Performing statistical inference in high-dimensional models is an outstanding challenge. A major source of difficulty is the absence of precise information on the distribution of high-dimensional regularized estimators. Here, we consider linear regression in the high-dimensional regime p n and the Lasso estimator. In this context, we would like to perform inference on a high-dimensional paramet...

In this paper we propose an estimator of the entropy of a continuous random variable. The estimator is obtained by modifying the estimator proposed by Vasicek (1976). Consistency of estimator is proved, and comparisons are made with Vasicek’s estimator (1976), van Es’s estimator (1992), Ebrahimi et al.’s estimator (1994) and Correa’s estimator (1995). The results indicate that the proposed esti...

In frequentist inference, we commonly use a single point (point estimator) or an interval (confidence interval/“interval estimator”) to estimate a parameter of interest. A very simple question is: Can we also use a distribution function (“distribution estimator”) to estimate a parameter of interest in frequentist inference in the style of a Bayesian posterior? The answer is affirmative, and con...

Summary Statistical inference in the presence of nuisance functionals with complex survey data is an important topic social and economic studies. The Gini index, Lorenz curves, quantile shares are among commonly encountered examples. usually handled by a plug-in nonparametric estimator main inferential procedure can be carried out through two-step generalized empirical likelihood method. Unfort...

Some di cult conceptual problems that have plagued Statistical Mechanics from the start, are explained by reference to a very simple experiment, which also explains why the MAXENT formalism gives reliable predictions. Then some of the inner workings of MAXENT are revealed by a general perturbation theorem, showing how a prediction is modi ed by adding a new constraint. It is illustrated by the ...

The paper is a study of properties of quasi-consequence operation which is a key notion of the so-called inferential approach in the theory of sentential calculi established in [5].The principal motivation behind the quasi-consequence, q-consequence for short, stems from the mathematical practice which treats some auxiliary assumptions as mere hypotheses rather than axioms and their further occ...