Related papers: Remarks on a parameter estimation for von Mises--F…
In this brief note we compute the Fisher information of a family of generalized normal distributions. Fisher information is usually defined for regular distributions, i.e. continuously differentiable (log) density functions whose support…
The Dvoretzky--Kiefer--Wolfowitz--Massart inequality gives a sub-Gaussian tail bound on the supremum norm distance between the empirical distribution function of a random sample and its population counterpart. We provide a short proof of a…
We study properties of Fisher distribution (von Mises-Fisher distribution, matrix Langevin distribution) on the rotation group SO(3). In particular we apply the holonomic gradient descent, introduced by Nakayama et al. (2011), and a method…
This survey covers state-of-the-art Bayesian techniques for the estimation of mixtures. It complements the earlier Marin, Mengersen and Robert (2005) by studying new types of distributions, the multinomial, latent class and t distributions.…
We appended an errata to the original submission. The purpose of this errata is to point out two errors in [2] and give a weakened version of those statements made.
This paper has been withdrawn by the author due to a gap in the proof of the main result.
The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…
This paper discusses some problems possibly arising when approximating via Monte-Carlo simulations the distributions of goodness-of-fit test statistics based on the empirical distribution function. We argue that failing to re-estimate…
In the usual statistical inference problem, we estimate an unknown parameter of a statistical model using the information in the random sample. A priori information about the parameter is also known in several real-life situations. One such…
Misprints in eq. (7), which propagate up to eq. (13), are corrected. References are updated.
Our main theorem is an extension of the well-known Mizoguchi-Takahaashi's fixed point theorem [N. Mizogochi and W. Takahashi, Fixed point theorems for multi-valued mappings on complete metric space, {\it J. Math. Anal. Appl.} 141 (1989)…
Yet another proof of Onsager-Machlup formula for diffusion processes on a Riemannian manifold after Takahashi-Watanabe, Fujita-Kotani. The proof is purely probabilistic and contains a precise study on an ergodic effect for a key Wiener…
The purpose of this note is to show that in a widely cited paper by Yakir [Ann. Statist. 25 (1997) 2117--2126, doi:10.1214/aos/1069362390], the proof that the so-called modified Shiryayev--Roberts procedure is exactly optimal is incorrect.…
We review the Bayesian theory of semiparametric inference following Bickel and Kleijn (2012) and Kleijn and Knapik (2013). After an overview of efficiency in parametric and semiparametric estimation problems, we consider the Bernstein-von…
We consider the sensitivity, with respect to a parameter \theta, of parametric families of operators A_{\theta}, vectors \pi_{\theta} corresponding to the adjoints A_{\theta}^{*} of A_{\theta} via A_{\theta}^{*}\pi_{\theta}=0 and one…
Estimate (3.39) which appears in the proof of Proposition 3.4 in [Ann. Probab. 27 (1999) 1414--1467, doi:10.1214/aop/1022677454] is wrong. We present below a corrected proof which introduces an extra factor 2 in equations (3.34) and (3.35).…
In this paper, we highlight a major error in the proofs of the important results of [D.Ch\'etelat and M. T. Wells(2012). Improved Multivariate Normal Mean Estimation with Unknown Covariance when p is Greater than n. The Annals of…
When estimating the directed information between two jointly stationary Markov processes, it is typically assumed that the recipient of the directed information is itself Markov of the same order as the joint process. While this assumption…
Missing data occur in a variety of applications of extreme value analysis. In the block maxima approach to an extreme value analysis, missingness is often handled by either ignoring missing observations or dropping a block of observations…
This paper extends the idea of a generalized estimator for a scalar parameter (Vos, 2022) to multi-dimensional parameters both with and without nuisance parameters. The title reflects the fact that generalized estimators provide more than…