An estimator is said to be unbiased if b(θ̂) = 0. If multiple unbiased estimates of θ are available, and the estimators can be averaged to reduce the variance, leading to the true parameter θ as more observations are available. Placing the unbiased restriction on the estimator simplifies the MSE minimization to depend only on its variance. The resulting estimator, called the Minimum Variance Unb...

We present an in-depth analysis of the sources variance in state-of-the-art unbiased volumetric transmittance estimators, and propose several new methods for improving their efficiency. These combine to produce a single estimator that is universally optimal relative prior work, with up orders magnitude lower at same cost, has zero any ray non-varying extinction. first reduce truncated power-ser...

In statistical inference, the point estimation problem is very crucial and has a wide range of applications. When, we deal with some concepts such as random variables, the parameters of interest and estimates may be reported/observed as imprecise. Therefore, the theory of fuzzy sets plays an important role in formulating such situations. In this paper, we rst recall the crisp uniformly minimum ...

because S is “unbiased” and T 2 is “biased.” That means E(S) = σ 6= E(T ), i.e., an “unbiased estimator” is a statistic whose expected value is the quantity to be estimated. The goodness of an estimator is sometimes measured by the smallness of its “mean squared error,” defined as E ( ([estimator]− [quantity to be estimated]) ) . By that criterion the biased estimator T 2 would be better than t...

In this paper we derive some unbiased estimators of the population mean under simple inverse sampling with replacement, using the class of Hansen-Hurwitz and Horvitz-Thompson type estimators and the post-stratification approach. We also compare the efficiency of resulting estimators together with Murthy's estimator. We show that in despite of general belief, the strategy consisting of inverse s...

Extended Abstract. It is a traditional way in biological, sociological, agricultural and geological studies to partition a geographical area into quadrats and then take a sample of them by a particular sampling design. We study the relevant characteristic of quadrats to estimate a parameter of the population. We suppose that the variable of interest has a positive spatial autocorrelation. Sampl...

This module motivates and introduces the minimum variance unbiased estimator (MVUE). This is the primary criterion in the classical (frequentist) approach to parameter estimation. We introduce the concepts of mean squared error (MSE), variance, bias, unbiased estimators, and the bias-variance decomposition of the MSE. The Minimum Variance Unbiased Estimator 1 In Search of a Useful Criterion In ...