**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Concept# Wald test

Summary

In statistics, the Wald test (named after Abraham Wald) assesses constraints on statistical parameters based on the weighted distance between the unrestricted estimate and its hypothesized value under the null hypothesis, where the weight is the precision of the estimate. Intuitively, the larger this weighted distance, the less likely it is that the constraint is true. While the finite sample distributions of Wald tests are generally unknown, it has an asymptotic χ2-distribution under the null hypothesis, a fact that can be used to determine statistical significance.
Together with the Lagrange multiplier test and the likelihood-ratio test, the Wald test is one of three classical approaches to hypothesis testing. An advantage of the Wald test over the other two is that it only requires the estimation of the unrestricted model, which lowers the computational burden as compared to the likelihood-ratio test. However, a major disadvantage is that (in finite samples) it is not invariant to changes in the representation of the null hypothesis; in other words, algebraically equivalent expressions of non-linear parameter restriction can lead to different values of the test statistic. That is because the Wald statistic is derived from a Taylor expansion, and different ways of writing equivalent nonlinear expressions lead to nontrivial differences in the corresponding Taylor coefficients. Another aberration, known as the Hauck–Donner effect, can occur in binomial models when the estimated (unconstrained) parameter is close to the boundary of the parameter space—for instance a fitted probability being extremely close to zero or one—which results in the Wald test no longer monotonically increasing in the distance between the unconstrained and constrained parameter.
Under the Wald test, the estimated that was found as the maximizing argument of the unconstrained likelihood function is compared with a hypothesized value . In particular, the squared difference is weighted by the curvature of the log-likelihood function.

Official source

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 (34)

Related people (11)

Related concepts (5)

Related courses (10)

Related lectures (35)

Score test

In statistics, the score test assesses constraints on statistical parameters based on the gradient of the likelihood function—known as the score—evaluated at the hypothesized parameter value under the null hypothesis. Intuitively, if the restricted estimator is near the maximum of the likelihood function, the score should not differ from zero by more than sampling error. While the finite sample distributions of score tests are generally unknown, they have an asymptotic χ2-distribution under the null hypothesis as first proved by C.

Chi-squared test

A chi-squared test (also chi-square or χ2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily used to examine whether two categorical variables (two dimensions of the contingency table) are independent in influencing the test statistic (values within the table). The test is valid when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants thereof.

Maximum likelihood estimation

In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.

BIO-449: Understanding statistics and experimental design

This course is neither an introduction to the mathematics of statistics nor an introduction to a statistics program such as R. The aim of the course is to understand statistics from its experimental d

MATH-562: Statistical inference

Inference from the particular to the general based on probability models is central to the statistical method. This course gives a graduate-level account of the main ideas of statistical inference.

Despite the large body of academic work on machine learning security, little is known about the occurrence of attacks on machine learning systems in the wild. In this paper, we report on a quantitative study with 139 industrial practitioners. We analyze at ...

Anthony Christopher Davison, Timmy Rong Tian Tse

Universal inference enables the construction of confidence intervals and tests without regularity conditions by splitting the data into two parts and appealing to Markov's inequality. Previous investigations have shown that the cost of this generality is a ...

Maximum Likelihood Estimation: Multivariate Statistics

Explores maximum likelihood estimation and multivariate hypothesis testing, including challenges and strategies for testing multiple hypotheses.

Likelihood Ratio Test: Hypothesis Testing

Covers the Likelihood Ratio Test and hypothesis testing methods using Maximum Likelihood Estimators.

Hypothesis Testing: Wilks' Theorem and P-Value

Explores hypothesis testing, Wilks' theorem, p-values, confidence intervals, and pivotal quantities.

Véronique Michaud, Baris Çaglar, Christophe Lopez

This paper reports the results of an international benchmark exercise on the measurement of fibre bed compaction behaviour. The aim was to identify aspects of the test method critical to obtain reliable results and to arrive at a recommended test procedure ...

2021