Estimates for the Points of Intersection of Two Polynomial Regressions

Robison, D. E.

doi:10.1080/01621459.1964.10480712

Cited by 39 publications

(11 citation statements)

References 15 publications

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“…For example, Robinson (1964) discussed maximum likelihood estimation with and without constraints on the change point assuming a normal distribution. Feder (1975) studied the asymptotic distribution theory in segmented least squares regression.…”

Section: Introductionmentioning

confidence: 99%

Composite change point estimation for bent line quantile regression

2015

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The bent line quantile regression describes the situation where the conditional quantile function of the response is piecewise linear but still continuous in covariates. In some applications, the change points at which the quantile functions are bent tend to be the same across quantile levels or for quantile levels lying in a certain region. To capture such commonality, we propose a composite estimation procedure to estimate model parameters and the common change point by combining information across quantiles. We establish the asymptotic properties of the proposed estimator, and demonstrate the efficiency gain of the composite change point estimator over that obtained at a single quantile level through numerical studies. In addition, three different inference procedures are proposed and compared for hypothesis testing and the construction of confidence intervals. The finite sample performance of the proposed procedures is assessed through a simulation study and the analysis of a real data.

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Section: Introductionmentioning

confidence: 99%

Composite change point estimation for bent line quantile regression

2015

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“…Joinpoint models have been used in many fields of statistical research such as generalized linear models, risk function, time series, nonparametric methods, and longitudinal studies. In 1961, Sprent used the least square method for estimating segmented regression parameters when the change points are assumed to be known;[ 24 ] in 1964, Robison applied maximum likelihood and conditional maximum likelihood methods for estimating the connected location two regression functions when there are N 1 observations in the first segment and N 2 observations in the second segment, assuming that the change points are known or unknown;[ 25 ] in 1996, Berman used nonlinear least squares method;[ 26 ] in 1980, Lerman proposed a grid search method to fit segmented regression curves;[ 27 ] in 1966, Hudson fitted segmented curves whose join points have to be estimated;[ 28 ] and in 2004, Kim and Fay proposed a procedure to compare two breast cancer incidence rates in two different genders and geographic regions using joinpoint linear regression model and least square method. [ 29 ]…”

Section: Introductionmentioning

confidence: 99%

Application of joinpoint regression in determining breast cancer incidence rate change points by age and tumor characteristics in women aged 30-69 (years) and in Isfahan city from 2001 to 2010

Dehkordi

Tazhibi

Babazade

2014

J Edu Health Promot

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Background and Objectives:Breast cancer is a major threat to women's health. Evaluation of the changes in trend of the incidence rate provides valuable information for the assessment and planning of development indicators of each country. The aim of the present study was to apply the JoinPoint regression model for determining changes in the trend of the breast cancer incidence rate in Isfahan.Materials and Methods:In this cross-sectional study, 3640 women with breast cancer referring to oncology and radiotherapy departments of Seyed-al-Shohada and Milad cancer treatment centers of Isfahan during 2001–2010 were studied and sampling was not done. Joinpoint regression model was used to investigate the pattern of breast cancer incidence rate. Response and independent variables were the natural logarithm of the age-standardized incidence rates and year of diagnosis of breast cancer, respectively, in which various levels of cancer tumor characteristics (P < 0.05) were analyzed.Results:The incidence rates increased annually in the age groups of 40–44 years (6.2%), 45–49 years (5.3%), and 55–59 years (5.3%). The trend of incidence rates in women with tumor size ≤2 cm (18.2%), well (moderately) differentiated tumor grade [8% (10.2%)], positive estrogen (progesterone) hormone receptor status [10.5% (6.9%)], and the proportion of positive lymph node to surgery node ≤25% (nonsignificant) was upward.Conclusion:The trend of incidence rates with tumor size ≤2 cm, well-differentiated tumor grade, moderately differentiated tumor grade, and positive estrogen and progesterone hormone receptors was upward. The pattern of breast cancer can help in cancer prevention and prognosis, and in selecting the best type of surgery.

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“…Sequential and fixed-sample-size varieties have been considered from both classical and Bayesian viewpoints, with numerous parametric and nonparametric approaches proposed. We refer the interested reader to several excellent surveys, including those by Hinkley et al (1980), Zacks (1983), Wolfe and Schechtman (1984), Carlin et al (1992), and Lai (1995 Quandt (1958) and Robison (1964). Historically, Chernoff and Zacks (1964) were among the first to consider a parametric Bayesian approach to changepoint estimation.…”

Section: Changepoint Estimation and Contact Point Determination In Thmentioning

confidence: 99%

Bayesian Change-Point Analysis for Atomic Force Microscopy and Soft Material Indentation

Rudoy

Yuen

Howe

et al. 2010

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary. Material indentation studies, in which a probe is brought into controlled physical contact with an experimental sample, have long been a primary means by which scientists characterize the mechanical properties of materials. More recently, the advent of atomic force microscopy, which operates on the same fundamental principle, has in turn revolutionized the nanoscale analysis of soft biomaterials such as cells and tissues. The paper addresses the inferential problems that are associated with material indentation and atomic force microscopy, through a framework for the change‐point analysis of pre‐contact and post‐contact data that is applicable to experiments across a variety of physical scales. A hierarchical Bayesian model is proposed to account for experimentally observed change‐point smoothness constraints and measurement error variability, with efficient Monte Carlo methods developed and employed to realize inference via posterior sampling for parameters such as Young's modulus, which is a key quantifier of material stiffness. These results are the first to provide the materials science community with rigorous inference procedures and quantification of uncertainty, via optimized and fully automated high throughput algorithms, implemented as the publicly available software package BayesCP. To demonstrate the consistent accuracy and wide applicability of this approach, results are shown for a variety of data sets from both macromaterials and micromaterials experiments—including silicone, neurons and red blood cells—conducted by the authors and others.

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Estimates for the Points of Intersection of Two Polynomial Regressions

Cited by 39 publications

References 15 publications

Composite change point estimation for bent line quantile regression

Composite change point estimation for bent line quantile regression

Application of joinpoint regression in determining breast cancer incidence rate change points by age and tumor characteristics in women aged 30-69 (years) and in Isfahan city from 2001 to 2010

Bayesian Change-Point Analysis for Atomic Force Microscopy and Soft Material Indentation

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