Asymptotics of maximum likelihood estimator in a two-phase linear regression model

Koul, Hira L.; Qian, Lianfen

doi:10.1016/s0378-3758(02)00273-2

Cited by 47 publications

(27 citation statements)

References 12 publications

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“…For the piecewise linear model, we use both continuous and discontinuous segment models. For discontinuous case, Koul and Qian (2002) and Koul et al (2003) derive that the asymptotic theory for maximum likelihood and M-estimators.…”

Section: Inferential Statistical Analysismentioning

confidence: 99%

“…To name a few for instance, it is called two-phase linear regression (Koul and Qian, 2002;Koul et al, 2003) and segmented regression model if Figure 12 displays the two-phase regression model fittings. As one can see, the segmented regression is discontinuous at change point (day 7) for 10 mg dosage but is almost continuous for unknown dosage as shown in Figure 12(b).…”

Section: Piecewise Linear Regression Modelmentioning

confidence: 99%

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Estimating tree resin dose effect on termites

Qian

Ryu

2006

Environmetrics

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SUMMARYThe aim of this study is to determine the effectiveness of a natural tropical tree resin in controlling termites thus providing protection from their destruction. Tree resin from the bark of tropical trees offers the potential for this protection. Termites were fed by filter paper soaked in tropical tree resin dissolved in a solvent at different concentrations for 15 days. The number of termites still alive on each day was observed and recorded. In this paper, we use four types of statistical models: Partially linear model, piecewise linear model, cubic smooth spline and mixed effect model to analyze the termite data. The results show that tropical tree resin, particularly at a higher concentration of 10 mg is significantly more effective in killing termites. We show that two dishes under 10 mg of tree resin were mistaken since the data for these two dishes are shown insignificantly different from data under 5 mg. The partially linear model shows that there is non-linear (piecewise linear) time effect. Both piecewise linear model and cubic spline smoothing show that the most effective period is the first week. The nonparametric smoothing, cubic spline, and piecewise linear model are not significantly different. Mixed effect model is consistent with partial linear model and piecewise linear model. The estimated treatment effect is time varying with a change point at day 7. Therefore, we suggest the piecewise linear model as the final simplest one for prediction. This model fits the data with adjusted R 2 ¼ 93.7 per cent and shows that on average, 10 mg is 68.9 per cent more efficient than 5 mg in killing termites during the first week.

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Section: Inferential Statistical Analysismentioning

confidence: 99%

Section: Piecewise Linear Regression Modelmentioning

confidence: 99%

Estimating tree resin dose effect on termites

Qian

Ryu

2006

Environmetrics

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“…Similar estimators are widely known, and their properties has been considered for example, by Borovkov [24], Hušková [17], Koul and Qian [16], and Koul et al [3].…”

Section: Estimatormentioning

confidence: 99%

“…We present a maximum likelihood estimator (MLE) of the time when the change point occurred. This obviously yields an estimation of a threshold [16].…”

Section: Introductionmentioning

confidence: 99%

Guaranteed maximum likelihood splitting tests of a linear regression model

Gurevich¹,

Vexler²

2006

Statistics

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We propose and examine a class of generalized maximum likelihood asymptotic power one tests for detection of various types of changes in a linear regression model. In economic and epidemiologic studies, such segmented regression models often occur as threshold models, where it is assumed that the exposure has no influence on the response up to a possible unknown threshold. An important task of such studies is testing the existence and estimation of this threshold. Guaranteed non-asymptotic upper bounds for the significance levels of these tests are presented. We demonstrate how the proposed tests were applied toward solving an actual problem encountered with real data.

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“…In the stochastic design regression model (1.3) Koul and Qian [24] consider an m which similar as in Hinkley [21,22] is a two-phase linear function but in contrast with a discontinuity at point θ. It is assumed that the error variable is independent of X, which is a stronger assumption than E( |X ) = 0.…”

Section: Introductionmentioning

confidence: 99%

Estimation of split-points in binary regression

Ferger¹

2009

Statistics &Amp; Decisions

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Let Y = m(X ) + be a regression model with a dichotomous output Y and a step function m with exact one jump at a point θ and two different levels a and b. In the applied sciences the parameter θ is interpreted as a split-point whereas b and 1 − a are known as positive and negative predictive value, respectively. We prove n-consistency and a weak convergence type result for a two-step plug-in maximum likelihood estimator of θ. The limit variable is not normal, but a maximizing point of a compound Poisson process on the real line. Estimation of (a, b) yields the usual √ n-consistency with normal limit. Both results can be extended to a multivariate weak limit theorem. It allows for the construction of asymptotic confidence intervals for (θ, a, b). The theory is applied to real life data of a large epidemiological study.

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Asymptotics of maximum likelihood estimator in a two-phase linear regression model

Cited by 47 publications

References 12 publications

Estimating tree resin dose effect on termites

Estimating tree resin dose effect on termites

Guaranteed maximum likelihood splitting tests of a linear regression model

Estimation of split-points in binary regression

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