scholarly journals Estimating the conditional density by histogram type estimators and model selection

2017 ◽  
Vol 21 ◽  
pp. 34-55
Author(s):  
Mathieu Sart
Keyword(s):  
Model Selection ◽  
Type Inequality ◽  
Estimation Procedure ◽  
Conditional Density ◽  
Distributed Data ◽  
Oracle Inequality ◽  
Random Partition ◽  
Selection Theorem ◽  
Piecewise Constant ◽  
Anisotropic Besov Spaces

We propose a new estimation procedure of the conditional density for independent and identically distributed data. Our procedure aims at using the data to select a function among arbitrary (at most countable) collections of candidates. By using a deterministic Hellinger distance as loss, we prove that the selected function satisfies a non-asymptotic oracle type inequality under minimal assumptions on the statistical setting. We derive an adaptive piecewise constant estimator on a random partition that achieves the expected rate of convergence over (possibly inhomogeneous and anisotropic) Besov spaces of small regularity. Moreover, we show that this oracle inequality may lead to a general model selection theorem under very mild assumptions on the statistical setting. This theorem guarantees the existence of estimators possessing nice statistical properties under various assumptions on the conditional density (such as smoothness or structural ones).

scholarly journals Detecting multiple generalized change-points by isolating single ones

Metrika ◽  
2021 ◽  
Author(s):  
Andreas Anastasiou ◽  
Piotr Fryzlewicz
Keyword(s):  
Model Selection ◽  
Linear Trend ◽  
Information Criterion ◽  
Change Points ◽  
Isolation Technique ◽  
New Approach ◽  
Piecewise Constant ◽  
Practical Performance ◽  
R Packages ◽  
The Times

AbstractWe introduce a new approach, called Isolate-Detect (ID), for the consistent estimation of the number and location of multiple generalized change-points in noisy data sequences. Examples of signal changes that ID can deal with are changes in the mean of a piecewise-constant signal and changes, continuous or not, in the linear trend. The number of change-points can increase with the sample size. Our method is based on an isolation technique, which prevents the consideration of intervals that contain more than one change-point. This isolation enhances ID’s accuracy as it allows for detection in the presence of frequent changes of possibly small magnitudes. In ID, model selection is carried out via thresholding, or an information criterion, or SDLL, or a hybrid involving the former two. The hybrid model selection leads to a general method with very good practical performance and minimal parameter choice. In the scenarios tested, ID is at least as accurate as the state-of-the-art methods; most of the times it outperforms them. ID is implemented in the R packages IDetect and breakfast, available from CRAN.

The Model Selection Curse

2019 ◽  
Vol 1 (2) ◽  
pp. 127-140 ◽  
Author(s):  
Kfir Eliaz ◽  
Ran Spiegler
Keyword(s):  
Machine Learning ◽  
Model Selection ◽  
Learning Algorithms ◽  
Personal Data ◽  
Estimation Procedure ◽  
Machine Learning Algorithms ◽  
Human Interaction ◽  
Truth Telling ◽  
Agent Based

A statistician takes an action on behalf of an agent, based on the agent’s self-reported personal data and a sample involving other people. The action that he takes is an estimated function of the agent’s report. The estimation procedure involves model selection. We ask the following question: Is truth-telling optimal for the agent given the statistician’s procedure? We analyze this question in the context of a simple example that highlights the role of model selection. We suggest that our simple exercise may have implications for the broader issue of human interaction with machine learning algorithms. (JEL C52)

scholarly journals Model Selection Criteria on Beta Regression for Machine Learning

2019 ◽  
Vol 1 (1) ◽  
pp. 427-449
Author(s):  
Patrícia Espinheira ◽  
Luana da Silva ◽  
Alisson Silva ◽  
Raydonal Ospina
Keyword(s):  
Machine Learning ◽  
Model Selection ◽  
Selection Criteria ◽  
Real Data ◽  
Estimation Procedure ◽  
Computational Procedure ◽  
Information Criteria ◽  
Beta Regression ◽  
Finite Sample ◽  
Model Selection Criteria

Beta regression models are a class of supervised learning tools for regression problems with univariate and limited response. Current fitting procedures for beta regression require variable selection based on (potentially problematic) information criteria. We propose model selection criteria that take into account the leverage, residuals, and influence of the observations, both to systematic linear and nonlinear components. To that end, we propose a Predictive Residual Sum of Squares (PRESS)-like machine learning tool and a prediction coefficient, namely P 2 statistic, as a computational procedure. Monte Carlo simulation results on the finite sample behavior of prediction-based model selection criteria P 2 are provided. We also evaluated two versions of the R 2 criterion. Finally, applications to real data are presented. The new criterion proved to be crucial to choose models taking into account the robustness of the maximum likelihood estimation procedure in the presence of influential cases.

scholarly journals Model Selection for Treatment Choice: Penalized Welfare Maximization

Econometrica ◽  
2021 ◽  
Vol 89 (2) ◽  
pp. 825-848
Author(s):  
Eric Mbakop ◽  
Max Tabord-Meehan
Keyword(s):  
Model Selection ◽  
Policy Maker ◽  
Population Based ◽  
Oracle Inequality ◽  
Statistical Decision ◽  
Welfare Maximization ◽  
Statistical Decision Problem ◽  
Sample Data ◽  
Selection For ◽  
Maximum Regret

This paper studies a penalized statistical decision rule for the treatment assignment problem. Consider the setting of a utilitarian policy maker who must use sample data to allocate a binary treatment to members of a population, based on their observable characteristics. We model this problem as a statistical decision problem where the policy maker must choose a subset of the covariate space to assign to treatment, out of a class of potential subsets. We focus on settings in which the policy maker may want to select amongst a collection of constrained subset classes: examples include choosing the number of covariates over which to perform best‐subset selection, and model selection when approximating a complicated class via a sieve. We adapt and extend results from statistical learning to develop the Penalized Welfare Maximization (PWM) rule. We establish an oracle inequality for the regret of the PWM rule which shows that it is able to perform model selection over the collection of available classes. We then use this oracle inequality to derive relevant bounds on maximum regret for PWM. An important consequence of our results is that we are able to formalize model‐selection using a “holdout” procedure, where the policy maker would first estimate various policies using half of the data, and then select the policy which performs the best when evaluated on the other half of the data.

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