Guttorp, Peter 1991 Statistical inference for branching processes. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the INAR(1) does not give a large enough variance to model this series. Non Gaussian conditional linear AR(1) models 19 6. 2 Example 2: Gold particles We repeated this procedure for another series on the same sample space, the first 60 values of the series of counts of gold particles as given by Guttorp (1991). Graph similar to those in Figure 1 (not shown) show the series and sample ACF are again consistent with CLAR(1) structure. LS estimates are = 0:583 and = 0:636. Using the same two models and as in Example 1, 0:850 for the series and the INAR(1) and conditionally Poisson ....

GUTTORP, P. (1991) Statistical inference for branching processes, Wiley, New York.

....event of non extinction. The present research is closer to Heyde s [8] Bayesian estimation of the offspring mean where the offspring law belongs to a power series family. Scott [12] extends Heyde s work. A review of the existing results with extensive discussions can also be found in Guttorp [7]. In the present study we obtain Bayes estimates for the offspring mean under different loss functions by considering power series offspring laws and assuming, in addition, that the process has stopped evolving, i.e. it is extinct. This additional assumption allows us to consider a more ....

....(see [1] Thm 3, p.52) with offspring mean (q ) 1. Therefore, estimating ( for the mortal process we obtain an estimate for the offspring mean of fZ n g in the non supercritical case or for (q ) if fZ n g is supercritical. For 3 further discussion on inference conditional upon extinction see [7], pp. 100102. In a Bayesian setting the question whether fZ n g is supercritical or not can be answered by computing the posterior probability that the offspring mean is greater than 1 or by constructing a credibility interval for the offspring mean. For convenience we will continue to write the ....

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Guttorp, P. (1991) Statistical Inference for Branching Processes. John Wiley, New York.

.... above results describe the probabilistic behavior of the process.The statistical problem of estimating the mean m and other parameters of a supercritical branching process has received considerable attention in the literature; for a classical treatment of the problem refer to the book of Guttorp [37]. More recently, Wei and Winnicki [61] Winnicki [62] Sriram, et.al. 57] and Datta and Sriram [35] investigated the estimation of m from a branching process with immigration. Applications in the context of polymerase chain reaction have been investigatedby Sun and Waterman [58] 3 Branching ....

Guttorp,P(1991): Statistical Inference for Branching Processes, John Wiley and Sons, New York.

.... devoted to branching processes with immigration when the immigration is independent of reproduction (Heyde and Seneta ( 20] and [21] Quine [26] Bhat and Adke [4] Ventakamaran [31] Winnicki ( 34] and [35] Hudson [24] Wei and Winnicki [32] Wei [33] Sriram [29] Sriram et al. [30] Guttorp [15], Dion and Yanev [8] In the case of state dependent immigration most of the works concern limit theorems (Foster [13] Pakes [25] Yanev and Yanev [36] Rahimov [28] and only a few people have studied the estimation problems for these processes with immigration (Rahimov [27] or for branching ....

.... b mn = P n 1 N k ) P n Gamma1 0 N k ) Gamma1 , mn = N n (N n Gamma1 ) Gamma1 and oe 2 n 1 = n Gamma1 P n k=1 (N k 1 Gamma mn 1N k ) 2 (N k ) Gamma1 (Heyde [18] 19] 22] Heyde and Leslie [23] Athreya and Ney [2] Basawa and Scott [3] Hall and Heyde [16] Guttorp [15]) The convergence of the normalized observed process to the variable WN0 ;fF n gn , limit of the normalized branching process N n , is derived using the classical results of martingales applied to the process fN bef n gn and taking into account the binomial variability of the migrating process ....

Guttorp, P. (1991) Statistical Inference for Branching Processes. Wiley, New York. p. 211.

....fN n;vn g n est r eduit a un simple processus de Galton Watson g en er e par F et not e fN n g n . Le comportement asymptotique d un tel processus ainsi que les propri et es des estimateurs de m sont connus (Heyde [8] 9] Heyde Leslie [10] Athreya Ney [1] Hall Heyde [7] Guttorp [6]) Dans le cas g en eral, fN n;vn g n correctement normalis e n est plus une martingale. On g en eralise ici les r esultats relatifs au cas simple. On montre que f Nn;vn pvn p Vn g n converge p.s. et dans L 2 vers la limite WN 0 ;F du processus de branchement f N n;V n 1 p V n 1 m n g n ....

....g n is reduced to a simple supercritical Galton Watson process generated by F and denoted by fN n g n . The asymptotic behaviour of such a process as well as the properties of the estimators of m are well known (Heyde [8] 9] Heyde Leslie [10] Athreya Ney [1] Hall Heyde [7] Guttorp [6]) fN n;vn g n correctly normalized is, generally, no longer a martingale. We extend here the results relative to the simple case. Let F n be the oe algebra generated by fN k;V k ; N k;v k g kn , p Vn = Pi n Gamma1 k=1 (1 Gamma ffi p v k ) for n 2, p V 1 = p V 0 = 1, m = 1 Gamma ffi p v )m ....

P. Guttorp (1991) Statistical Inference for Branching Processes. Wiley, New York, 211p.

.... by Nedelman to analyze the use of internal controls in Q PCR experiments (Nedelman et al. 1992b) as well as most of the other current protocols of Q PCR (Nedelman et al. 1992a) 6 The estimation of the mean value of the offspring distribution is a classical problem in branching process theory (Guttorp, 1991). In the case of PCR, the offspring mean is the rate of amplification which can be estimated by: m n = N n N n 1 . This estimator converges almost surely towards m as n tends to infinity. This is the strongest type of convergence for a random variable. It means that an estimate of m can be ....

Guttorp, P. 1991. Statistical inference for branching processes. John Wiley & Sons, Inc, NewYork.

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Guttorp, Peter 1991 Statistical inference for branching processes. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York.

No context found.

P. Guttorp. Statistical Inference for Branching Processes. Wiley, 1991.

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