Maximum likelihood estimation

area: Statistics and Bayesian methods · 10 papers in the last 7 days

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\hat\theta = \arg\max_{\theta} \sum_{i=1}^{n} \log f(x_i \mid \theta)

Chooses the parameters under which the observed data are most probable.

LaTeX: \hat\theta = \arg\max_{\theta} \sum_{i=1}^{n} \log f(x_i \mid \theta)

Names searched for: maximum likelihood, MLE

Variables and notation#

theta is the parameter vector, x_i observations, f the modeled probability density/mass and n sample size; log likelihood sums independent-observation contributions.

Worked example#

For three successes and one failure in independent Bernoulli trials, log likelihood=3 ln p+ln(1−p), maximized at p=3/4.

MLE maximizes the sampling likelihood; Bayesian MAP also includes a prior. Dependence, misspecification and boundary parameters require care; a maximized likelihood is not the probability that the model is true.

Sources and further reading#

NIST/SEMATECH e-Handbook: maximum likelihood estimation

Examples use illustrative inputs, not observed research results. Logarithms are natural unless stated otherwise. Guide updated 2026-11-05. Prepared by Scholar4AI. Editorial and verification policy.

Key findings#

Maximum likelihood estimation was mentioned in 95 papers in the last 30 days (2026-10-07 to 2026-11-05), ranking #10 of the 248 equations and models mentioned.
By journal category: Statistics (34), Economics (22), Management (9), Operations Research (6), Information Systems (6), Finance (5), Higher Education and Research (5), AI (4), Health Economics and Policy (2), Tourism and Hospitality (1) and Marketing (1).
Most of them appeared in Statistics and Computing (6), Journal of Statistical Theory and Practice (4) and Statistical Papers (4).
Often mentioned together with Logistic regression (logit) (17), Structural equation modeling (SEM) (13) and Information criteria (AIC and BIC) (12).
Datasets named in the same papers: World Development Indicators (World Bank) (5), Facebook (3) and Labour Force Surveys (2).
From Nov 2023 to Oct 2026, 3,557 archived papers mentioned Maximum likelihood estimation in their title, abstract or keywords (the search of earlier months' full texts is still under way), most of them in Sep 2026 (141).
From 2017 to 2026 (so far), Maximum likelihood estimation was mentioned in 5,068 papers in the tracked journals, most of them in statistics (1,916), economics (1,116) and AI (612).
1,088 of them were published in 2025, against 212 in 2017.
Since 2023, the institutions with the most of these papers were Centre National de la Recherche Scientifique (97), KU Leuven (48) and University College London (45).
The journals publishing most of them were Statistics and Computing (177), Journal of Econometrics (104) and Statistical Papers (103).
The most-cited of them is “A Survey on Self-Supervised Learning: Algorithms, Applications, and Future Trends” (IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024), with 579 citations.

Mentions over 36 months#

Papers mentioning it by publication month, Nov 2023 to Oct 2026 (titles, abstracts and keywords; the full texts of earlier months are still being searched)
Trend	Nov 23–Oct 24	Nov 24–Oct 25	Nov 25–Oct 26	36 months
	1,177	1,125	1,255	3,557

Papers per year#

20172026 (so far)

Papers per publication year and category
Category	2017	2018	2019	2020	2021	2022	2023	2024	2025	2026 (so far)
Statistics	127	129	140	132	144	154	164	289	314	323
Economics	28	31	24	37	45	24	97	309	263	258
AI	25	24	16	23	23	18	52	159	166	106
Operations Research	17	12	16	12	10	18	39	116	113	116
Finance	8	6	4	0	4	5	31	104	65	105
Management	1	1	0	2	3	0	21	94	91	84
Higher Education and Research	0	0	0	1	0	0	2	28	23	34
Health Economics and Policy	3	2	2	5	1	1	7	24	16	18
Marketing	1	0	0	1	0	1	2	23	20	15
Information Systems	2	0	1	0	0	0	3	8	11	17
Tourism and Hospitality	0	0	0	0	0	0	6	11	3	16
Accounting	0	0	0	0	1	0	1	6	3	7
All categories	212	205	203	213	231	221	425	1,171	1,088	1,099

