the Fisher (2) model for experiments and to the switching regression model of Quandt The parameter of interest considered in this paper is the mean effect of treatment on the treated. It is not always the parameter of interest in evaluating social programs [see Heckman and Robb (6), Heckman (7), Heckman and Smith (8) and Heckman et al. (9)], but it is commonly used. It gives the expected gain from treatment for those who receive it. For covariate vector X, it is defined asSometimes interest focuses on the average impact for X in some region K, e.g.,in the definition of ⌬(X) can be i...

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Weighted Distributions Arising Out of Methods of Ascertainment: What Population Does a Sample Represent?

Cited by 128 publications

References 23 publications

On a representation of weighted distributions

On a representation of weighted distributions

Combining information from different sources to estimate a common effect and use of multiple measurements for ecological assessment

Sources of selection bias in evaluating social programs: An interpretation of conventional measures and evidence on the effectiveness of matching as a program evaluation method

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