Using a Chen-Stein identity to obtain low variance simulation estimators

This paper is concerned with developing low variance simulation estimators of probabilities related to the sum of Bernoulli random variables. It shows how to utilize an identity used in the Chen-Stein approach to bounding Poisson approximations to obtain low variance estimators. Applications and numerical examples in such areas as pattern occurrences, generalized coupon collecting, system reliability, and multivariate normals are presented. We also consider the problem of estimating the probability that a positive linear combination of Bernoulli random variables is greater than some specified value, and present a simulation estimator that is always less than the Markov inequality bound on that probability.

The Estimation of Finite Population Variance Under Stratified Sampling Technique

The efficiency of the study variable can be improved by incorporating the information from the known auxiliary variables. Usually two techniques ratio and regression estimation are used with the help of auxiliary information in different approaches to acquire the high precision of the estimators. Considering the very heterogeneous population to get the size of the sample it may be originating impossible to get a sufficiently accurate and precise estimate by taking the simple random sampling technique from the complete population. Occasionally taking sample issue may differ significantly in different part of the entire population. For example, under study population consists of people living in apartments, own homes, hospitals and prisons or people living in plain regions and hill regions so in such situations the stratified sampling is one of the most commonly used approach to get a representative sample in survey sampling from different cross units of the population. The present study is set out on the recommendation of generalized variance estimators for finite population variance incorporating stratified sampling scheme with the information of single and two transformed auxiliary variables. The expressions of bias and mean square error (MSE) are obtained for the advised exponential type estimators. The conditions are obtained for which the anticipated estimators are better than the usual estimator. An empirical and simulation study is conducted to prove the superiority of the recommended estimator.

Robust Error Estimation Based on Factor-Graph Models for Non-Line-of-Sight Localization

This paper presents a method to estimate the covariances of the inputs in a factor-graph formulation for localization under non-line-of-sight conditions. A general solution, based on covariance estimation and M estimators in linear regression problems, is presented that is shown to give unbiased estimators of multiple variances and are robust against outliers. An iteratively re-weighted least squares (IRLS) algorithm is proposed to jointly compute the proposed variance estimators and the state estimates for the non-linear factor graph optimization. The efficacy of the method is illustrated in a simulation study using a robot localization problem under various process and measurement models and measurement outlier scenarios. A case study involving a Global Positioning System (GPS) based localization in an urban environment and data containing multipath problems demonstrates the application of the proposed technique.

L-Moments and Calibration-Based Estimators for Variance Parameter

The subject of variance estimation is one of the most important topics in statistics. It has been clarified by many different research studies due to its various applications in the human and natural sciences. Different variance estimators are built based on traditional moments that are especially influenced by the existence of extreme values. In this paper, with the presence of extreme values, we proposed some new calibration estimators for variance based on L-moments under double-stratified random sampling. A simulation study with COVID-19 data is performed to evaluate the efficiency of the proposed estimators. All results indicate that the proposed estimators are often superior and highly efficient compared to the existing traditional estimator.

A flexible point and variance estimator to assess bird/bat fatality from carcass searches

Estimation of bird and bat fatalities due to collision with anthropogenic structures (such as power lines or wind turbines) is an important ecological issue. However, searching for collision victims usually only detects a proportion of the true number of collided individuals. Various mortality estimators have previously been proposed to correct for this incomplete detection, based on regular carcass searches and additional field experiments. However, each estimator implies specific assumptions/restrictions, which may easily be violated in practice. In this study, we extended previous approaches and developed a versatile algorithm to compute point and variance estimates for true carcass numbers. The presented method allows for maximal flexibility in the data structure. Using simulated data, we showed that our point and variance estimators ensured unbiased estimates under various challenging data conditions. The presented method may improve the estimation of true collision numbers, as an important pre-condition for calculating collision rates and evaluating measures to reduce collision risks, and may thus provide a basis for management decisions and/or compensation actions with regard to planned or existing wind turbines and power lines.

Comparison of Variance Estimators for Systematic Environmental Sample Surveys: Considerations for Post-Stratified Estimation

The estimation of the sampling variance of point estimators under two-dimensional systematic sampling designs remains a challenge, and several alternative variance estimators have been proposed in the past few decades. In this work, we compared six alternative variance estimators under Horvitz-Thompson (HT) and post-stratification (PS) point estimation regimes. We subsampled a multitude of species-specific forest attributes from a large, spatially balanced national forest inventory to compare the variance estimators. A variance estimator that assumes a simple random sampling design exhibited positive relative bias under both HT and PS point estimation regimes ranging between 1.23 to 1.88 and 1.11 to 1.78 for HT and PS, respectively. Alternative estimators reduced this positive bias with relative biases ranging between 1.01 to 1.66 and 0.90 to 1.64 for HT and PS, respectively. The alternative estimators generally obtained improved efficiencies under both HT and PS, with relative efficiency values ranging between 0.68 to 1.28 and 0.68 to 1.39, respectively. We identified two estimators as promising alternatives that provide clear improvements over the simple random sampling estimator for a wide variety of attributes and under HT and PS estimation regimes.