## A (1986) Robust Statistics. The Approach Based on Influence Functions

- R Hampel F, M Ronchetti E, J Rousseeuw P, W Stahel
- 1986

- Published 2009

1 Scope of the Chapter This chapter deals with the estimation of unknown arguments of a univariate distribution. It includes both point and interval estimation using maximum likelihood and robust methods. 2 Background to the Problems Statistical inference is concerned with the making of inferences about a population using the observed part of the population called a sample. The population can usually be described using a probability model which will be written in terms of some unknown parameters. For example, the hours of relief given by a drug may be assumed to follow a Normal distribution with mean and variance 2 ; it is then required to make inferences about the arguments, and 2 , on the basis of an observed sample of relief times. There are two main aspects of statistical inference: the estimation of the arguments and the testing of hypotheses about the arguments. In the example above, the values of the argument 2 may be estimated and the hypothesis that ! 3 tested. This chapter is mainly concerned with estimation but the test of a hypothesis about an argument is often closely linked to its estimation. Tests of hypotheses which are not linked closely to estimation are given in the chapter on nonparametric statistics (Chapter g08). There are two types of estimation to be considered in this chapter: point estimation and interval estimation. Point estimation is when a single value is obtained as the best estimate of the argument. However, as this estimate will be based on only one of a large number of possible samples, it can be seen that if a different sample were taken, a different estimate would be obtained. The distribution of the estimate across all the possible samples is known as the sampling distribution. The sampling distribution contains information on the performance of the estimator, and enables estimators to be compared. For example, a good estimator would have a sampling distribution with mean equal to the true value of the argument; that is, it should be an unbiased estimator; also the variance of the sampling distribution should be as small as possible. When considering an argument estimate it is important to consider its variability as measured by its variance, or more often the square root of the variance, the standard error. The sampling distribution can be used to find interval estimates or confidence intervals for the argument. A confidence interval is an …

@inproceedings{2009NAGLC,
title={NAG Library Chapter Introduction g 07 – Univariate Estimation},
author={},
year={2009}
}