Robert W. Keener

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We model the effect of gonadotropin-releasing hormone (GnRH) on the production of luteinizing hormone (LH) by the ovine pituitary. GnRH, released by the hypothalamus, stimulates the secretion of LH from the pituitary. If stimulus pulses are regular, LH response will follow a similar pattern. However, during application of GnRH at high frequencies or(More)
Standard renewal theory is concerned with expectations related to sums of positive i.i.d. variables, S = n n I i=l z. 1 We generalize this theory to the case where {S.} is a Markov chain on 1 the real line with stationary transition probabilities satisfying a drift condition. The expectations we are concerned with satisfy generalized renewal equations, and(More)
Let Y have a symmetric Dirichlet multinomial distributions in R m , and let S m = h(Y 1)+· · ·+h(Y m). We derive a central limit theorem for S m as the sample size n and the number of cells m tend to infinity at the same rate. The rate of convergence is shown to be of order m 1/6. The approach is based on approximation of marginal distributions for the(More)
In Probability proportional to size (PPS) sampling, the sizes for nonsampled units are not required for the usual Horvitz-Thompson or Hajek estimates, and this information is rarely included in public use data files. Previous studies have shown that incorporating information on the sizes of the nonsampled units through semiparamteric models can result in(More)
Let {Sn = (Xn, Wn)} n≥0 be a random walk with Xn ∈ R and Wn ∈ R m. Let τ = τa = inf{n : Xn > a}. The main results presented are two term asymptotic expansions for the joint distribution of Sτ and τ and the marginal distribution of h(Sτ /a, τ /a) in the limit a → ∞. These results are used to study the distribution of t-statistics in sequential experiments(More)
This research was motivated by a clinical trial with bladder cancer patients who went through a surgery and were followed up for cancer recurrence. One of the main objectives of the trial was to evaluate the time to cancer recurrence in patients in control and experimental groups. At the time of recurrence, the disease stage was also evaluated. Because the(More)
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