The Modal Age of Statistics

Chacón, José E.

doi:10.1111/insr.12340

Cited by 40 publications

(35 citation statements)

References 93 publications

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“…Methodology based on modes or local maxima of nonparametrically estimated functions has seen a resurgence in recent years; see, e.g., Chen et al (2016), Chen, Genovese and Wasserman (2015), and Qiao and Polonik (2016). A recent survey on estimation and inference for the mode and on mode-based methodology is given by Chacón (2018b).…”

Section: Introduction and Overviewmentioning

confidence: 99%

Univariate log-concave density estimation with symmetry or modal constraints

Doss

Wellner²

2019

Electron. J. Statist.

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We study nonparametric maximum likelihood estimation of a log-concave density function f 0 which is known to satisfy further constraints, where either (a) the mode m of f 0 is known, or (b) f 0 is known to be symmetric about a fixed point m. We develop asymptotic theory for both constrained log-concave maximum likelihood estimators (MLE's), including consistency, global rates of convergence, and local limit distribution theory. In both cases, we find the MLE's pointwise limit distribution at m (either the known mode or the known center of symmetry) and at a point x 0 = m. Software to compute the constrained estimators is available in the R package logcondens.mode.The symmetry-constrained MLE is particularly useful in contexts of location estimation. The mode-constrained MLE is useful for mode-regression. The mode-constrained MLE can also be used to form a likelihood ratio test for the location of the mode of f 0 . These problems are studied in separate papers. In particular, in a separate paper we show that, under a curvature assumption, the likelihood ratio statistic for the location of the mode can be used for hypothesis tests or confidence intervals that do not depend on either tuning parameters or nuisance parameters.

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Section: Introduction and Overviewmentioning

confidence: 99%

Univariate log-concave density estimation with symmetry or modal constraints

Doss

Wellner²

2019

Electron. J. Statist.

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“…The main part of the proof is the proof of the first result (5). The second result (6) follows from the √ n-uniform consistency of the quantile regression estimator and the delta method.…”

Section: Limiting Distributionsmentioning

confidence: 95%

“…For example, [25] argue that the mode is the most intuitive measure of central tendency for positively skewed data found in many econometric applications such as wages, prices, and expenditures ( [25], p. 93). See also [7] and [5] for recent reviews on modal regression.…”

Section: Introductionmentioning

confidence: 99%

Quantile regression approach to conditional mode estimation

Ota¹,

Kato²,

Hara³

2019

Electron. J. Statist.

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In this paper, we consider estimation of the conditional mode of an outcome variable given regressors. To this end, we propose and analyze a computationally scalable estimator derived from a linear quantile regression model and develop asymptotic distributional theory for the estimator. Specifically, we find that the pointwise limiting distribution is a scale transformation of Chernoff's distribution despite the presence of regressors. In addition, we consider analytical and subsampling-based confidence intervals for the proposed estimator. We also conduct Monte Carlo simulations to assess the finite sample performance of the proposed estimator together with the analytical and subsampling confidence intervals. Finally, we apply the proposed estimator to predicting the net hourly electrical energy output using Combined Cycle Power Plant Data.Date: The first arXiv version:

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“…This way of computing the tendency is similar to Chernoff's (1964) kernel-based definition of the mode. Chacón (2020) praises the use of modal approaches in problems where it is not sensible to make strong hypothesis about the data distribution, as is the case we are handling here.…”

Section: Floating References For Unsupervised Change Detectionmentioning

confidence: 99%

Unsupervised Change Detection Driven by Floating References: A Pattern Analysis Approach

Negri

Frery

2021

Pattern Anal Applic

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The Earth's environment is continually changing due to both human and natural factors. Timely identification of the location and kind of change is of paramount importance in several areas of application. Because of that, Remote Sensing change detection is a topic of great interest. The development of precise change detection methods is a constant challenge. This study introduces a novel unsupervised change detection method based on data clustering and optimization. The proposal is less dependent on radiometric normalization than classical approaches. We carried experiments with remote sensing images and simulated data sets to compare the proposed method with other unsupervised well-known techniques. At its best, the proposal improves by 50 % the accuracy concerning the second best technique. Such improvement is most noticeable with uncalibrated data. Experiments with simulated data reveal that the proposal is better than all other compared methods at any practical significance level. The results show the potential of the proposed method.

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The Modal Age of Statistics

Cited by 40 publications

References 93 publications

Univariate log-concave density estimation with symmetry or modal constraints

Univariate log-concave density estimation with symmetry or modal constraints

Quantile regression approach to conditional mode estimation

Unsupervised Change Detection Driven by Floating References: A Pattern Analysis Approach

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