Jump Regression Analysis
Reference work entry
First Online:
DOI: https://doi.org/10.1007/978-3-642-04898-2_320
Nonparametric regression analysis provides statistical tools for estimating regression curves or surfaces from noisy data. Conventional nonparametric regression procedures, however, are only appropriate for estimating continuous regression functions. When the underlying regression function has jumps, functions estimated by the conventional procedures are not statistically consistent at the jump positions. Recently, regression analysis for estimating jump regression functions is under rapid development (Qiu 2005), which is briefly introduced here.
1-D Jump Regression Analysis
In one-dimensional (1-D) cases, the
jump regression analysis (JRA) model has the form
$${y}_{i} = f({x}_{i}) + {\epsilon }_{i},\;\;\mbox{ for }i = 1,2,\ldots ,n,$$
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References and Further Reading
- Gijbels I, Lambert A, Qiu P (2006) Edge-preserving image denoising and estimation of discontinuous surfaces. IEEE Trans Pattern Anal Mach Intell 28:1075–1087CrossRefGoogle Scholar
- Joo J, Qiu P (2009) Jump detection in a regression curve and its derivative. Technometrics 51:289–305CrossRefMathSciNetGoogle Scholar
- Qiu P (1998) Discontinuous regression surfaces fitting. Ann Stat 26:2218–2245CrossRefMATHGoogle Scholar
- Qiu P (2005) Image processing and jump regression analysis. Wiley, New YorkCrossRefMATHGoogle Scholar
- Qiu P (2007) Jump surface estimation, edge detection, and image restoration. J Am Stat Assoc 102:745–756CrossRefMATHGoogle Scholar
- Qiu P, Yandell B (1997) Jump detection in regression surfaces. J Comput Graph Stat 6:332–354MathSciNetGoogle Scholar
- Sun J, Qiu P (2007) Jump detection in regression surfaces using both first-order and second-order derivatives. J Comput Graph Stat 16:289–311CrossRefMathSciNetGoogle Scholar
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