What question did this study set out to answer?

To establish maximum likelihood estimators and associated confidence intervals for the unknown intersection point of two polynomial regression functions under unconstrained and bounded conditions.

March 1, 1964Journal of the American Statistical AssociationOpen Access

Estimates for the Points of Intersection of Two Polynomial Regressions

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To establish maximum likelihood estimators and associated confidence intervals for the unknown intersection point of two polynomial regression functions under unconstrained and bounded conditions.
Assumed normal distribution of errors across two true regression functions.
Calculated maximum likelihood estimators based on the intersection of sample regression curves.
Applied the Student t-distribution to determine confidence intervals and derived a restrained estimator for intersection points restricted to a defined interval.
Demonstrated that without constraints, the maximum likelihood estimator of the intersection abscissa directly equals the intersection of the sample regressions.
Established that confidence intervals for the intersection abscissa can be derived using the Student t-distribution.
Formulated a restrained maximum likelihood estimator and corresponding confidence limits for scenarios where the intersection point is confined to a known interval.

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Implication

Theoretical analysis reveals maximum likelihood estimators for intersection points in polynomial regressions, indicating methods to calculate confidence intervals under bound constraints.

Cite This Study

D. E. Robison (1964) studied this question.

synapsesocial.com/papers/6a11cd758ac3726642dce290 https://doi.org/10.1080/01621459.1964.10480712

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Implication

Theoretical analysis reveals maximum likelihood estimators for intersection points in polynomial regressions, indicating methods to calculate confidence intervals under bound constraints.

Estimates for the Points of Intersection of Two Polynomial Regressions

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Discussion

Implication

Cite This Study

Estimates for the Points of Intersection of Two Polynomial Regressions

Key Points

Discussion

Implication

Cite This Study

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