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Abstract:

Let (xi, yi), i = 1, …, n, be a sequence of observations such that yi= bi+ cxi+ ui, where biand c are unknown parameters, and {ui) and {xi) are independent sequences of independent, identically distributed random variables. The likelihood ratio test is derived for the hypothesis that bi= b (i = 1, …, n), against the alternative that bi= b (i ≤ i0) and bi= b + d (i > i0) for some b, i0, and d ≠ 0, assuming the ui’s are normal. Quantiles of the test statistic are computed by simulation, and the consistency of the test is proved. Some asymptotic properties of the test statistic are shown. © 1978, Taylor & Francis Group, LLC.

Registro:

Documento: Artículo
Título:A bivariate test for the detection of a systematic change in mean
Autor:Maronna, R.; Yohai, V.J.
Filiación:Buenos Aires, 1057, Argentina
Departamento de Matemática, Ciudad Universitaria, Buenos Aires, Argentina
Palabras clave:Bivariate slippage; Change in mean; Monte Carlo method; Slippage; Test consistency
Año:1978
Volumen:73
Número:363
Página de inicio:640
Página de fin:645
DOI: http://dx.doi.org/10.1080/01621459.1978.10480070
Título revista:Journal of the American Statistical Association
Título revista abreviado:J. Am. Stat. Assoc.
ISSN:01621459
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01621459_v73_n363_p640_Maronna

Referencias:

  • Anderson, T.W., Darling, D.A., Asymptotic Theory of Certain ‘Goodness of Fit Criteria Based on Stochastic Processes (1952) The Annals of Mathematical Statistics, 23, pp. 193-212
  • Andrews, D.F., Bickel, P.J., Hampel, F.R., Huber, P.J., Rogers, W.H., Tukey, J.W., (1972) Robust Estimates of Location, , Princeton, N.J.: Princeton University Press
  • Billingsley, P., (1968) Convergence of Probability Measures, , New York: John Wiley & Sons
  • Breiman, L., (1968) Probability, , Reading, Mass.: Addison–Wesley Publishing Co
  • Brown, R.L., Durbin, J., Evans, J.M., Techniques for Testing the Constancy of Regression Relationships over Time (1975) Journal of the Royal Statistical Society, 37, pp. 149-192. , Ser. B, (with discussion)
  • Chemoff, H., Zacks, S., Estimating the Current Mean of a Normal Distribution which is Subjected to Changes in Time (1964) The Annals of Mathematical Statistics, 35, pp. 999-1018
  • Farley, J.U., Hinich, M.J., A Test for a Shifting Slope Coefficient in a Linear Model (1970) Journal of the American Statistical Association, 65, pp. 1320-1329
  • Ferreira, P.E., A Bayesian Analysis of a Switching Regression Model: Known Number of Regimes (1975) Journal of the American Statistical Association, 70, pp. 370-374
  • Hawkins, D.M., Testing a Sequence of Observations for a Shift in Location (1977) Journal of the American Statistical Association, 72, pp. 180-186
  • Hinkley, D.V., Inference About the Change-Point in a Sequence of Random Variables (1970) Biometrika, 57, pp. 1-17
  • Kendall, M.G., Stuart, A., (1961) The Advanced Theory of Statistics, 2. , London: Charles W. Griffin & Co
  • Quandt, R.E., The Estimation of the Parameters of a Linear Regression System Obeying two Separate Regimes (1958) Journal of the American Statistical Association, 53, pp. 873-880
  • Quandt, R.E., Tests of the Hypothesis that a Linear Regression System Obeys two Separate Regimes (1960) Journal of the American Statistical Association, 55, pp. 324-330
  • Sen, A., Srivastava, M.S., On Tests for Detecting Change in Mean (1975) The Annals of Statistics, 3, pp. 98-108

Citas:

---------- APA ----------
Maronna, R. & Yohai, V.J. (1978) . A bivariate test for the detection of a systematic change in mean. Journal of the American Statistical Association, 73(363), 640-645.
http://dx.doi.org/10.1080/01621459.1978.10480070
---------- CHICAGO ----------
Maronna, R., Yohai, V.J. "A bivariate test for the detection of a systematic change in mean" . Journal of the American Statistical Association 73, no. 363 (1978) : 640-645.
http://dx.doi.org/10.1080/01621459.1978.10480070
---------- MLA ----------
Maronna, R., Yohai, V.J. "A bivariate test for the detection of a systematic change in mean" . Journal of the American Statistical Association, vol. 73, no. 363, 1978, pp. 640-645.
http://dx.doi.org/10.1080/01621459.1978.10480070
---------- VANCOUVER ----------
Maronna, R., Yohai, V.J. A bivariate test for the detection of a systematic change in mean. J. Am. Stat. Assoc. 1978;73(363):640-645.
http://dx.doi.org/10.1080/01621459.1978.10480070