相关论文: On likelihood ratio tests

Parametric inference posits a statistical model that is a specified family of probability distributions. Restricted inference, e.g., restricted likelihood ratio testing, attempts to exploit the structure of a statistical submodel that is a…

We consider whether the asymptotic distributions for the log-likelihood ratio test statistic are expected to be Gaussian or chi-squared. Two straightforward examples provide insight on the difference.

The modes of a statistical population are high frequency points around which most of the probability mass is accumulated. For the particular case of circular densities, we address the problem of testing if, given an observed sample of a…

We connect the power of Confidence Intervals in different Frequentist methods to their reliability. We show that in the case of a bounded parameter a biased method which near the boundary has large power in testing the parameter against…

The likelihood ratio test is widely used in exploratory factor analysis to assess the model fit and determine the number of latent factors. Despite its popularity and clear statistical rationale, researchers have found that when the…

This paper studies the least upper bounds on coverage probabilities of the empirical likelihood ratio confidence regions based on estimating equations. The implications of the bounds on empirical likelihood inference are also discussed.

This paper reviews the most common situations where one or more regularity conditions which underlie classical likelihood-based parametric inference fail. We identify three main classes of problems: boundary problems, indeterminate…

When presenting forensic evidence, such as a DNA match, experts often use the Likelihood ratio (LR) to explain the impact of evidence . The LR measures the probative value of the evidence with respect to a single hypothesis such as 'DNA…

In this paper, we develop a simple approach for testing multiple statistical hypotheses based on the observations of a number of probability ratios enumerated consecutively with respect to the index of hypotheses. Explicit and tight bounds…

A new method based on the rejection sampling for finding statistical tests is proposed. This method is conceptually intuitive, easy to implement, and applicable for arbitrary dimension. To illustrate its potential applicability, three…

The design of optimal test statistics is a key task in frequentist statistics and for a number of scenarios optimal test statistics such as the profile-likelihood ratio are known. By turning this argument around we can find the profile…

Binary classifiers trained on a certain proportion of positive items introduce a bias when applied to data sets with different proportions of positive items. Most solutions for dealing with this issue assume that some information on the…

We present a new way of testing ordered hypotheses against all alternatives which overpowers the classical approach both in simplicity and statistical power. Our new method tests the constrained likelihood ratio statistic against the…

In the report the approach to estimation of quality of planned experiments is considered. This approach is based on the analysis of uncertainty, which will take place under the future hypotheses testing about the existence of a new…

A simple and common type of medical research involves the comparison of one treatment against another. The logical aim should be both to establish which treatment is superior and the strength of evidence supporting this conclusion, a task…

It is well known that there is no direct one-to-one relation between $p$-values and likelihood ratios or Bayes factors, since their relation crucially involves the sample size $n$. We investigate their (asymptotic) relation in a…

A new approach to adaptive design of clinical trials is proposed in a general multiparameter exponential family setting, based on generalized likelihood ratio statistics and optimal sequential testing theory. These designs are easy to…

Much of science is (rightly or wrongly) driven by hypothesis testing. Even in situations where the hypothesis testing paradigm is correct, the common practice of basing inferences solely on p-values has been under intense criticism for over…

Is it possible for a large sequence of measurements or observations, which support a hypothesis, to counterintuitively decrease our confidence? Can unanimous support be too good to be true? The assumption of independence is often made in…

We consider the problem of hypotheses testing with the basic simple hypothesis: observed sequence of points corresponds to stationary Poisson process with known intensity. The alternatives are stationary self-exciting point processes. We…