Related papers: Quantifying nuisance parameter effects via decompo…
We propose a general approach to construct weighted likelihood estimating equations with the aim of obtaining robust parameter estimates. We modify the standard likelihood equations by incorporating a weight that reflects the statistical…
We investigate the role of noise in optimization algorithms for learning over-parameterized models. Specifically, we consider the recovery of a rank one matrix $Y^*\in R^{d\times d}$ from a noisy observation $Y$ using an…
Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is…
We often estimate a parameter of interest psi when the identifying conditions involve a nuisance parameter theta. Examples from causal inference are Inverse Probability Weighting, Marginal Structural Models and Structural Nested Models. To…
We provide an analytical argument for understanding the likely nature of parameter shifts between those coming from an analysis of a dataset and from a subset of that dataset, assuming differences are down to noise and any intrinsic…
In this paper we consider the problem of estimating a parameter of a probability distribution when we have some prior information on a nuisance parameter. We start by the very simple case where we know perfectly the value of the nuisance…
In this article we study a class of parameters with the so-called `mixed bias property'. For parameters with this property, the bias of the semiparametric efficient one step estimator is equal to the mean of the product of the estimation…
We study the high-dimensional linear model with noise distribution known up to a scale parameter. With an $\ell_1$-penalty on the regression coefficients, we show that a transformation of the log-likelihood allows for a choice of the tuning…
We examine the problem of variance components testing in general mixed effects models using the likelihood ratio test. We account for the presence of nuisance parameters, i.e. the fact that some untested variances might also be equal to…
Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Oftentimes, the number of observations is small, and it is thus important to…
Consider observing an undirected network that is `noisy' in the sense that there are Type I and Type II errors in the observation of edges. Such errors can arise, for example, in the context of inferring gene regulatory networks in genomics…
We propose a two-sample extended empirical likelihood for inference on the difference between two p-dimensional parameters defined by estimating equations. The standard two-sample empirical likelihood for the difference is Bartlett…
The penalized profile sampler for semiparametric inference is an extension of the profile sampler method (Lee, Kosorok and Fine, 2005) obtained by profiling a penalized log-likelihood. The idea is to base inference on the posterior…
We provide (high probability) bounds on the condition number of random feature matrices. In particular, we show that if the complexity ratio $\frac{N}{m}$ where $N$ is the number of neurons and $m$ is the number of data samples scales like…
Random-effects models are frequently used to synthesise information from different studies in meta-analysis. While likelihood-based inference is attractive both in terms of limiting properties and of implementation, its application in…
Although treatment effects can be estimated from observed outcome distributions obtained from proper randomization in clinical trials, covariate adjustment is recommended to increase precision. For important treatment effects, such as odds…
Does the asymptotic variance of the maximum composite likelihood estimator of a parameter of interest always decrease when the nuisance parameters are known? Will a composite likelihood necessarily become more efficient by incorporating…
We obtain two theorems extending the use of a saddlepoint approximation to multiparameter problems for likelihood ratio-like statistics which allow their use in permutation and rank tests and could be used in bootstrap approximations. In…
Experimental research on behavior and cognition frequently rests on stimulus or subject selection where not all characteristics can be fully controlled, even when attempting strict matching. For example, when contrasting patients to…
Rank two parametric perturbations of operators and matrices are studied in various settings. In the finite dimensional case the formula for a characteristic polynomial is derived and the large parameter asymptotics of the spectrum is…