Related papers: Minimum penalized Hellinger distance for model sel…
The statistical regression technique is an extraordinarily essential data fitting tool to explore the potential possible generation mechanism of the random phenomenon. Therefore, the model selection or the variable selection is becoming…
Our purpose in this paper is to apply the general methodology for model selection based on T-estimators developed in Birg\'{e} [Ann. Inst. H. Poincar\'{e} Probab. Statist. 42 (2006) 273--325] to the particular situation of the estimation of…
Akaike's Bayesian information criterion (ABIC) has been widely used in geophysical inversion and beyond. However, little has been done to investigate its statistical aspects. We present an alternative derivation of the marginal distribution…
Estimating the density of a distribution from its samples is a fundamental problem in statistics. Hypothesis selection addresses the setting where, in addition to a sample set, we are given $n$ candidate distributions -- referred to as…
We define two minimum distance estimators for dependent data by minimizing some approximated Maximum Mean Discrepancy distances between the true empirical distribution of observations and their assumed (parametric) model distribution. When…
How can we find a subset of training samples that are most responsible for a specific prediction made by a complex black-box machine learning model? More generally, how can we explain the model's decisions to end-users in a transparent way?…
The main purpose of this paper is to introduce first a new family of empirical test statistics for testing a simple null hypothesis when the vector of parameters of interest are defined through a specific set of unbiased estimating…
Choosing a shrinkage method can be done by selecting a penalty from a list of pre-specified penalties or by constructing a penalty based on the data. If a list of penalties for a class of linear models is given, we provide comparisons based…
In this paper we make a first attempt at understanding how to build an optimal approximate normal factor analysis model. The criterion we have chosen to evaluate the distance between different models is the I-divergence between the…
The joint modeling of mean and dispersion (JMMD) provides an efficient method to obtain useful models for the mean and dispersion, especially in problems of robust design experiments. However, in the literature on JMMD there are few works…
The exploration of associations between random objects with complex geometric structures has catalyzed the development of various novel statistical tests encompassing distance-based and kernel-based statistics. These methods have various…
We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent ($\rho$-mixing, $m$-dependent)…
In this article we propose a general class of risk measures which can be used for data based evaluation of parametric models. The loss function is defined as generalized quadratic distance between the true density and the proposed model.…
Longitudinal data are common in clinical trials and observational studies, where missing outcomes due to dropouts are always encountered. Under such context with the assumption of missing at random, the weighted generalized estimating…
$f$-divergences, which quantify discrepancy between probability distributions, are ubiquitous in information theory, machine learning, and statistics. While there are numerous methods for estimating $f$-divergences from data, a limit…
A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of…
We study the problem of finding the index of the minimum value of a vector from noisy observations. This problem is relevant in population/policy comparison, discrete maximum likelihood, and model selection. We develop an asymptotically…
The use of historical controls offers a valuable alternative when traditional randomized controlled trials are not feasible. However, such approaches may introduce bias due to temporal changes in patient populations, diagnostic criteria,…
For many data-intensive tasks, feature selection is an important preprocessing step. However, most existing methods do not directly and intuitively explore the intrinsic discriminative information of features. We propose a novel feature…
This paper studies the model selection problem in a large class of causal time series models, which includes both the ARMA or AR($\infty$) processes, as well as the GARCH or ARCH($\infty$), APARCH, ARMA-GARCH and many others processes. We…