Related papers: Empirical likelihood on the full parameter space
We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically…
Empirical likelihood method has been applied to short-memory time series models by Monti (1997) through the Whittle's estimation method. Yau (2012) extended this idea to long-memory time series models. Asymptotic distributions of the…
Many common loss functions such as mean-squared-error, cross-entropy, and reconstruction loss are unnecessarily rigid. Under a probabilistic interpretation, these common losses correspond to distributions with fixed shapes and scales. We…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
We adopt an empirical approach to the characterization of the distribution of twin primes within the set of primes, rather than in the set of all natural numbers. The occurrences of twin primes in any finite sequence of primes are like…
The algorithmic theory of randomness is well developed when the underlying space is the set of finite or infinite sequences and the underlying probability distribution is the uniform distribution or a computable distribution. These…
Vecchia's approximate likelihood for Gaussian process parameters depends on how the observations are ordered, which can be viewed as a deficiency because the exact likelihood is permutation-invariant. This article takes the alternative…
This paper formulates a penalized empirical likelihood (PEL) method for inference on the population mean when the dimension of the observations may grow faster than the sample size. Asymptotic distributions of the PEL ratio statistic is…
Likelihood-based inferences have been remarkably successful in wide-spanning application areas. However, even after due diligence in selecting a good model for the data at hand, there is inevitably some amount of model misspecification:…
In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived…
The likelihood function plays a pivotal role in statistical inference; it is adaptable to a wide range of models and the resultant estimators are known to have good properties. However, these results hinge on correct specification of the…
This paper proposes a local representation for Empirical Likelihood (EL). EL admits the classical local linear quadratic representation by its likelihood ratio property. A local estimator is derived by using the new representation.…
Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…
Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in \mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption…
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…
Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…
A composite likelihood is a non-genuine likelihood function that allows to make inference on limited aspects of a model, such as marginal or conditional distributions. Composite likelihoods are not proper likelihoods and need therefore…
The likelihood function is central to both frequentist and Bayesian formulations of parametric statistical inference, and large-sample approximations to the sampling distributions of estimators and test statistics, and to posterior…
The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…
Economic and financial models -- such as vector autoregressions, local projections, and multivariate volatility models -- feature complex dynamic interactions and spillovers across many time series. These models can be integrated into a…