Iterative estimating equations: Linear convergence and asymptotic properties

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size increases to infinity. Furthermore, we show that the limiting estimator is consistent and asymptotically efficient, as expected. The method applies to semiparametric regression models with unspecified covariances among the observations. In the special case of linear models, the procedure reduces to iterative reweighted least squares. Finite sample performance of the procedure is studied by simulations, and compared with other methods. A numerical example from a medical study is considered to illustrate the application of the method.

The Learning Component of Dynamic Allocation Indices

For a multiarmed bandit problem with exponential discounting the optimal allocation rule is defined by a dynamic allocation index defined for each arm on its space. The index for an arm is equal to the expected immediate reward from the arm, with an upward adjustment reflecting any uncertainty about the prospects of obtaining rewards from the arm, and the possibilities of resolving those uncertainties by selecting that arm. Thus the learning component of the index is defined to be the difference between the index and the expected immediate reward. For two arms with the same expected immediate reward the learning component should be larger for the arm for which the reward rate is more uncertain. This is shown to be true for arms based on independent samples from a fixed distribution with an unknown parameter in the cases of Bernoulli and normal distributions, and similar results are obtained in other cases.

Time-dependent instantaneous mortality rates from multiple tagging experiments with exact times of release and recovery

Instantaneous natural mortality rates and a nonparametric hunting mortality function are estimated from a multiple-year tagging experiment with arbitrary, time-dependent fishing or hunting mortality. Our theory allows animals to be tagged over a range of times in each year, and to take time to mix into the population. Animals are recovered by hunting or fishing, and death events from natural causes occur but are not observed. We combine a long-standing approach based on yearly totals, described by Brownie et al. (1985, Statistical Inference from Band Recovery Data: A Handbook, Second edition, United States Fish and Wildlife Service, Washington, Resource Publication, 156), with an exact-time-of-recovery approach originated by Hearn, Sandland and Hampton (1987, Journal du Conseil International pour l'Exploration de la Mer, 43, 107-117), who modeled times at liberty without regard to time of tagging. Our model allows for exact times of release and recovery, incomplete reporting of recoveries, and potential tag shedding. We apply our methods to data on the heavily exploited southern bluefin tuna (Thunnus maccoyii).

Stock assessment report on Queensland east coast red throat emperor (Lethrinus miniatus) fishery

The Red Throat Emperor fishery was assessed using an age-structured model that incorporated all available information on catch, catch per unit effort (CPUE) and age structure and a surplus production model fitted to the catch and CPUE data. The Great Barrier Reef (GBR) was divided into five regions: Townsville, Mackay, Storm Cay, Swain reefs, and Capricorn Bunker. Age structure varied greatly between regions, with fish aged 5-8 years predominating in the Townsville region, 4-7 years in the Mackay, Storm Cay and Swains regions, and 2-3 years in the Capricorn-Bunker region. These differences were explained by different age-dependent vulnerabilities to fishing between the regions. The age-structured model estimated that exploitable biomass fell to about 60% of virgin biomass in the late 1990s, due mainly to years of poor recruitment, but recovered to around 70% by 2004. Further recovery can be expected due to the fishery not meeting its total allowable commercial catch (TACC) of 700 t in recent years. The current TACC of 700 t, combined with a recreational-charter catch of around 450 t, contains little margin for error, especially in view of high year-to-year variability of recruitment of red throat emperor and stresses on the GBR from land clearing, coastal development and climate change. The state of the population needs to be monitored closely. Further data on age structures after 2000 will provide more certainty to this assessment.

