Accuracy Of Variance Estimates Research Articles

Variance estimation of the risk difference when using propensity-score matching and weighting with time-to-event outcomes.

Observational studies are increasingly being used in medicine to estimate the effects of treatments or exposures on outcomes. To minimize the potential for confounding when estimating treatment effects, propensity score methods are frequently implemented. Often outcomes are the time to event. While it is common to report the treatment effect as a relative effect, such as the hazard ratio, reporting the effect using an absolute measure of effect is also important. One commonly used absolute measure of effect is the risk difference or difference in probability of the occurrence of an event within a specified duration of follow-up between a treatment and comparison group. We first describe methods for point and variance estimation of the risk difference when using weighting or matching based on the propensity score when outcomes are time-to-event. Next, we conducted Monte Carlo simulations to compare the relative performance of these methods with respect to bias of the point estimate, accuracy of variance estimates, and coverage of estimated confidence intervals. The results of the simulation generally support the use of weighting methods (untrimmed ATT weights and IPTW) or caliper matching when the prevalence of treatment is low for point estimation. For standard error estimation the simulation results support the use of weighted robust standard errors, bootstrap methods, or matching with a naïve standard error (i.e., Greenwood method). The methods considered in the article are illustrated using a real-world example in which we estimate the effect of discharge prescribing of statins on patients hospitalized for acute myocardial infarction.

On variance of sample matrix eigenvalue

The variance of a matrix eigenvalue estimator is considered. This estimator is a function of simple random sample variances and covariances of a multidimensional random variable whose distribution is not necessarily normal. The variance of the eigenvalue estimator is approximated based on the Taylor expansion for a function of simple random sample moments. A method for approximating the variance of the canonical correlation estimator is also proposed. A simulation analysis of the accuracy of variance estimation is presented. The considered approximation of variance can be applied to assessing the variance of a statistic which is the solution of any implicit interdependence functions of sample moments.

Randomized response estimation in multiple frame surveys

ABSTRACTLarge-scale surveys are increasingly delving into sensitive topics such as gambling, alcoholism, drug use, sexual behaviour and domestic violence. Sensitive, stigmatizing or even incriminating themes are difficult to investigate by using standard data-collection techniques since respondents are generally reluctant to release information concerning their personal sphere. Furthermore, such topics usually pertain elusive population (e.g. irregular immigrants and homeless, alcoholics, drug users, rape and sexual assault victims) which are difficult to sample since not adequately covered in a single sampling frame. On the other hand, researchers often utilize more than one data-collection mode (i.e. mixed-mode surveys) in order to increase response rates and/or improve coverage of the population of interest. Surveying sensitive and elusive populations and mixed-mode researches are strictly connected with multiple frame surveys which are becoming widely used to decrease bias due to undercoverage of the target population. In this work, we combine sensitive research and multiple frame surveys. In particular, we consider statistical techniques for handling sensitive data coming from multiple frame surveys using complex sampling designs. Our aim is to estimate the mean of a sensitive variable connected to undesirable behaviours when data are collected by using the randomized response theory. Some estimators are constructed and their properties theoretically investigated. Variance estimation is also discussed by means of the jackknife technique. Finally, a Monte Carlo simulation study is conducted to evaluate the performance of the proposed estimators and the accuracy of variance estimation.

The largest Cramer-Rao lower bound for variance estimation of acoustic signals

The Cramer-Rao Lower Bounds (CRLBs) for variance estimation of acoustic signals is discussed. The CRLB expresses the lower limit of the variance of estimation errors of an unbiased estimator. It is empirically known that the accuracy of variance estimation is improved as the signal length is long because the CRLB for variance estimation is inverse proportion to the length of a signal. Therefore, when the variance of estimation errors is desired to be lower than a certain value, the signal length must be longer than the length that is determined by the CRLB. If the distribution of a signal is known, the CRLB can be easily formulated. In practice, however, acoustic signals follow various distributions and they are unknown in advance. In our research, we focus on the distribution that gives the largest CRLB for variance estimation. In order to find such a distribution, we compare the CRLBs for variance estimation using various signal models. Our results conclude that the Gaussian distribution gives the largest CRLB for variance estimation.

Bootstrap Algorithms for Risk Models with Auxiliary Variable and Complex Samples

Resampling methods are often invoked in risk modelling when the stability of estimators of model parameters has to be assessed. The accuracy of variance estimates is crucial since the operational risk management affects strategies, decisions and policies. However, auxiliary variables and the complexity of the sampling design are seldom taken into proper account in variance estimation. In this paper bootstrap algorithms for finite population sampling are proposed in presence of an auxiliary variable and of complex samples. Results from a simulation study exploring the empirical performance of some bootstrap algorithms are presented.

Numerical problems connected with accuracy of variance estimation

A very efficient algorithm for calculating the variance of an estimator of the variance of an estimator of the population total of a finite population, under simple random sampling without replacement, is proposed in the paper.