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On the maximum likelihood estimation of respiratory response slopes

On the maximum likelihood estimation of respiratory response slopes y variable are both subject to random errors. The model is xi = E‘i + 6i yi = p& + ci i = 1, l l l ’ n (I) where xi and yi are observed values. The usual assumptions are 1) the ti are unobservable normal random variables with mean p; 2) 6i and Ei are independent normal random variables with zero means; and 3) they are all mutually independent, i.e. E(E‘) = p, E(6) = E(c) = 0 var(E) = a:, var(6) = a& var(E) = af cov(6, e) = cov([, 6) = COV(f, c) = 0 I (2) in the literature have centered on appropriate methods for estimating a respiratory control response slope when both ventilation and arterial (alveolar) COz are-observed with error. Kermack and Haldane (4) proposed a reduced major axis approach. Daubenspeck and Ogden (2) suggested directional statistics -methods. Sherrill and Swanson developed a modified reduced major axis (RMAM) technique (6), and Mardia et al. (5) suggested a maximum likelihood (ML) appreach, under the assumption of a bivariate normal distributi .on The slope estimate in the ML approach is given, by a *method of moments solution, as y/X (3, 5). However, when the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Physiology The American Physiological Society

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