Efficient estimates in linear and nonlinear regression with heteroscedastic errors |
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| Institution: | 3. Department of Cardiology, Division Heart and Lungs, University Medical Center Utrecht, Utrecht, The Netherlands;1. Department of Marine Science, Skidaway Institute of Oceanography, University of Georgia, 10 Ocean Science Circle, Savannah, GA 31411-1011, United States;2. College of Fisheries and Ocean Sciences, University of Alaska Fairbanks, Fairbanks, AK 99775, United States;3. Florida International University, Applied Research Center, 10555 West Flagler St., Miami, FL 33174, United States;4. Department of Earth, Ocean, and Atmospheric Science, Florida State University, Tallahassee, FL 32306, United States;1. College of Technology Management, National Tsing Hua University, Hsinchu 30013, Taiwan;2. Rutgers Business School, Rutgers University, Piscataway, NJ 08854, U.S.A |
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| Abstract: | In this paper we consider the heteroscedastic regression model defined by the structural relation Y = r(V, β) + s(W)ε, where V is a p-dimensional random vector, W is a q-dimensional random vector, β is an unknown vector in some open subset B of Rm, r is a known function from Rp × B into R, s is an unknown function on Rq, and ε is an unobservable random variable that is independent of the pair (V, W). We construct asymptotically efficient estimates of the regression parameter β under mild assumptions on the functions r and s and on the distributions of ε and (V, W). |
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