Parameter estimation based on empirical transforms

In this thesis, we provide a unified treatment of the topic of parameter estimation using integral transforms, such as the characteristic function and moment generating function. This topic encompasses a wealth of methods, which typically vary from each other in relation to the type of weight function and choice of integral transform that is being employed. We show that the integrated squared error method dominates alternative transform methods, particularly in terms of robustness. We present a convenient and flexible approach to dealing with the difficulty here surrounding the necessary weight function, and illustrate the success of this approach on the mixture of two normal distributions. Furthermore, we show that the integrated squared error method also outperforms the maximum likelihood method for this distribution, particularly with samples with outliers or a small number of observations

Hidden Markov Models for Extended Batch Data

Batch marking provides an important and efficient way to estimate the survival probabilities and population sizes of wild animals. It is particularly useful when dealing with animals that are difficult to mark individually. For the first time, we provide the likelihood for extended batch-marking experiments. It is often the case that samples contain individuals that remain unmarked, due to time and other constraints, and this information has not previously been analyzed. We provide ways of modeling such information, including an open N-mixture approach. We demonstrate that models for both marked and unmarked individuals are hidden Markov models; this provides a unified approach, and is the key to developing methods for fast likelihood computation and maximization. Likelihoods for marked and unmarked individuals can easily be combined using integrated population modeling. This allows the simultaneous estimation of population size and immigration, in addition to survival, as well as efficient estimation of standard errors and methods of model selection and evaluation, using standard likelihood techniques. Alternative methods for estimating population size are presented and compared. An illustration is provided by a weather-loach data set, previously analyzed by means of a complex procedure of constructing a pseudo likelihood, the formation of estimating equations, the use of sandwich estimates of variance, and piecemeal estimation of population size. Simulation provides general validation of the hidden Markov model methods developed and demonstrates their excellent performance and efficiency. This is especially notable due to the large numbers of hidden states that may be typically require

A generic method for estimating and smoothing multispecies biodiversity indices using intermittent data

Biodiversity indicators summarise extensive, complex ecological data sets and are important in influencing government policy. Component data consist of time-varying indices for each of a number of different species. However, current biodiversity indicators suffer from multiple statistical shortcomings. We describe a state-space formulation for new multispecies biodiversity indicators, based on rates of change in the abundance or occupancy probability of the contributing individual species. The formulation is flexible and applicable to different taxa. It possesses several advantages, including the ability to accommodate the sporadic unavailability of data, incorporate variation in the estimation precision of the individual species’ indices when appropriate, and allow the direct incorporation of smoothing over time. Furthermore, model fitting is straightforward in Bayesian and classical implementations, the latter adopting either efficient Hidden Markov modelling or the Kalman filter. Conveniently, the same algorithms can be adopted for cases based on abundance or occupancy data—only the subsequent interpretation differs. The procedure removes the need for bootstrapping which can be prohibitive. We recommend which of two alternatives to use when taxa are fully or partially sampled. The performance of the new approach is demonstrated on simulated data, and through application to three diverse national UK data sets on butterflies, bats and dragonflies. We see that uncritical incorporation of index standard errors should be avoided

Variance estimation for integrated population models

Abstract State-space models are widely used in ecology. However, it is well known that in practice it can be difficult to estimate both the process and observation variances that occur in such models. We consider this issue for integrated population models,which incorporate state-space models for population dynamics. To some extent, the mechanism of integrated population models protects against this problem, but it can still arise, and two illustrations are provided, in each of which the observation variance is estimated as zero. In the context of an extended case study involving data on British Grey herons, we consider alternative approaches for dealing with the problem when it occurs. In particular, we consider penalised likelihood, a method based on fitting splines and a method of pseudo-replication, which is undertaken via a simple bootstrap procedure. For the case study of the paper, it is shown that when it occurs, an estimate of zero observation variance is unimportant for inference relating to the model parameters of primary interest. This unexpected finding is supported by a simulation study

Methods for joint inference from panel survey and demographic data

A number of methods for joint inference from animal abundance and demographic data have been proposed in recent years, each with its own advantages. A new approach to analyzing panel survey and demographic data simultaneously is described. The approach fits population-dynamics models to the survey data, rather than to a single index of abundance derived from them and thus avoids disadvantages inherent ill analyzing such an index. The methodology is developed and illustrated with British Lapwing data, and the results are compared with those obtained from existing approaches. The estimates of demographic parameters and population indices are similar for all methods. The results of a simulation study show that the new method performs well in terms of mean squared error

A comparative simulation study of wavelet shrinkage estimators for Poisson counts

Using computer simulations, the finite sample performance of a number of classical and Bayesian wavelet shrinkage estimators for Poisson counts is examined. For the purpose of comparison, a variety of intensity functions, background intensity levels, sample sizes, primary resolution levels, wavelet filters and performance criteria are employed. A demonstration is given of the use of some of the estimators to analyse a data set arising in high-energy astrophysics. Following the philosophy of reproducible research, the MATLAB programs and real-life data example used in this study are made freely available

Efficient and robust estimation for the one-sided stable distribution of index

We show how the empirical Laplace transform provides a simple estimation procedure for the one-sided stable distribution of index that is both efficient and robust.Empirical transform Influence function Laplace transform Robustness Stable law Transform variable selection

Integrated Squared Error Estimation of Cauchy Parameters

We show that integrated squared error estimation of the parameters of a Cauchy distribution, based on the empirical characteristic function, is simple, robust and efficient. The k-L estimator of Koutrouvelis (Biometrika 69 (1982) 205) is more difficult to use, less robust and at best only marginally more efficient. (C) 2001 Elsevier Science B.V. All rights reserved

Integrated squared error estimation of normal mixtures

Based on the empirical characteristic function, the integrated squared error criterion for normal mixtures is shown to have a simple form for a particular weight function. When the parameter of that function is chosen as the smoothed cross-validation selector in kernel density estimation, the estimator which minimises the criterion is shown to perform well in a simulation study. In comparison with maximum likelihood and a new recently proposed method there are better bias and standard deviation results for the method of this paper. Furthermore, the new estimator is less likely to fail and is appreciably more robust

Efficient and robust estimation for the one-sided stable distribution of index (1)-(2)

We show how the empirical Laplace transform provides a simple estimation procedure for the one-sided stable distribution of index 1/2 that is both efficient and robust