On the non-existence of consistent estimates in Galton-Watson processes

1982 ◽  
Vol 19 (4) ◽  
pp. 842-846 ◽  
Author(s):  
Richard Lockhart
Keyword(s):  
Offspring Distribution ◽  
Lattice Size ◽  
Single Realization ◽  
The Mean ◽  
Watson Process ◽  
Mean Variance

Estimation of the offspring distribution from a single realization of a supercritical Galton-Watson process is studied. It is shown that, based on population totals, a parameter of the offspring distribution cannot be estimated unless it is determined by the mean, variance, lattice size and lattice offset of the offspring distribution.

On the non-existence of consistent estimates in Galton-Watson processes

1982 ◽  
Vol 19 (04) ◽  
pp. 842-846
Author(s):  
Richard Lockhart
Keyword(s):  
Offspring Distribution ◽  
Lattice Size ◽  
Single Realization ◽  
The Mean ◽  
Watson Process ◽  
Mean Variance

Estimation of the offspring distribution from a single realization of a supercritical Galton-Watson process is studied. It is shown that, based on population totals, a parameter of the offspring distribution cannot be estimated unless it is determined by the mean, variance, lattice size and lattice offset of the offspring distribution.

On estimating the variance of the offspring distribution in a simple branching process

1974 ◽  
Vol 6 (03) ◽  
pp. 421-433 ◽  
Author(s):  
C. C. Heyde
Keyword(s):  
Rate Of Convergence ◽  
Central Limit ◽  
Branching Process ◽  
Limit Theory ◽  
Offspring Distribution ◽  
Iterated Logarithm ◽  
Single Realization ◽  
Watson Process ◽  
Limit Result ◽  
Strongly Consistent

A single realization {Z n , 0 ≦n≦N + 1} of a supercritical Galton-Watson process (so called) is considered and it is required to estimate the variance of the offspring distribution. A prospective estimator is proposed, where , and is shown to be strongly consistent on the non-extinction set. A central limit result and an iterated logarithm result are provided to give information on the rate of convergence of the estimator. It is also shown that the estimation results are robust in the sense that they continue to apply unchanged in the case where immigration occurs. Martingale limit theory is employed at each stage in obtaining the limit results.

On estimating the variance of the offspring distribution in a simple branching process

1974 ◽  
Vol 6 (3) ◽  
pp. 421-433 ◽  
Author(s):  
C. C. Heyde
Keyword(s):  
Rate Of Convergence ◽  
Central Limit ◽  
Branching Process ◽  
Limit Theory ◽  
Offspring Distribution ◽  
Iterated Logarithm ◽  
Single Realization ◽  
Watson Process ◽  
Limit Result ◽  
Strongly Consistent

A single realization {Zn, 0 ≦n≦N + 1} of a supercritical Galton-Watson process (so called) is considered and it is required to estimate the variance of the offspring distribution. A prospective estimator is proposed, where , and is shown to be strongly consistent on the non-extinction set. A central limit result and an iterated logarithm result are provided to give information on the rate of convergence of the estimator. It is also shown that the estimation results are robust in the sense that they continue to apply unchanged in the case where immigration occurs. Martingale limit theory is employed at each stage in obtaining the limit results.

Comparison Between the Mean-Variance Optimal and the Mean-Quadratic-Variation Optimal Trading Strategies

2013 ◽  
Vol 20 (5) ◽  
pp. 415-449 ◽  
Author(s):  
S. T. Tse ◽  
P. A. Forsyth ◽  
J. S. Kennedy ◽  
H. Windcliff
Keyword(s):  
Quadratic Variation ◽  
Trading Strategies ◽  
Optimal Trading ◽  
The Mean ◽  
Mean Variance
Sign in / Sign up

Export Citation Format

Share Document