Where the papers come from#

Journals with the most papers, since 2023
#	Journal	Papers
1	Statistics and Computing	177
2	Journal of Econometrics	104
3	Statistical Papers	103
4	Computational Statistics	88
5	Computational Statistics & Data Analysis	79
6	Journal of Statistical Theory and Practice	70
7	Journal of Multivariate Analysis	67
8	IEEE Transactions on Pattern Analysis and Machine Intelligence	61
9	Machine Learning	60
10	Annals of Operations Research	54

Institutions with the most papers, since 2023
#	Institution	Papers
1	Centre National de la Recherche Scientifique	97
2	KU Leuven	48
3	University College London	45
4	University of Leeds	39
5	University of Bologna	38
6	Vrije Universiteit Amsterdam	37
7	Monash University	36
8	Sapienza University of Rome	34
9	Erasmus University Rotterdam	32
10	The University of Sydney	32

Countries with the most papers, since 2023
#	Country	Papers
1	United States	694
2	United Kingdom	637
3	China	450
4	Italy	428
5	Germany	406
6	France	247
7	Spain	243
8	Netherlands	223
9	Australia	217
10	Japan	143

Keywords with the most papers, since 2023
#	Keyword	Papers
1	maximum likelihood estimation	390
2	parameter estimation	106
3	COVID-19 pandemic	92
4	expectation-maximization algorithm	79
5	asymptotic normality	77
6	consistency	65
7	Bayesian estimation	63
8	maximum likelihood estimator	56
9	model selection	53
10	asymptotic properties	52

Most-cited papers#

Most-cited papers since 2017
#	Citations	Per month	Title	Journal	Published	Authors
1	579	20.2	A Survey on Self-Supervised Learning: Algorithms, Applications, and Future Trends	IEEE Transactions on Pattern Analysis and Machine Intelligence	2024-06-17	Jie Gui, Tuo Chen, Jing Zhang et al.
2	396	11.6	Plant disease detection and classification techniques: a comparative study of the performances	Journal Of Big Data	2024-01-02	Wubetu Barud Demilie
3	315	4.0	How to use instrumental variables in addressing endogeneity? A step-by-step procedure for non-specialists	Industrial Marketing Management	2020-03-19	Subhan Ullah, Ghasem Zaefarian, Farid Ullah
4	295	9.6	Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospects	IEEE Transactions on Pattern Analysis and Machine Intelligence	2024-04-10	Kexin Zhang, Qingsong Wen, Chaoli Zhang et al.
5	285	10.3	A Comprehensive Survey on Test-Time Adaptation Under Distribution Shifts	International Journal of Computer Vision	2024-07-18	Jian Liang, Ran He, Tieniu Tan
6	238	2.8	EKLT: Asynchronous Photometric Feature Tracking Using Events and Frames	International Journal of Computer Vision	2019-08-22	Daniel Gehrig, Henri Rebecq, Guillermo Gallego et al.
7	230	14.9	Physics-informed neural networks for PDE problems: a comprehensive review	Artificial Intelligence Review	2025-07-24	Kuang Luo, Jingshang Zhao, Ying‐Ping Wang et al.
8	222	3.0	Unscented kalman filter with process noise covariance estimation for vehicular ins/gps integration system	Information Fusion	2020-08-05	Gaoge Hu, Bingbing Gao, Yongmin Zhong et al.
9	202	7.1	Data oversampling and imbalanced datasets: an investigation of performance for machine learning and feature engineering	Journal Of Big Data	2024-06-17	Muhammad Mujahid, Erol Kına, Furqan Rustam et al.
10	200	2.1	Maximum Likelihood Estimation-Based Joint Sparse Representation for the Classification of Hyperspectral Remote Sensing Images	IEEE Transactions on Neural Networks and Learning Systems	2018-10-29	Jiangtao Peng, Luoqing Li, Yuan Yan Tang

Archive counts by publication year: a paper counts when its title, abstract or keywords name the equation, or when OpenAlex's full-text search finds it there (searched for the last 30 days' papers and, by a pass over the past years, for older ones). Names added to the list later are looked for in older papers as the archive is read again.

