Estimation in the General Linear Model when the Accuracy is Specified Before Data Collection

Finster, Mark

doi:10.1214/aos/1176349546

Cited by 24 publications

(8 citation statements)

References 30 publications

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“…The technical difficulties associated with proving uniform continuity in probability for such estimators are formidable and appear at present to be intractable. Finster (1985) discusses fixed-size confidence regions of general shape, not necessarily ellipsoidal, for the case of normally distributed errors and least squares estimates. The approach in the present paper can be used in this more general setting.…”

Section: Nm(~ -Fl) 7" N(o 0-21"-1)mentioning

confidence: 99%

“…In this case, (1.11) suggests using the stopping rule once sampling is terminated. Previous work on fixed-size confidence regions in regression models, under the assumption of normally distributed errors and using least squares estimates, has been done by Gleser (1965), Albert (1966), Srivastava (1967Srivastava ( , 1971 and Finster (1985). For pioneering work on fixed-size confidence intervals, see Chow and Robbins (1965).…”

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Sequential estimation in regression models using analogues of trimmed means

Martinsek

1989

Ann Inst Stat Math

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Section: Nm(~ -Fl) 7" N(o 0-21"-1)mentioning

confidence: 99%

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confidence: 99%

Sequential estimation in regression models using analogues of trimmed means

Martinsek

1989

Ann Inst Stat Math

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“…Second-order approximations for some other sequential procedures for point and fixed-width interval (fixed-size confidence region) estimation problems have been derived by several authors. For some citations, one may refer to Swanepoel and van Wyk (1982), Finster (1983Finster ( , 1985, Chaturvedi (1986a,b;1987, 1988, Singh and Chaturvedi (1988a,b;1989 estimation. Consideration was given to a family of loss functions and a cost function of the general form.…”

Section: Introductionmentioning

confidence: 99%

Second-Order Approximations to Two Classes of Sequential Estimation Procedures

Chaturvedi

Gupta

1995

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For the model considered by Chaturvedi, Pandey and Gupta (1991). two classes of sequential procedures are developed to construct contidcnce regions (which may be interval, elllpso~dal or spherical) of 'pre-assigned width and coverage probability' for the parameters of interest and for the minimum r~s k point estimation (takingloss to be quadratic plus linear cost of sampling) of the nuisance parameter. Second-Order approximations are derived for the expected sample w e , cvverage probability and 'regret' associated with the two classes ofsequential procedures. A simplc and direct method of ohtaming the asymptoticdistribution of the stopping time is provided. By means of examples, it is illustrated that several estimation problems can be tackled with the help of proposed classes of sequentla1 procedures.AMS IYXO (lusvficut~un 62L12

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“…Since data are collected in two stages, a different experimental design can be used at each stage; let J1 and J2 be the experimental design measures for the first and second stages, respectively. Gleser (1965), Albert (1966) ' Srivastava (1967' Srivastava ( , 1971) and Finster (1985) all used similar restrictions on the experimental design in their purely sequential regression procedures, requiring that Cr=, xixT/n converge to a positive definite matrix as n t m. Bishop (1978) used a different restriction on the experimental design; he achieved a desired elliptical accuracy in regression experiments by applying Stein's (1945) two-stage procedure to each of k fixed design points.…”

Section: Introductionmentioning

confidence: 99%

TWO-stage accurate estimation in the general linear model

Lohr

1993

Sequential Analysis

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This paper presents a two-stage procedure for estimating the parameters and response surface in the general linear model, when different experimental designs are used for the two stages of data collection. A first set of observations is collected according to a known experimental design, and the information from that first sample is used to determine the number of additional observations (collected using the second experimental design) necessary to estimate the parameters or response surface to a predeter-1 2 LOHR mined joint precision. Asymptotic results are given which depend on the size of the first sample and on the experimental designs.

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Estimation in the General Linear Model when the Accuracy is Specified Before Data Collection

Cited by 24 publications

References 30 publications

Sequential estimation in regression models using analogues of trimmed means

Sequential estimation in regression models using analogues of trimmed means

Second-Order Approximations to Two Classes of Sequential Estimation Procedures

TWO-stage accurate estimation in the general linear model

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