Estimation theory

Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements. In estimation theory, two approaches are generally considered: The probabilistic approach (described in this article) assumes that the measured data is random with probability distribution dependent on the parameters of interest The set-membership approach assumes that the measured data vector belongs to a set which depends on the parameter vector. For example, it is desired to estimate the proportion of a population of voters who will vote for a particular candidate. That proportion is the parameter sought; the estimate is based on a small random sample of voters. Alternatively, it is desired to estimate the probability of a voter voting for a particular candidate, based on some demographic features, such as age. Or, for example, in radar the aim is to find the range of objects (airplanes, boats, etc.) by analyzing the two-way transit timing of received echoes of transmitted pulses. Since the reflected pulses are unavoidably embedded in electrical noise, their measured values are randomly distributed, so that the transit time must be estimated. As another example, in electrical communication theory, the measurements which contain information regarding the parameters of interest are often associated with a noisy signal. For a given model, several statistical "ingredients" are needed so the estimator can be implemented. The first is a statistical sample – a set of data points taken from a random vector (RV) of size N. Put into a vector, Secondly, there are M parameters whose values are to be estimated.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (20)

Related people (13)

Related concepts (81)

Related courses (69)

Related lectures (749)

Related MOOCs (2)

A Functional Perspective on Information Measures

Amedeo Roberto Esposito

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a proble

EPFL2022

Statistical Emulation of Neural Simulators: Application to Neocortical L2/3 Large Basket Cells

Werner Alfons Hilda Van Geit, Idan Segev, Oren Amsalem

Many scientific systems are studied using computer codes that simulate the phenomena of interest. Computer simulation enables scientists to study a broad range of possible conditions, generating large

FRONTIERS MEDIA SA2022

A Modular Workflow for Model Building, Analysis, and Parameter Estimation in Systems Biology and Neuroscience

Daniel Keller, Andrii Stepaniuk

Neuroscience incorporates knowledge from a range of scales, from single molecules to brain wide neural networks. Modeling is a valuable tool in understanding processes at a single scale or the interac

HUMANA PRESS INC2021

Estimation theory

Wiener filter

In signal processing, the Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant (LTI) filtering of an observed noisy process, assuming known stationary signal and noise spectra, and additive noise. The Wiener filter minimizes the mean square error between the estimated random process and the desired process. The goal of the Wiener filter is to compute a statistical estimate of an unknown signal using a related signal as an input and filtering that known signal to produce the estimate as an output.

Detection theory

Detection theory or signal detection theory is a means to measure the ability to differentiate between information-bearing patterns (called stimulus in living organisms, signal in machines) and random patterns that distract from the information (called noise, consisting of background stimuli and random activity of the detection machine and of the nervous system of the operator). In the field of electronics, signal recovery is the separation of such patterns from a disguising background.

Selected Topics on Discrete Choice

Discrete choice models are used extensively in many disciplines where it is important to predict human behavior at a disaggregate level. This course is a follow up of the online course “Introduction t

Selected Topics on Discrete Choice

FIN-414: Optimization methods

This course presents the problem of static optimization, with and without (equality and inequality) constraints, both from the theoretical (optimality conditions) and methodological (algorithms) point

MATH-442: Statistical theory

The course aims at developing certain key aspects of the theory of statistics, providing a common general framework for statistical methodology. While the main emphasis will be on the mathematical asp

MATH-342: Time series

A first course in statistical time series analysis and applications.

Proof for Rademacher Control MATH-412: Statistical machine learning

Presents a proof for Rademacher control of the expected estimation error, focusing on empirical process control.

Estimating R: Marginal and Conditional Distributions MATH-233: Probability and statistics

Covers the estimation of R using bivariate normal distributions and explores the marginal and conditional distributions of X₁ and X₂.

Recursive Least Squares ENV-548: Sensor orientation

Covers the Recursive Least Squares method for parameter estimation based on observation equations and design matrices.