Papers mentioning Maximum likelihood estimation, newest first. Newest 50 of 95 papers; all of them are in /data/papers.json.
Date	Title	Journal	Authors	Affiliations
2026-11-02	Approximating the Sampling Distributions of Weibull Parameter MLEs with Applications	Journal of Statistical Theory and Practice	Buu‐Chau Truong, Peter Mphekgwana, Nabendu Pal	Ton Duc Thang University; University of Limpopo; University of Louisiana at Lafayette
2026-10-31	Product combination purchase choice model based on item-level sales data	Journal of Revenue and Pricing Management	Shiming Deng, Bohan Ouyang, Mingyu Xu et al.	Huazhong University of Science and Technology
2026-10-31	Nonparametric maximum likelihood estimation for competing risks frailty models	Lifetime Data Analysis	Chew-Seng Chee, Il Do Ha, Youngjo Lee et al.	Pukyong National University; Seoul National University; Chungnam National University
2026-10-31	Political Favoritism, Public Funds and Manufacturing Firm Performance in Hungary	Comparative Economic Studies	Vivien Czeczeli, Jarko Fidrmuc, Gábor Kutasi	Ludovika University of Public Service; Zeppelin Universität gemeinnützige GmbH; Mendel University in Brno
2026-10-31	Quadratic functional variable transformation of the exponential-gamma distribution for flexible lifetime modelling	Statistical Papers	Taiwo Michael Ayeni, Elijah Ayooluwa Odukoya, Huichan Zhao	Georgia State University; Federal University of Technology and Environmental Sciences
2026-10-31	Individual effectiveness, team cohesion, and academic performance in cooperative teams: Evidence from bias-corrected peer evaluations	The International Journal of Management Education	Pilar Abad, Lidia Muñoz-Fernández	Universidad Rey Juan Carlos
2026-10-31	Robust mask-based appointment scheduling in primary care practices	Health Care Management Science	Sabrina Schmitz, Martin Comis, Christina Büsing	RWTH Aachen University
2026-10-31	Explaining forest value perceptions across Europe: A multilevel analysis of individual and geographic variation	Forest Policy and Economics	Moses Kazungu, Marcel Hunziker	Swiss Federal Institute for Forest, Snow and Landscape Research
2026-10-31	The personnel inquiry records: a historical microdatabase of elites and families in prewar Japan	Japanese Economic Review	Hiroshi Kumanomido, Suguru Otani, Yutaro Takayasu	Ludwig-Maximilians-Universität München; The University of Tokyo; Hitotsubashi University
2026-10-30	Maximum likelihood estimation of fractional Ornstein-Uhlenbeck process with discretely sampled data	Journal of Econometrics	Xiaohu Wang, Weilin Xiao, Jun Yu et al.	Fudan University; Zhejiang University; University of Macau; …
2026-10-29	Spatial Effects of Sex on Job Quality in a Developing Country	Networks and Spatial Economics	Jhon James Mora, Diana Yaneth Herrera Duque, Juan Tomás Sayago	Universidad Icesi; University of Iowa
2026-10-28	Forecasting volatility in periods of financial turbulence: a new state-dependent model	Journal of Economics and Finance	Fabio Gobbi, Sabrina Mulinacci	University of Bologna
2026-10-28	F-modeling-based empirical Bayes estimation for the reciprocal shape parameter of the Pareto distribution	Statistical Papers	Yeil Kwon	Wichita State University
2026-10-28	Distributional Properties of Gold and Bitcoin Returns Across Crisis Regimes: A Comparative Analysis	Journal of Statistical Theory and Practice	Priyanka Nagar, Luca A. Gabin, Keotshepile Mandona	Stellenbosch University
2026-10-28	Forward and backward smoothing for noisy nonstationary time series with an application of detecting recent change points	Japanese Journal of Statistics and Data Science	Seisho Sato, Naoto Kunitomo	The University of Tokyo; The Institute of Statistical Mathematics
2026-10-28	German farmers' preferences for peatland rewetting schemes: Autonomy, flexibility and institutional trust	Land Use Policy	Marius Michels, Oliver Mußhoff	University of Göttingen; Humboldt-Universität zu Berlin
2026-10-28	Teaching quality and socioeconomic inequalities in student achievement: Meta-Analytic evidence from PISA 2022	Educational Research Review	Tamara Kastorff, Pia Todtenhöfer, Samuel Greiff	Technical University of Munich
2026-10-28	Path-breaking to Innovate: Patenting in Internet of Things (IoT) Technologies	Journal of Business Research	Jun Du, James H. Love, Xiaocan Yuan	University of Manchester; University of Leeds; Aston University
