Abstract
This paper deals with a testing problem for each of the interaction parameters of the Lotka–Volterra ordinary differential equations system~(ODE). In short, when the rates of birth and death are fixed, we would like to test if each interaction parameter is higher or lower than a fixed reference rate. We choose a statistical model where the actual population sizes are modelled as random perturbations of the solutions to this ODE. By assuming that the random perturbations follow correlated Ornstein–Uhlenbeck processes, we propose the uniformly most powerful test concerning each interaction parameter of the ODE and, we establish the asymptotic properties of the test. Further, we illustrate the suggested test on the Canadian mink–muskrat data set.
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This research has received the financial support from Natural Sciences and Engineering Research Council of Canada and Institut des Sciences Mathématiques.
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Nkurunziza, S. Testing interaction in some predator–prey populations. Stat Papers 50, 527–551 (2009). https://doi.org/10.1007/s00362-007-0096-x
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DOI: https://doi.org/10.1007/s00362-007-0096-x
Keywords
- Correlated Ornstein–Uhlenbeck process
- Ergodic and stationary process
- Gaussian process
- Wiener process
- Uniformly most powerful test
- Interaction parameter
- Lotka–Volterra ODE