Fishing power increases continue in Queensland's east coast trawl fishery, Australia

The Queensland east coast trawl fishery is by far the largest prawn and scallop otter trawl fleet in Australia in terms of number of vessels, with 504 vessels licensed to fish for species including tiger prawns, endeavour prawns, red spot king prawns, eastern king prawns and saucer scallops by the end of 2004. The vessel fleet has gradually upgraded characteristics such as engine power and use of propeller nozzles, quad nets, global positioning systems (GPS) and computer mapping software. These changes, together with the ever-changing profile of the fleet, were analysed by linear mixed models to quantify annual efficiency increases of an average vessel at catching prawns or scallops. The analyses included vessel characteristics (treated as fixed effects) and vessel identifier codes (treated as random effects). For the period from 1989 to 2004 the models estimated overall fishing power increases of 6% in the northern tiger, 6% in the northern endeavour, 12% in the southern tiger, 18% in the red spot king, 46% in the eastern king prawn and 15% in the saucer scallop sector. The results illustrate the importance of ongoing monitoring of vessel and fleet characteristics and the need to use this information to standardise catch rate indices used in stock assessment and management.

Introduction, establishment, and potential geographic range of Carmenta sp. nr ithacae (Lepidoptera: Sesiidae), a biological control agent for Parthenium hysterophorus (Asteraceae) in Australia

Parthenium (Parthenium hysterophorus L.), a major weed causing economic, environmental, and human and animal health problems in Australia and several countries in Asia, Africa, and the Pacific, has been a target for biological control in Australia since the mid-1970s. Nine species of insects and two rust fungi have been introduced as biological control agents into Australia. These include Carmenta sp. nr ithacae, a root feeding agent from Mexico. The larvae of C. sp. nr ithacae bore through the stem-base into the root where they feed on the cortical tissue of the taproot. During 1998-2002, 2,816 larval-infested plants and 387 adults were released at 31 sites across Queensland, Australia. Evidence of field establishment was first observed in two of the release sites in central Queensland in 2004. Annual surveys at these sites and nonrelease sites during 2006-2011 showed wide variations in the incidence and abundance of C. sp. nr ithacae between years and sites. Surveys at three of the nine release sites in northern Queensland and 16 of the 22 release sites in central Queensland confirmed the field establishment of C. sp. nr ithacae in four release sites and four nonrelease sites, all in central Queensland. No field establishment was evident in the inland region or in northern Queensland. A CLIMEX model based on the native range distribution of C. sp. nr ithacae predicts that areas east of the dividing range along the coast are more suitable for field establishment than inland areas. Future efforts to redistribute this agent should be restricted to areas identified as climatically favorable by the CLIMEX model.

Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual’s previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag–recapture data and tag–recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

Modelling interactions between farm-level structural adjustment and a regional economy: A case of the Australian rice industry

Climate change and on-going water policy reforms will likely contribute to on-farm and regional structural adjustment in Australia. This paper gathers empirical evidence of farm-level structural adjustments and integrates these with a regional equilibrium model to investigate sectoral and regional impacts of climate change and recent water use policy on rice industry. We find strong evidence of adjustments to the farming system, enabled by existing diversity in on-farm production. A further loss of water with additional pressures to adopt less intensive and larger-scale farming, will however reduce the net number of farm businesses, which may affect regional rice production. The results from a regional CGE model show impacts on the regional economy over and above the direct cost of the environmental water, although a net reduction in real economic output and real income is partially offset by gains in rest of the Australia through the reallocation or resources. There is some interest within the industry and from potential new corporate entrants in the relocation of some rice production to the north. However, strong government support would be crucial to implement such relocation.

