## Designs for Regression in Time Series when the Regression Functions are Not Completely Known with Applications to Signal Detection Problem |

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### Contents

by a Probability Density Function | 4 |

i REVIEW OF LITERATURE | 7 |

CHAPTER nil THE EXISTENCE OF A REGULAR SEQUENCE | 13 |

5 other sections not shown

### Common terms and phrases

Ajn(X almost everywhere equal asymptotically Bayesian asymptotically optimal Chapter continuous function continuous time series converges convexity covariance kernel criterion D-optimal defined in lemma definition Definitioni dense set design points design problems design Tn discontinuity points discussed equal interval equal spacing design equation equi-continuous exists finite number function h functions defined gm(x Hence hn(t implies kernel Hilbert space least squares estimate Let Tn lim inf lim n2 matrix measure preserving measure zero method min-max minimize n2 max noise number of zeros observations one-one optimal design optimal sequence probability density function proof of lemma proof of theorem Proofi Let prove PTnf Q.E.D. Lemma Q.E.D. Theorem regression regular sequence Remarki reproducing kernel Hilbert Riemann integrable RS(h Sacks and Ylvisaker Sacks and Ylvisaker's satisfies sequence of designs signal detection problem Since solution solve Suppose Theorem 3•5 thesis tion uniformly University of Wisconsin variance vector Wahba wj(t Ylvisaker 1966