Shape-constrained partial identification of a population mean under unknown probabilities of sample selection

@article{Miratrix2017ShapeconstrainedPI,
  title={Shape-constrained partial identification of a population mean under unknown probabilities of sample selection},
  author={Luke Miratrix and Stefan Wager and Jos{\'e} R. Zubizarreta},
  journal={arXiv: Statistics Theory},
  year={2017}
}
A prevailing challenge in the biomedical and social sciences is to estimate a population mean from a sample obtained with unknown selection probabilities. Using a well-known ratio estimator, Aronow and Lee (2013) proposed a method for partial identification of the mean by allowing the unknown selection probabilities to vary arbitrarily between two fixed extreme values. In this paper, we show how to leverage auxiliary shape constraints on the population outcome distribution, such as symmetry or… 

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References

SHOWING 1-10 OF 15 REFERENCES

Interval estimation of population means under unknown but bounded probabilities of sample selection

Applying concepts from partial identification to the domain of finite population sampling, we propose a method for interval estimation of a population mean when the probabilities of sample selection

Semiparametric Exponential Families for Heavy-Tailed Data

We propose a semiparametric method for fitting the tail of a heavy-tailed population given a relatively small sample from that population and a larger sample from a related background population. We

Spectral Density Ratio Models for Multivariate Extremes

The modeling of multivariate extremes has received increasing recent attention because of its importance in risk assessment. In classical statistics of extremes, the joint distribution of two or more

Using specially designed exponential families for density estimation

i this paper have Y being portions of the real line or of the plane, but the methodology applies just as well to higher dimensionalities and to more complicated spaces. . Estimates of g y are

On the theory of ratio estimates

Estimated variances, yielded by large sample approach, are adjusted by a proportional regression approach; subsequently, under the assump­ tion of normality, exact statements on confidence intervals

Inference and Modeling with Log-concave Distributions

Log-concave distributions are an attractive choice for modeling and inference, for several reasons: The class of log-concave distributions contains most of the commonly used parametric distributions

Partial Identification of Probability Distributions

Missing Outcomes.- Instrumental Variables.- Conditional Prediction with Missing Data.- Contaminated Outcomes.- Regressions, Short and Long.- Response-Based Sampling.- Analysis of Treatment Response.-

On logarithmic concave measures and functions

The purpose of the present paper is to give a new proof for the main theorem proved in [3] and develop further properties of logarithmic concave measures and functions. Having in mind the

Convex Optimization

A comprehensive introduction to the subject of convex optimization shows in detail how such problems can be solved numerically with great efficiency.

Brownian motion

“I did not believe that it was possible to study the Brownian motion with such a precision.” From a letter from Albert Einstein to Jean Perrin (1909).