This paper develops a threshold regression model , where the threshold is determined by an unknown relation between two variables . The threshold function is estimated fully nonparametrically . The observations are allowed to be cross-sectionally dependent and the model can be applied to determine an unknown spatial border for sample splitting over a random field. The uniform rate of convergence and the nonstandard limiting distribution of the nonparametric threshold estimator are derived. The root-n consistency and the asymptotic normality of the regression slope parameter estimatorare also obtained. Empirical relevance is illustrated by estimating an economic border induced by the housing price difference between Queens and Brooklyn in New York City, where the economic border deviates substantially from the administrative one .
This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to determine an unknown spatial border for sample splitting over a random field. We derive the uniform rate of convergence and the nonstandard limiting distribution of the nonparametric threshold estimator . We also obtain the root-n consistency and the asymptotic normality of the regression coefficient estimator. Our model has broad empirical relevance as illustrated by estimating the tipping point in social segregation problems as a function of demographic characteristics; and determining metropolitan area boundaries using nighttime light intensity collected from satellite imagery. We find that the new empirical results are substantially different from the existing studies .
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, where the threshold is determined by an unknown relation
where an unknown relationship
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. The threshold function is estimated fully nonparametrically . The observations are allowed
nonparametrically determines the threshold. We allow the observations
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and
so that
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The
We derive the
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are derived. The
. We also obtain the
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slope parameter estimatorare also obtained. Empirical relevance is
coefficient estimator. Our model has broad empirical relevance as
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an economic border induced by the housing price difference between Queens and Brooklyn in New York City, where the economic border deviates substantially from
R
administrative one
tipping point in social segregation problems as a function of demographic characteristics; and determining metropolitan area boundaries using nighttime light intensity collected from satellite imagery. We find that the new empirical results are substantially different from the existing studies