What is estimation bias

We start by considering parameters and statistics. We consider random variables from a known type of distribution, but with an unknown parameter in this distribution. This parameter made be part of a population, or it could be part of a probability density function. We also have a function of our random variables, and this is called a statistic. The statistic X 1 , X 2 ,. We now define unbiased and biased estimators. We want our estimator to match our parameter, in the long run.

In more precise language we want the expected value of our statistic to equal the parameter. If this is the case, then we say that our statistic is an unbiased estimator of the parameter.

If an estimator is not an unbiased estimator, then it is a biased estimator. Although a biased estimator does not have a good alignment of its expected value with its parameter, there are many practical instances when a biased estimator can be useful. One such case is when a plus four confidence interval is used to construct a confidence interval for a population proportion. To see how this idea works, we will examine an example that pertains to the mean. The statistic. When we calculate the expected value of our statistic, we see the following:.

Since the expected value of the statistic matches the parameter that it estimated, this means that the sample mean is an unbiased estimator for the population mean. Actively scan device characteristics for identification. Use precise geolocation data. In our daily lives, we tend to employ various types of estimators without even realizing it. Following are some types of estimators that we commonly use:.

In this case, you are likely to get an interval estimate of the price, instead of a point estimate. You estimate the efforts needed to complete your next home improvement project using some estimation technique such as the Work Breakdown Structure.

You ask an odd number of your friends, who they think will win the next election, and you accept the majority result. In statistical modeling, the mean, especially the mean of the population , is a fundamental parameter that is often estimated. Following is a data set of surface temperatures in the North Eastern Atlantic ocean at a certain time of year:. This data set contains many missing readings. Which estimator should we use? But then, so do the first two! In any case, this is probably a good point to understand a bit more about the concept of bias.

Suppose you are shooting basketballs. While some balls make it through the net, you find that most of your throws are hitting a point below the hoop. In this case, whatever technique you are using to estimate the correct angle and speed of the throw is underestimating the unknown correct values of angle and speed.

Your estimator has a negative bias. With practice, your throwing technique improves, and you are able to dunk more often. And from a bias perspective, you begin overshooting the basket approximately just as often as undershooting it. In the second figure, the bias has undoubtedly reduced because of a more uniform spreading out of the missed shots, but that has also lead to a higher spread, a.

The first technique appears to have a larger bias and a smaller variance and it is vice versa for the second technique. This is no coincidence and it can be easily proved in fact, we will prove it later! We can see that the location of the basket orange dot at the center of the two figures is a proxy for the unknown population mean for the angle of throw and speed of throw that will guarantee a dunk.

Any mean -unbiased minimum-variance estimator minimizes the risk expected loss with respect to the squared-error loss function , as observed by Gauss.

Note that, when a transformation is applied to a mean-unbiased estimator, the result need not be a mean-unbiased estimator of its corresponding population statistic. That is, for a non-linear function f and a mean-unbiased estimator U of a parameter p , the composite estimator f U need not be a mean-unbiased estimator of f p. For example, the square root of the unbiased estimator of the population variance is not a mean-unbiased estimator of the population standard deviation.

Normal bell curve - Poisson - Bernoulli. Confounding variable - Pearson product-moment correlation coefficient - Rank correlation Spearman's rank correlation coefficient , Kendall tau rank correlation coefficient. Linear regression - Nonlinear regression - Logistic regression.

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Recent Blogs Community portal forum. Register Don't have an account? Bias of an estimator. Edit source History Talk 0. For other uses in statistics, see Bias statistics. Romano and A. Cancel Save.