Regression problems with controllable variables subject to error

Федоров, В. В.

doi:10.1093/biomet/61.1.49

Cited by 49 publications

(21 citation statements)

References 4 publications

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“…The last result is more general than a similar one from Fedorov (1974) and it is the obvious corollary of Theorem 5 from Wu (1981). …”

Section: T(in -I) -+ N(0m-1 )mentioning

confidence: 64%

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Statistical Analysis and Forecasting of Economic Structural Change

Hackl¹

1989

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“…The last result is more general than a similar one from Fedorov (1974) and it is the obvious corollary of Theorem 5 from Wu (1981). …”

Section: T(in -I) -+ N(0m-1 )mentioning

confidence: 64%

“…It is known [Wu (1981) In cases when 0'2 is a function of z: O' 2 (z,'Y), which can also depend upon 'Y, one has to apply iterative least square estimation [Fedorov (1974); Jobson and Fuller (1980) is not consistent.…”

Section: The Regression Model With a Variance Containing Unknown Paramentioning

confidence: 99%

Statistical Analysis and Forecasting of Economic Structural Change

Hackl¹

1989

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“…However, in Fedorov, 1974, it was shown that generally the estimator defined by (7) is not consistent and that the following "iterated" least squares estimators should be used instead: the logistic function considered in this paper) the probability Pn that the limits for (10) and (12) coincide tends to one when the number of observation n tends to infinity, i.e.…”

Section: Estimation Met Hodmentioning

confidence: 93%

“…For our purpose a simpler approach based on the.results by Fedorov, 1974, see also Seber and Wild, 1989, Ch 10.9, appears to be sufficient.…”

Section: Logmentioning

confidence: 99%

Heteroscedasticity generated by errors in predictors

Downing¹,

Федоров²,

Nanstad³

1995

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“…Standard statistical packages do not provide appropriate options. Fedorov (1974) and Donev (2000) apply iterative procedures where the method of weighted least squares is used to obtain an estimate of R. For example, Donev (2000) calculates the weights using Eq. (5) and updates them at each iteration by ÿnding the maximum likelihood estimates for the variance components, until the search converges.…”

Section: Unknown F Matrix; Unknown 2 Imentioning

confidence: 99%

Design of experiments in the presence of errors in factor levels

Donev

2004

Journal of Statistical Planning and Inference

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This paper is concerned with the statistical properties of experimental designs where the factor levels cannot be set precisely. When the errors in setting the factor levels cannot be measured, design robustness is explored. However, when the actual design could be measured at the end of the investigation, its optimality is of interest. D-optimality could be assessed in di erent ways. Several measures are compared. Evaluating them is di cult even in simple cases. Therefore, in general, simulations are used to obtain their values. It is shown that if D-optimality is measured by the expected value of the determinant of the information matrix of the experimental design, as has been suggested in the past, on average the designs appear to improve with the variance of the error in setting the factor levels. However, we argue that the criterion of D-optimality should be based on the inverse of the information matrix. In this case it is shown that the experiment could be better or worse than the planned one. It is also recognized that setting the factor levels with error could lead to an increased risk of losing observations, which on its own could reduce considerably the optimality of the experimental designs. Advice on choosing the design region in such a way that such a risk is controlled to an acceptable level is given.

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Regression problems with controllable variables subject to error

Cited by 49 publications

References 4 publications

Statistical Analysis and Forecasting of Economic Structural Change

Statistical Analysis and Forecasting of Economic Structural Change

Heteroscedasticity generated by errors in predictors

Design of experiments in the presence of errors in factor levels

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