Adaptive estimation of the threshold point in threshold regression

Yu, Ping

doi:10.1016/j.jeconom.2013.09.002

Cited by 23 publications

(34 citation statements)

References 49 publications

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“…From Yu (2008), it is known that to …nd b we need only check the middle points of the contiguous q i 's in the optimization process. In other words, the argmax operator (or argmin operator in Theorem 1 which gives the asymptotic distribution of b ) is a middle-point operator.…”

Section: Construction Of the Idke Ofmentioning

confidence: 99%

“…If we neglect the factor f (x i ; 0 )f (x i ) in z`i, the asymptotic distribution is the same as that of the LSE in the parametric model, see Section 4.1 of Yu (2008). The factor f (x i ; 0 ) appears in the limit theory because the random denominator in the kernel has been eliminated in estimating the jumps of E [yjx; q]; see (5).…”

Section: Assumption Ementioning

confidence: 99%

“…As for the threshold parameter in (1), our results show that can be estimated at the rate n even if no instruments are available -so instruments have no import on this convergence rate. Instead, as with the earlier …nding in Yu (2008), the role of instrumentation for is not to improve the convergence rate or to provide identi…cation, but to improve e¢ ciency. In summary, instrumentation plays di¤erent roles in the estimation of the system parameters , and : only for do instruments have the conventional role of delivering identi…cation, whereas for and the presence of instruments serves to improve convergence rates or e¢ ciency.…”

Section: Introductionmentioning

confidence: 98%

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Threshold regression with endogeneity

Phillips

2018

Journal of Econometrics

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This paper studies estimation in threshold regression with endogeneity. Three key results di¤er from those in regular models. First, both the threshold point and the threshold e¤ect parameters are shown to be identi…ed without the need for instrumentation. Second, in partially linear threshold models, both parametric and nonparametric components rely on the same data, which prima facie suggests identi…cation failure. But, as shown here, the discontinuity structure of the threshold itself supplies identifying information for the parametric coe¢ cients without the need for extra randomness in the regressors. Third, instrumentation plays di¤erent roles in the estimation of the system parameters, delivering identi…cation for the structural coe¢ cients in the usual way, but raising convergence rates for the threshold e¤ect parameters and improving e¢ ciency for the threshold point. Simulation studies corroborate the theory and the asymptotics. An empirical application is conducted to explore the e¤ects of 401(k) retirement programs on savings, illustrating the relevance of threshold models in treatment e¤ects evaluation in the presence of endogeneity.

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Section: Construction Of the Idke Ofmentioning

confidence: 99%

Section: Assumption Ementioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Threshold regression with endogeneity

Phillips

2018

Journal of Econometrics

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“…When there is a threshold effect in variance in model (2.1) as Chan (1993), Li and Ling (2012) discussed the limiting distribution of the estimated threshold. In this case, the approximation in Theorem 4.1 should be asymmetric, see a further discussion in Yu (2012) and Yu (2015).…”

Section: Approximating Distributions Of Thementioning

confidence: 99%

“…This is because we took the left end-point of the interval on which (2.4) achieves its minimum. This negative bias issue can be overcome by using its middle-point, see Yu (2012) and Yu (2015). We do not pursue this issue here since the bias is negligible for large sample size and we also use the left end-point M…”

Section: Simulation Studymentioning

confidence: 99%

Statistical Inference for Structurally Changed Threshold Autoregressive Models

Gao¹,

Ling²

2019

STAT SINICA

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In this paper, we study the theory and methodology for statistical inferences of threshold and change-point in the threshold autoregressive models. It is shown that the least squares estimators (LSE) of the threshold and change-point are n-consistent, and converge weakly to the minimizer of a compound Poisson process and the location of minima of a two-sided random walk, respectively.When the magnitude of change in the parameters of the state regimes or the time horizon is small, it is further shown that these limiting distributions can be approximated by a class of known distributions. The LSE of slope parameters are √ n-consistent and asymptotically normal. Furthermore, a likelihood-ratio based confidence set is given for the threshold and change-point, respectively. Simulation study is carried out to assess the performance of our procedure. The proposed theory and methodology are further illustrated by a tree-ring dataset.

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Segment regression model average with multiple threshold variables and multiple structural breaks

Liu

2023

Can J Statistics

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We propose a new model averaging approach to investigate segment regression models with multiple threshold variables and multiple structural breaks. We first fit a series of models, each with a single threshold variable and multiple breaks over its domain, using a two‐stage change point detection method. Then these models are combined together to produce a weighted ensemble through a frequentist model averaging approach. Consequently, our segment regression model averaging (SRMA) method may help identify complicated subgroups in a heterogeneous study population. A crucial step is to determine the optimal weights in the model averaging, and we follow the familiar non‐concave penalty estimation approach. We provide theoretical support for SRMA by establishing the consistency of individual fitted models and estimated weights. Numerical studies are carried out to assess the performance in low‐ and high‐dimensional settings, and comparisons are made between our proposed method and a wide range of existing alternative subgroup estimation methods. Two real economic data examples are analyzed to illustrate our methodology.

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Adaptive estimation of the threshold point in threshold regression

Cited by 23 publications

References 49 publications

Threshold regression with endogeneity

Threshold regression with endogeneity

Statistical Inference for Structurally Changed Threshold Autoregressive Models

Segment regression model average with multiple threshold variables and multiple structural breaks

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