C Sanchez Reduction Saetas

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C Sanchez Reduction Saetas

  1. 1. Reduction of saetas W.González-Manteiga and C. Sánchez-Sellero Department of Statistics and Operations Research University of Santiago de Compostela
  2. 2. Estimation of a saeta as a linear model The available data , denoted by Y, can be expressed as a function of known quantities, in the matrix X, unknow parameters, which determine the saeta, and some errors. It can be written in matrix form as a linear model: is assumed to be normal with mean zero and covariance matrix
  3. 3. Estimator and its properties The estimator can be obtained by which satisfies
  4. 4. <ul><li>Once a saeta is estimated under the reference (XYZ), </li></ul><ul><li>which is the corresponding saeta under the reference (X’Y’Z’)? </li></ul><ul><li>2. Once the saeta is estimated, </li></ul><ul><li>which is the new saeta under the restriction that it should go through the origin (X=0, Y=0, Z=0)? </li></ul>s s’ s 0 y x z x’ y’
  5. 5. 1. Once a saeta is estimated under the reference (XYZ), which is the corresponding saeta under the reference (X’Y’Z’)? Proposal: Obtain confidence regions for saeta’s
  6. 6. 2. Once the saeta is estimated, which is the new saeta under the restriction that it should go through the origin (X=0, Y=0, Z=0)? A linear model can be estimated under a linear restriction by In that case, and (assumption that it goes through the origin) can be tested by the F -test:
  7. 7. 3. Once two saeta’s, S’_1 and S’_2 are estimated under two references and data sets, which is the best saeta S that is based on the information coming from the two data sets? s s 1 ’ s 0 y x z φ s 2 ’ Detector 1 Detector 2 x 1 x 2
  8. 8. 3. Once two saeta’s, S’_1 and S’_2 are estimated under two references and data sets, which is the best saeta S that is based on the information coming from the two data sets? Proposal: Test the equality of two saeta’s
  9. 9. 1' (Slight modification of question 1, where the reference is rotated). s’ s s 0 y x z φ x’ y’

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