Tests for means with additional information

Sinha, Bimal K.; Clément, Bernard; Giri, Narayan C.

doi:10.1080/03610928508828986

Cited by 2 publications

(2 citation statements)

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“…It is our aim here to find a simple Downloaded by [Dalhousie University] at 21:19 25 December 2014 BETA DISTRIBUTION approximation which can be used for theoretical purposes, for example, po\ver calcdations. Also one sometimes faces a linear combination of noncentral beta distributions (see Sinha, Clkment and Giri (1985)). Then if one can approximate the noncentral beta distribution by a central beta distribution, the methods of the first part of this paper can be applied for a second approximation.…”

Section: Methodsmentioning

confidence: 99%

On approximations involving the beta distribution

Jóhannesson

Giri

1995

Communications in Statistics - Simulation and Computation

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In part 1 we give two approximations where a linear combination of central beta variables is approximated by a single beta variable. Extensive numerical computations are done to compare these approximations for the case of two central beta variable with parameters (bl, al), (b2, a2) with a special attention for the case bl = bz. They show that these approximations are sufficiently good for most cases. The second part of this paper compare four similar approximations for noncentral beta variables and conclude that three of them are sufficiently good for most practical purposes. 489

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Section: Methodsmentioning

confidence: 99%

On approximations involving the beta distribution

Jóhannesson

Giri

1995

Communications in Statistics - Simulation and Computation

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“…Since double sampling is at random, the problem is equivalent to that of multivariate data with "missing completely at random" (e.g., Anderson 1957 or Little andRubin 1987), or it can be viewed as having additional information in the sense of Sinha and Clement (1985) and others. Although the results from those works are useful in some respects, our focus is quite different in that the missing values are true values and the complete vector contains variables whose role is that of surrogates.…”

Section: Modelingmentioning

confidence: 99%

Double Sampling for Exact Values in Some Multivariate Measurement Error Problems

Buonaccorsi

1990

Journal of the American Statistical Association

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Increasing attention is being given to measurement error models in which the dimension of the proxy or surrogate values is different from that of the missing true values. Even if they are of the same dimension, the error model may not be the simple additive one of observed = true + error, where the error has mean O. The use of broader models relating true and observed values requires the use of external or internal data containing some true values to calibrate/validate the measurement error model. This article considers a multivariate normal framework in which measurement error is allowed in any subset of the variables with a broad class of multivariate regression models relating true and observed values. The classical additive model is a special case. Multiple regression with random regressors (the structural case) is treated within this framework. Correcting for measurement error is made possible through double sampling in which true values are obtained for a randomly chosen subset of the main study units. Maximum likelihood estimators and their asymptotic properties are developed for both unrestricted and restricted models, where the latter arise through specific assumptions about the nature of the measurement error. Detailed results are given for simple linear regression in which case optimal double sampling rates are determined for estimating the slope with minimum variance subject to cost considerations. An example is presented based on the use of infrared measurements as surrogates for characteristics of wheat.

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Tests for means with additional information

Cited by 2 publications

References 5 publications

On approximations involving the beta distribution

On approximations involving the beta distribution

Double Sampling for Exact Values in Some Multivariate Measurement Error Problems

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