2026-10-27	Dirty by design? Gig work challenges, stigma, and identity threat in crowdwork	Journal of Business Research	Ward van Zoonen, Monika E. von Bonsdorff, Marjo Elisa Siltaoja	Vrije Universiteit Amsterdam; University of Jyväskylä
2026-10-27	Revisiting the price elasticity of charitable giving: Meta-analysis of tax incentives and matching donations	Journal of Economic Behavior & Organization	Gwen-Jirō Clochard, Shubham Dey, Shusaku Sasaki et al.	Institute of Social and Economic Research, The University of Osaka; The University of Osaka
2026-10-27	Effects of multi-attributional diversity for targets and perceivers of stereotypes in computer-supported collaborative learning	Computers in Human Behavior	Jennifer Hochstein, Laura Froehlich, Niels Seidel et al.	FernUniversität in Hagen; UiT The Arctic University of Norway; University of Vienna
2026-10-27	Estimating mixed memberships in multi-layer networks	Pattern Recognition	Huan Qing, Xiaofei Xu	Chongqing University of Technology; Wuhan University
2026-10-26	Variation in Health State Utility Values Across Preference-Based Instruments: A Systematic Review and Meta-analysis of Behavioural Risk Factors	Applied Health Economics and Health Policy	Nirmali Ruth Sivapragasam, David Brain, Gayani Amarasinghe et al.	Queensland University of Technology; Duke-NUS Medical School
2026-10-26	Beyond access: Engagement with conversational AI-assisted feedback shapes cognitive load in digital game-based learning	Computers in Human Behavior	Anna Wenzel, Jan-Martin Geiger, Andreas Liening	TU Dortmund University; University of Münster
2026-10-26	Local increment inference for time-inhomogeneous drift in Gaussian processes	Japanese Journal of Statistics and Data Science	Yasutaka Shimizu	Waseda University
2026-10-25	The cultural roots of state-owned enterprises: evidence from Europe	Public Choice	Ákos Dombi, Piotr Matuszak, Katarzyna Szarzec	Eötvös Loránd University; Instytut Nauk Ekonomicznych; Polish Academy of Sciences; …
2026-10-25	Assessing the dynamic role of artificial intelligence in driving economic growth in sub-Saharan Africa	Future Business Journal	Emmanuel Baffour Gyau, Jodian J. Blake, Seidu Musah et al.	Jiangsu University; American College of Education
2026-10-24	Recovery Curves for the PHQ-8 and GAD-7: Clinical Utility and Implementation of Measurement-based Care in a Real-world Outpatient Setting	Administration and Policy in Mental Health and Mental Health Services Research	Mary Beth Connolly Gibbons, Robert Gallop, Nicholas Brian Allen et al.	University of Pennsylvania; West Chester University; University of Oregon
2026-10-24	Effects of trade barriers on foreign direct investment: Evidence from Chinese solar panels	Energy Economics	A. Oriana Montti	Universidad Pontificia Comillas
2026-10-24	Exact divide-and-recombine estimation for negative binomial regression: a simulation study and application to SPARCS hospital length-of-stay data	BMC Medical Research Methodology	Md. Mahadi Hassan Nayem	University of Chittagong
2026-10-23	Saving behavior and associated factors: Evidence from Ethiopia	Finance Research Open	Kebede Abrha Mengstu, Zenebe Gebreegziabher, Haftom Bayray Kahsay et al.	Mekelle University; Ethiopian Policy Studies Institute; University of Copenhagen; …
2026-10-23	Markov-Switching Multifractal Models for High-Frequency Trade Counts	Computational Economics	Zhamilya Mussayeva, Karim Moussa	Vrije Universiteit Amsterdam
2026-10-23	Port efficiency beyond the terminal: weather exposure, cargo-origin concentration and logistics vulnerability	Transport Policy	William Barros Miranda, Ticiana Grecco Zanon Moura, Lorena García-Alonso et al.	Universidad de Oviedo
2026-10-23	Generalized and scalable deep Gaussian process emulation	Computational Statistics & Data Analysis	Deyu Ming, Daniel Williamson	University College London; University of Exeter
2026-10-22	Partially privacy-protected logistic regression with L1 penalty and sign constraint	AStA Advances in Statistical Analysis	Hyungwoo Kim, Hosik Choi, Woojoo Lee	Pukyong National University; University of Seoul; Seoul National University
2026-10-22	Do long-term yields help to estimate short-term risk premia?	Journal of Financial Economics	Andrea Berardi, Roger Brown, Stephen M. Schaefer	Ca' Foscari University of Venice; London Business School