Quantitative methods to measure pigmentation variation in farmed Giant Tiger Prawns, Penaeus monodon, and the effects of different harvest methods on cooked colour

Cooked prawn colour is known to be a driver of market price and a visual indicator of product quality for the consumer. Although there is a general understanding that colour variation exists in farmed prawns, there has been no attempt to quantify this variation or identify where this variation is most prevalent. The objectives of this study were threefold: firstly to compare three different quantitative methods to measure prawn colour or pigmentation, two different colorimeters and colour quantification from digital images. Secondly, to quantify the amount of pigmentation variation that exists in farmed prawns within ponds, across ponds and across farms. Lastly, to assess the effects of ice storage or freeze-thawing of raw product prior to cooking. Each method was able to detect quantitative differences in prawn colour, although conversion of image based quantification of prawn colour from RGB to Lab was unreliable. Considerable colour variation was observed between prawns from different ponds and different farms, and this variation potentially affects product value. Different post-harvest methods prior to cooking were also shown to have a profound detrimental effect on prawn colour. Both long periods of ice storage and freeze thawing of raw product were detrimental to prawn colour. However, ice storage immediately after cooking was shown to be beneficial to prawn colour. Results demonstrated that darker prawn colour was preserved by holding harvested prawns alive in chilled seawater, limiting the time between harvesting and cooking, and avoiding long periods of ice storage or freeze thawing of uncooked product.

Generalization of Dynkin's Identity and Some Applications

Let X(t) be a right continuous temporally homogeneous Markov pro- cess, Tt the corresponding semigroup and A the weak infinitesimal genera- tor. Let g(t) be absolutely continuous and r a stopping time satisfying E.( S f I g(t) I dt) < oo and E.( f " I g'(t) I dt) < oo Then for f e 9iJ(A) with f(X(t)) right continuous the identity Exg(r)f(X(z)) - g(O)f(x) = E( 5 " g'(s)f(X(s)) ds) + E.( 5 " g(s)Af(X(s)) ds) is a simple generalization of Dynkin's identity (g(t) 1). With further restrictions on f and r the following identity is obtained as a corollary: Ex(f(X(z))) = f(x) + k! Ex~rkAkf(X(z))) + n-1E + (n ) )!.E,(so un-1Anf(X(u)) du). These identities are applied to processes with stationary independent increments to obtain a number of new and known results relating the moments of stopping times to the moments of the stopped processes.

Random matrices: Universality of ESDs and the circular law

Given an n x n complex matrix A, let mu(A)(x, y) := 1/n vertical bar{1 <= i <= n, Re lambda(i) <= x, Im lambda(i) <= y}vertical bar be the empirical spectral distribution (ESD) of its eigenvalues lambda(i) is an element of C, i = l, ... , n. We consider the limiting distribution (both in probability and in the almost sure convergence sense) of the normalized ESD mu(1/root n An) of a random matrix A(n) = (a(ij))(1 <= i, j <= n), where the random variables a(ij) - E(a(ij)) are i.i.d. copies of a fixed random variable x with unit variance. We prove a universality principle for such ensembles, namely, that the limit distribution in question is independent of the actual choice of x. In particular, in order to compute this distribution, one can assume that x is real or complex Gaussian. As a related result, we show how laws for this ESD follow from laws for the singular value distribution of 1/root n A(n) - zI for complex z. As a corollary, we establish the circular law conjecture (both almost surely and in probability), which asserts that mu(1/root n An) converges to the uniform measure on the unit disc when the a(ij) have zero mean.

Supercritical age-dependent branching Markov processes and their scaling limits

This paper studies the long-time behavior of the empirical distribution of age and normalized position of an age-dependent supercritical branching Markov process. The motion of each individual during its life is a random function of its age. It is shown that the empirical distribution of the age and the normalized position of all individuals alive at time t converges as t -> infinity to a deterministic product measure.

Central Limit Theorem for truncated heavy tailed Banach valued random vectors

In this paper the question of the extent to which truncated heavy tailed random vectors, taking values in a Banach space, retain the characteristic features of heavy tailed random vectors, is answered from the point of view of the central limit theorem.

T. E. Harris and branching processes

T. E. Harris was a pioneer par excellence in many fields of probability theory. In this paper, we give a brief survey of the many fundamental contributions of Harris to the theory of branching processes, starting with his doctoral work at Princeton in the late forties and culminating in his fundamental book ``The Theory of Branching Processes,'' published in 1963.