Selected Works of C.C. Heyde (Selected Works in Probability and Statistics)

Front Matter....Pages i-xxxvii
Author’s Pick....Pages 1-1
Chris Heyde’s Contribution to Inference in Stochastic Processes....Pages 2-4
Chris Heyde’s Work on Rates of Convergence in the Central Limit Theorem....Pages 5-7
Chris Heyde’s Work in Probability Theory, with an Emphasis on the LIL....Pages 8-11
Chris Heyde on Branching Processes and Population Genetics....Pages 12-15
On a Property of the Lognormal Distribution....Pages 16-18
Two Probability Theorems and Their Application to Some First Passage Problems....Pages 19-28
Some Renewal Theorems with Application to a First Passage Problem....Pages 29-41
Some Results on Small-Deviation Probability Convergence Rates for Sums of Independent Random Variables....Pages 42-52
A Contribution to the Theory of Large Deviations for Sums of Independent Random Variables....Pages 53-58
On Large Deviation Problems for Sums of Random Variables which are not Attracted to the Normal Law....Pages 59-62
On the Influence of Moments on the Rate of Convergence to the Normal Distribution....Pages 63-70
On Large Deviation Probabilities in the Case of Attraction to a Non-Normal Stable Law....Pages 71-76
On the Converse to the Iterated Logarithm Law....Pages 77-83
A Note Concerning Behaviour of Iterated Logarithm Type....Pages 84-89
On Extended Rate of Convergence Results for the Invariance Principle....Pages 90-91
On the Maximum of Sums of Random Variables and the Supremum Functional for Stable Processes....Pages 92-102
Some Properties of Metrics in a Study on Convergence to Normality....Pages 103-114
Extension of a Result of Seneta for the Super-Critical Galton–Watson Process....Pages 115-118
On the Implication of a Certain Rate of Convergence to Normality....Pages 119-124
A Rate of Convergence Result for the Super-Critical Galton-Watson Process....Pages 125-128
On the Departure from Normality of a Certain Class of Martingales....Pages 129-133
Some Almost Sure Convergence Theorems for Branching Processes....Pages 134-137
Some Central Limit Analogues for Supercritical Galton-Watson Processes....Pages 138-146
An Invariance Principle and Some Convergence Rate Results for Branching Processes....Pages 147-154
Improved classical limit analogues for Galton-Watson processes with or without immigration....Pages 159-169
Analogues of Classical Limit Theorems for the Supercritical Galton-Watson Process with Immigration....Pages 170-180
On Limit Theorems for Quadratic Functions of Discrete Time Series....Pages 181-189
Martingales: A Case for a Place in the Statistician’s Repertoire....Pages 191-199
On the Influence of Moments on Approximations by Portion of a Chebyshev Series in Central Limit Convergence....Pages 200-213
Estimation Theory for Growth and Immigration Rates in a Multiplicative Process....Pages 214-235
An Iterated Logarithm Result for Martingales and its Application in Estimation Theory for Autoregressive Processes....Pages 237-248
On the Uniform Metric in the Context of Convergence to Normality....Pages 249-261
Invariance Principles for the Law of the Iterated Logarithm for Martingales and Processes with Stationary Increments....Pages 262-270
An Iterated Logarithm Result for Autocorrelations of a Stationary Linear Process....Pages 271-275
On Estimating the Variance of the Offspring Distribution in a Simple Branching Process....Pages 276-288
A Nonuniform Bound on Convergence to Normality....Pages 289-293
Remarks on efficiency in estimation for branching processes....Pages 294-300
The Genetic Balance between Random Sampling and Random Population Size....Pages 301-304
On a unified approach to the law of the iterated logarithm for martingales....Pages 305-317
The Effect of Selection on Genetic Balance when the Population Size is Varying....Pages 318-320
On Central Limit and Iterated Logarithm Supplements to the Martingale Convergence Theorem....Pages 321-338
A Log Log Improvement to the Riemann Hypothesis for the Hawkins Random Sieve....Pages 339-344
On an Optimal Asymptotic Property of the Maximum Likelihood Estimator of a Parameter from a Stochastic Process....Pages 345-353
On Asymptotic Posterior Normality for Stochastic Processes....Pages 355-360
On the Survival of a Gene Represented in a Founder Population....Pages 361-369
An alternative approach to asymptotic results on genetic composition when the population size is varying....Pages 370-375
On the Asymptotic Equivalence of L p Metrics for Convergence to Normality....Pages 376-385
Quasi-likelihood and Optimal Estimation....Pages 386-399
Fisher Lecture....Pages 400-410
On Best Asymptotic Confidence Intervals for Parameters of Stochastic Processes....Pages 411-415
A quasi-likelihood approach to estimating parameters in diffusion-type processes....Pages 416-423
Asymptotic Optimality....Pages 424-425
On Defining Long-Range Dependence....Pages 426-431
A Risky Asset Model with Strong Dependence through Fractal Activity Time....Pages 432-437
Statistical estimation of nonstationary Gaussian processes with long-range dependence and intermittency....Pages 438-463