2026-10-22	Long term survival model with frailt terms based on the power variance function family	Statistical Methods & Applications	Michelle M. Sacramento, Gladys D. C. Barriga, Vicente G. Cancho et al.	Universidade de São Paulo; Universidade Estadual Paulista (Unesp)
2026-10-22	Turning adversity into opportunity: Managerial interventions and employee responses to observed customer mistreatment	International Journal of Hospitality Management	Xiaowen Hu, Hongmin Yan, Siran Zhan	Queensland University of Technology; University of Manchester; Aston University; …
2026-10-21	Exploring inequalities in 15-minute walkable neighborhoods: A typology of perceived accessibility-preference mismatch	Transportation Research Part A Policy and Practice	Kunbo Shi, Lingkun Meng, Yang Hu et al.	Beijing Jiaotong University; University of Hong Kong; Nanjing University; …
2026-10-21	A unified likelihood approach for progressive multistate frailty models under double censoring: application to retinopathy of prematurity	BMC Medical Research Methodology	Aniseh Dadgar, Hojjat Zeraati, Fatemeh Bazvand et al.	Tehran University of Medical Sciences; Farabi Hospital
2026-10-21	The effect of increased instruction time on students’ academic achievement: A three-level meta-analysis	Educational Research Review	Zhi Zeng, Mianmian Zhou, Haiyun Gan et al.	Chinese University of Hong Kong
2026-10-21	Unamortized black-box variational inference for joint response and response time models	Behaviormetrika	Rudolf Debelak, Dylan Molenaar	École Polytechnique Fédérale de Lausanne; University of Amsterdam
2026-10-21	The impact of regional growth on internal migration: a district-level analysis for Malawi	World Development	Mauro Lanati, Rainer Thiele	University of Florence; Kiel Institute for the World Economy; Christian-Albrechts-Universität zu Kiel
2026-10-21	Investigating the determinants of gaming app disengagement: A mixed methods–grounded theory approach	Information & Management	Haroon Iqbal Maseeh, Charles Jebarajakirthy	Griffith University; Sunway University
2026-10-21	Modeling STEM persistence in college: the mediating roles of academic preparation and academic behaviors for students with attention-deficit/hyperactivity disorder	International Journal of STEM Education	Xiaping Li, Nolgie Oquendo-Colón, Cynthia Finelli et al.	University of Michigan; Colorado School of Mines
2026-10-21	Buffering institutional erosion: organizational ties and SME exports under populism	Journal of International Business Studies	Xiaolong Shui, Luyang Chen, Michael Witt	University of Bristol; University of Westminster; King's College London
2026-10-20	Regression analysis of interval-censored failure time data in the presence of random change points and a cured subgroup	Statistics and Computing	Yichen Lou, Mingyue Du, Jianguo Sun	Nanyang Technological University; Jilin University; Southern University of Science and Technology
2026-10-20	Social support processes link gratitude and well-being across cultures and over time	Journal of Happiness Studies	Carley Vornlocher, Alexandra S. Wormley	Arizona State University; University of Michigan
2026-10-20	R-estimation with right-censored data	Lifetime Data Analysis	Glen A. Satten, Mo Li, Ni Zhao et al.	Emory University; University of Louisiana at Lafayette; Johns Hopkins University; …
2026-10-20	General oracle inequalities for a penalized log-likelihood criterion based on non-stationary data	Stochastic Processes and their Applications	Julien Aubert, Luc Lehéricy, Patricia Reynaud-Bouret	Centre National de la Recherche Scientifique; Université Côte d'Azur; Laboratoire Jean-Alexandre Dieudonné

Cite this page

Scholar4AI. (2026). Maximum likelihood estimation. Journal and Conference Research Rankings. Retrieved November 5, 2026, from https://scholar4ai.com/equations/maximum-likelihood-estimation

@misc{scholar4ai-equations-maximum-likelihood-estimation,
  author = {{Scholar4AI}},
  title = {Maximum likelihood estimation},
  year = {2026},
  howpublished = {\url{https://scholar4ai.com/equations/maximum-likelihood-estimation}},
  urldate = {2026-11-05},
  note = {Journal and Conference Research Rankings; data from OpenAlex (CC0); licensed CC BY-NC 4.0}
}

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