Estimating the parameters of a circle by heteroscedastic regression models

Yin, Su-Ju; Wang, Song-Gui

doi:10.1016/s0378-3758(03)00206-4

Cited by 6 publications

(12 citation statements)

References 7 publications

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“…Overall, 2SHR showed the highest efficiency compared to LS and NLS. This result is similar to Yin and Wang's (2004) conclusion when fitting circular data; that is, the two-stage method is uniformly better than the ordinary least squares method. Bootstrapping improved the estimation efficiency for each method and showed 2SHR retained higher efficiency than LS and NLS.…”

Section: Discussionsupporting

confidence: 84%

“…When there is no lag, a simple linear regression is enough to analyze the system. When the lag is 1/4 period, circular fitting methods, such as the heteroscedastic regression model by Yin and Wang (2004) and the algebraic (noniterative) circle fitting algorithm by Al-Sharadqah and Chernov (2009), can be used to fit the data. In this study, three methods are developed to model the hysteresis system with a sinusoidal input forcing function and a lag between 0 and 1/4 period.…”

Section: Models and Parametersmentioning

confidence: 99%

“…Berman et al presented a detailed statistical analysis of the circular parameter estimates for the model with known angular differences. Later, Yin and Wang (2004) incorporated heteroscedastic errors into Berman's model and developed a two-stage method for fitting circular data. Al-Sharadqah and Chernov (2009) reviewed several circular fitting methods: geometric, Kasa, Pratt, and Taubin; they also proposed a new algebraic "non-iterative" fitting algorithm for circular data.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Estimation of Elliptical Hysteresis with Application to the Characterization of Heat Stress

Yang

Parkhurst

2015

JABES

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When biological systems undergo hysteretic behavior of stress and recovery due to global warming or other changes in environment and resources, modeling hysteresis becomes increasingly important. A system displays hysteresis if the output depends on past history of changes in the input. Moreover, the trajectory of rate-dependent hysteresis may be viewed as a loop when the period is known. Consider the thermoregulatory response of an animal, hysteresis appears as the delay in body temperature when an animal experiences heat stress produced by elevated air temperature. If air temperature is controlled as a sinusoidal, the hysteresis loop shows an elliptical pattern. The parameters of such loops are useful for describing rhythmic biological processes. Three analytic methods, linear, nonlinear, and two-step harmonic, are developed to fit an elliptical hysteretic process. Formulas for parameters that characterize the dynamics are obtained. Statistical efficiency of parameter estimation is evaluated by simulations using both the delta method and bootstrap. Overall, two-step simple harmonic regression with bootstrap produces the most efficient estimates for parameters of the elliptical hysteresis loop. Application of this procedure to control-chamber data reveals differences between animals in response to heat stress.

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Section: Discussionsupporting

confidence: 84%

Section: Models and Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient Estimation of Elliptical Hysteresis with Application to the Characterization of Heat Stress

Yang

Parkhurst

2015

JABES

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“…There are many other approaches to the circle fitting problem in the modern literature [4,10,35,28,29,31,33,36,38], but most of them are either quite slow or can be reduced to one of the algebraic fits [14, Chapter 8].…”

Section: Algebraic Circle Fitsmentioning

confidence: 99%

“…For simplicity, we can set n ∼ 1/σ for smaller samples and n ∼ 1/σ 2 for larger samples. Then Table 1 presents the corresponding typical magnitudes of each of the four terms in (35). We see that for larger samples the fourth order term coming from the bias may be just as big as the leading second-order term, hence it would be unwise to ignore it.…”

Section: Error Analysis: a General Schemementioning

confidence: 99%

Error analysis for circle fitting algorithms

Al-Sharadqah¹,

Chernov²

2009

Electron. J. Statist.

176

100

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We study the problem of fitting circles (or circular arcs) to data points observed with errors in both variables. A detailed error analysis for all popular circle fitting methods -geometric fit, Kåsa fit, Pratt fit, and Taubin fit -is presented. Our error analysis goes deeper than the traditional expansion to the leading order. We obtain higher order terms, which show exactly why and by how much circle fits differ from each other. Our analysis allows us to construct a new algebraic (non-iterative) circle fitting algorithm that outperforms all the existing methods, including the (previously regarded as unbeatable) geometric fit.

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Fitting circles to data with correlated noise

Chernov¹,

Sapirstein²

2008

Computational Statistics & Data Analysis

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Estimating the parameters of a circle by heteroscedastic regression models

Cited by 6 publications

References 7 publications

Efficient Estimation of Elliptical Hysteresis with Application to the Characterization of Heat Stress

Efficient Estimation of Elliptical Hysteresis with Application to the Characterization of Heat Stress

Error analysis for circle fitting algorithms

Fitting circles to data with correlated noise

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