Unbiased simulation of rare events in continuous time

Best linear unbiased estimators in continuous time regression models

In this paper the problem of best linear unbiased estimation is investigated for continuous-time regression models. We prove several general statements concerning the explicit form of the best linear unbiased estimator (BLUE), in particular when the error process is a smooth process with one or several derivatives of the response process available for construction of the estimators. We derive the explicit form of the BLUE for many specific models including the cases of continuous autoregressive errors of order two and integrated error processes (such as integrated Brownian motion). The results…

On the Non-Existence of Unbiased Estimators in Constrained Estimation Problems

We address the problem of existence of unbiased constrained parameter estimators. We show that if the constrained set of parameters is compact and the hypothesized distributions are absolutely continuous with respect to one another, then there exists no unbiased estimator. Weaker conditions for the absence of unbiased constrained estimators are also specified. We provide several examples which demonstrate the utility of these conditions.

Nearly unbiased variable selection under minimax concave penalty

We propose MC+, a fast, continuous, nearly unbiased and accurate method of penalized variable selection in high-dimensional linear regression. The LASSO is fast and continuous, but biased. The bias of the LASSO may prevent consistent variable selection. Subset selection is unbiased but computationally costly. The MC+ has two elements: a minimax concave penalty (MCP) and a penalized linear unbiased selection (PLUS) algorithm. The MCP provides the convexity of the penalized loss in sparse regions to the greatest extent given certain thresholds for variable selection and unbiasedness. The PLUS co…

单参数指数族中自然参数倒数的无偏估计及其推广

Unbiased estimation in one-parameter exponential families for the inverse of the natural parameter with extensions

本文研究单参数连续指数族中自然参数倒数的无偏估计，给出多类模型应用，并推广至负幂及完全单调函数的估计。

Estimating migration proportions from discretely observed continuous diffusion processes

We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution cumulants. We use the non - uniform distribution of the observation time intervals to obtain consistent and unbiased estimators for these parameters. Closed form expressions for migration proportions between spatial domains are derived as functions of these parameters. The models are applied to estimate migration patterns from satellite tag data.

使用欠阻尼 Langevin 动力学的无偏估计

Unbiased Estimation using Underdamped Langevin Dynamics

本文提出一种基于双重随机化估计和欠阻尼 Langevin 动力学离散版本的无偏估计方法，以消除离散化与有限迭代偏差，并证明其方差和成本性质。