Abundance estimation with a categorical covariate subject to missing in continuous-time capture-recapture studies

Abstract

In continuous-time capture-recapture experiments, individual heterogeneity has a large effect on the capture probability. To account for the heterogeneity, we consider an individual covariate, which is categorical and subject to missing. In this article, we develop a general model to summarize three kinds of missing mechanisms, and propose a maximum likelihood estimator of the abundance. A likelihood ratio confidence interval of the abundance is also proposed. We illustrate the proposed methods by simulation studies and a real data example of a bird species prinia subflava in Hong Kong.     

Inference in Semi‐Parametric Dynamic Models for Repeated Count Data

This paper deals with a longitudinal semi‐parametric regression model in a generalised linear model setup for repeated count data collected from a large number of independent individuals. To accommodate the longitudinal correlations, we consider a dynamic model for repeated counts which has decaying auto‐correlations as the time lag increases between the repeated responses. The semi‐parametric regression function involved in the model contains a specified regression function in some suitable time‐dependent covariates and a non‐parametric function in some other time‐dependent covariates. As far as the inference is concerned, because the non‐parametric function is of secondary interest, we estimate this function consistently using the independence assumption‐based well‐known quasi‐likelihood approach. Next, the proposed longitudinal correlation structure and the estimate of the non‐parametric function are used to develop a semi‐parametric generalised quasi‐likelihood approach for consistent and efficient estimation of the regression effects in the parametric regression function. The finite sample performance of the proposed estimation approach is examined through an intensive simulation study based on both large and small samples. Both balanced and unbalanced cluster sizes are incorporated in the simulation study. The asymptotic performances of the estimators are given. The estimation methodology is illustrated by reanalysing the well‐known health care utilisation data consisting of counts of yearly visits to a physician by 180 individuals for four years and several important primary and secondary covariates.     

Nonparametric Estimation of the Number of Drug Users in Hong Kong Using Repeated Multiple Lists

We update a previous approach to the estimation of the size of an open population when there are multiple lists at each time point. Our motivation is 35 years of longitudinal data on the detection of drug users by the Central Registry of Drug Abuse in Hong Kong. We develop a two‐stage smoothing spline approach. This gives a flexible and easily implemented alternative to the previous method which was based on kernel smoothing. The new method retains the property of reducing the variability of the individual estimates at each time point. We evaluate the new method by means of a simulation study that includes an examination of the effects of variable selection. The new method is then applied to data collected by the Central Registry of Drug Abuse. The parameter estimates obtained are compared with the well known Jolly–Seber estimates based on single capture methods.     

Robust Smoothed Rank Estimation Methods for Accelerated Failure Time Model Allowing Clusters

Smoothed Gehan rank estimation methods are widely used in accelerated failure time (AFT) models with/without clusters. However, most methods are sensitive to outliers in the covariates. In order to solve this problem, we propose robust approaches based on the smoothed Gehan rank estimation methods for the AFT model, allowing for clusters by employing two different weight functions. Simulation studies show that the proposed methods outperform existing smoothed rank estimation methods regarding their biases and standard deviations when there are outliers in the covariates. The proposed methods are also applied to a real dataset from the “Major cardiovascular interventions” study.     

Probability Generating Function Based Jeffrey's Divergence for Statistical Inference

Statistical inference procedures based on transforms such as characteristic function and probability generating function have been examined by many researchers because they are much simpler than probability density functions. Here, a probability generating function based Jeffrey's divergence measure is proposed for parameter estimation and goodness-of-fit test. Being a member of the M-estimators, the proposed estimator is consistent. Also, the proposed goodness-of-fit test has good statistical power. The proposed divergence measure shows improved performance over existing probability generating function based measures. Real data examples are given to illustrate the proposed parameter estimation method and goodness-of-fit test.     

Bayesian Conditional Mean Estimation in Log‐Normal Linear Regression Models with Finite Quadratic Expected Loss

Log‐normal linear regression models are popular in many fields of research. Bayesian estimation of the conditional mean of the dependent variable is problematic as many choices of the prior for the variance (on the log‐scale) lead to posterior distributions with no finite moments. We propose a generalized inverse Gaussian prior for this variance and derive the conditions on the prior parameters that yield posterior distributions of the conditional mean of the dependent variable with finite moments up to a pre‐specified order. The conditions depend on one of the three parameters of the suggested prior; the other two have an influence on inferences for small and medium sample sizes. A second goal of this paper is to discuss how to choose these parameters according to different criteria including the optimization of frequentist properties of posterior means.     

Visualization for Large‐scale Gaussian Updates

In geostatistics and also in other applications in science and engineering, it is now common to perform updates on Gaussian process models with many thousands or even millions of components. These large‐scale inferences involve modelling, representational and computational challenges. We describe a visualization tool for large‐scale Gaussian updates, the ‘medal plot’. The medal plot shows the updated uncertainty at each observation location and also summarizes the sharing of information across observations, as a proxy for the sharing of information across the state vector (or latent process). As such, it reflects characteristics of both the observations and the statistical model. We illustrate with an application to assess mass trends in the Antarctic Ice Sheet, for which there are strong constraints from the observations and the physics.