Exact Simulation for Diffusion Bridges: An Adaptive Approach

Exact simulation approaches for a class of diffusion bridges have recently been proposed based on rejection sampling techniques. The existing rejection sampling methods may not be practical owing to small acceptance probabilities. In this paper we propose an adaptive approach that improves the existing methods significantly under certain scenarios. The idea of the new method is based on a layered process, which can be simulated from a layered Brownian motion with reweighted layer probabilities. We will show that the new exact simulation method is more efficient than existing methods theoretically and via simulation

A Review on the Exact Monte Carlo Simulation

Perfect Monte Carlo sampling refers to sampling random realizations exactly from the target distributions (without any statistical error). Although many different methods have been developed and various applications have been implemented in the area of perfect Monte Carlo sampling, it is mostly referred by researchers to coupling from the past (CFTP) which can correct the statistical errors for the Monte Carlo samples generated by Markov chain Monte Carlo (MCMC) algorithms. This paper provides a brief review on the recent developments and applications in CFTP and other perfect Monte Carlo sampling methods

Mean Empirical Likelihood

Empirical likelihood methods are widely used in different settings to construct the confidence regions for parameters which satisfy the moment constraints. However, the empirical likelihood ratio confidence regions may have poor accuracy, especially for small sample sizes and multi-dimensional situations. A novel Mean Empirical Likelihood (MEL) method is proposed. A new pseudo dataset using the means of observation values is constructed to define the empirical likelihood ratio and it is proved that this MEL ratio satisfies Wilks’ theorem. Simulations with different examples are given to assess its finite sample performance, which shows that the confidence regions constructed by Mean Empirical Likelihood are much more accurate than that of the other Empirical Likelihood methods

Linear transformation models for censored data under truncation

In many observational cohort studies, a pair of correlated event times are usually observed for each individual. This paper develops a new approach for the semiparametric linear transformation model to handle the bivariate survival data under both truncation and censoring. By incorporating truncation, the potential referral bias in practice is taken into account. A class of generalised estimating equations are proposed to obtain unbiased estimates of the regression parameters. Large sample properties of the proposed estimator are provided. Simulation studies under different scenarios and analyses of real-world datasets are conducted to assess the performance of the proposed estimator

Efficient Empirical Likelihood Inference for recovery rate of COVID-19 under Double-Censoring

Doubly censored data are very common in epidemiology studies. Ignoring censorship in the analysis may lead to biased parameter estimation. In this paper, we highlight that the publicly available COVID19 data may involve high percentage of double-censoring and point out the importance of dealing with such missing information in order to achieve better forecasting results. Existing statistical methods for doubly censored data may suffer from the convergence problems of the EM algorithms or may not be good enough for small sample sizes. This paper develops a new empirical likelihood method to analyse the recovery rate of COVID19 based on a doubly censored dataset. The efficient influence function of the parameter of interest is used to define the empirical likelihood (EL) ratio. We prove that $-2\log$(EL-ratio) asymptotically follows a standard $\chi^2$ distribution. This new method does not require any scale parameter adjustment for the log-likelihood ratio and thus does not suffer from the convergence problems involved in traditional EM-type algorithms. Finite sample simulation results show that this method provides much less biased estimate than existing methods, when censoring percentage is large. The method application to the COVID19 data will help researchers in other field to achieve better estimates and forecasting results

Empirical Likelihood Based on Synthetic Right Censored Data

In this paper, we develop a Mean Empirical Likelihood (MeanEL) method for right censored data. This MeanEL approach is based on traditional empirical likelihood methods but uses synthetic data to construct an EL ratio statistics, which is shown to have a $\chi^2$ limiting distribution. Different simulation studies show that the MeanEL confidence intervals tend to have more accurate coverage probabilities than other existing Empirical Likelihood methods. Theoretical comparisons of different EL methods are also provided under a general framework