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Topic · Applied Mathematics

Statistical and numerical algorithms

Statistical and numerical algorithms is a research topic within Applied Mathematics. Science Explorer counts 12k research works in it since 1950. 10.1% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the theory, algorithms, and applications of Total Least Squares (TLS) methods, including Singular Spectrum Analysis, weighted least squares, geodetic transformations, forecasting models, errors-in-variables models, structured low-rank approximation, parameter estimation, and time series analysis.

  • Total Least Squares
  • Singular Spectrum Analysis
  • Weighted Least Squares
  • Geodetic Transformations
  • Forecasting
  • Errors-in-Variables Models
  • Structured Low-Rank Approximation
  • Parameter Estimation
  • Time Series Analysis
  • Regression
Research works
12k
fractional, since 1950
In the world top 10%
1.3k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+4%
the tick is no change
Largest producer
China
26% of the 10 largest, 2022-now
Statistical and numerical algorithms

Which countries lead Statistical and numerical algorithms research?

By volume, China and the United States publish the most (312 and 278 works in 2022-now).

By volume, 2022-now

  1. 1 China 312 works
  2. 2 United States 278 works
  3. 3 Russia 170 works
  4. 4 Germany 87 works
  5. 5 India 73 works
  6. 6 France 63 works
  7. 7 United Kingdom 60 works
  8. 8 Italy 55 works
  9. 9 Indonesia 47 works
  10. 10 Japan 43 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 26.3%United States: 23.4%Russia: 14.3%Germany: 7.3%6 others listed: 28.8%26%largest
China312 · 26.3%United States278 · 23.4%Russia170 · 14.3%Germany87 · 7.3%6 others listed342 · 28.8%

Shares of the rows listed above, not of the whole node.

Which institutions lead Statistical and numerical algorithms research?

By volume in 2022-now, Russian Academy of Sciences publishes the most Statistical and numerical algorithms research, followed by Centre National de la Recherche Scientifique and Chinese Academy of Sciences.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 49 works
  2. 2 Centre National de la Recherche ScientifiqueFrance 23 works
  3. 3 Chinese Academy of SciencesChina 16 works
  4. 4 St Petersburg UniversityRussia 10 works
  5. 5 Lomonosov Moscow State UniversityRussia 9 works
  6. 6 National Academy of Sciences of UkraineUkraine 9 works
  7. 7 Tongji UniversityChina 8 works
  8. 8 Sapienza University of RomeItaly 8 works
  9. 9 Moscow Aviation InstituteRussia 7 works
  10. 10 Wuhan UniversityChina 6 works

Who are the leading researchers in Statistical and numerical algorithms?

The most-cited researchers publishing on Statistical and numerical algorithms include Robert John Tibshirani, Karl John Friston and Donald B. Rubin.

  1. 1 Robert John Tibshirani United States 396k citations
  2. 2 Karl John Friston United Kingdom 310k citations
  3. 3 Donald B. Rubin United States 301k citations
  4. 4 Trevor Hastie United States 301k citations
  5. 5 Ralph B. D’Agostino United States 255k citations
  6. 6 Leo Breiman United States 243k citations
  7. 7 Gordon K. Smyth Australia 237k citations
  8. 8 Peter M. Bentler United States 233k citations
  9. 9 Jerome H. Friedman United States 224k citations
  10. 10 G. Mitselmakher France 223k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Statistical and numerical algorithms?

The most cited paper in Statistical and numerical algorithms is "A theory for multiresolution signal decomposition: the wavelet representation" (Stéphane Mallat, 1989), with 21,434 citations. Next come "Information Theory and an Extension of the Maximum Likelihood Principle" (18,124) and "An Analysis of Transformations" (15,274).

Most cited papers
#PaperReleasedCitations
1 A theory for multiresolution signal decomposition: the wavelet representation Stéphane Mallat · IEEE Transactions on Pattern Analysis and Machine Intelligence Jul 1989 21,434
2 Information Theory and an Extension of the Maximum Likelihood Principle Hirotogu Akaike · Springer series in statistics Book chapter 1998 18,124
3 An Analysis of Transformations George E. P. Box, David Roxbee Cox · Journal of the Royal Statistical Society Series B (Statistical Methodology) Jul 1964 15,274
4 A Caution Regarding Rules of Thumb for Variance Inflation Factors Robert M. O’Brien · Quality & Quantity 12 Mar 2007 11,097
5 Ridge Regression: Biased Estimation for Nonorthogonal Problems Arthur E. Hoerl, Robert W. Kennard · Technometrics Feb 1970 9,491
All 95 most cited papers, with filters and sorting

Where is Statistical and numerical algorithms research done?

The largest centres of Statistical and numerical algorithms research in 2022-now are Moscow (Russia), Beijing (China), Shanghai (China) and Saint Petersburg (Russia). Among places with at least 20 works in it, it is an unusually large share of all research in Saint Petersburg, Kyiv and Moscow.

Largest cities, 2022-now

  1. 1 MoscowRussia 68 works
  2. 2 BeijingChina 53 works
  3. 3 ShanghaiChina 31 works
  4. 4 Saint PetersburgRussia 26 works
  5. 5 KyivUkraine 21 works
  6. 6 ParisFrance 20 works
  7. 7 WuhanChina 19 works
  8. 8 Xi'anChina 17 works
  9. 9 NanjingChina 16 works
  10. 10 TokyoJapan 16 works

Where it is the local speciality

  1. Saint PetersburgRU · 26.0 works5.7×
  2. KyivUA · 21.4 works4.4×
  3. MoscowRU · 68.1 works3.9×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Statistical and numerical algorithms than the world average.

See Statistical and numerical algorithms on the map

Where is the best place to study Statistical and numerical algorithms?

Among universities, judged by research, St Petersburg University, Tongji University and Lomonosov Moscow State University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1St Petersburg UniversityRussia 53.84.4%13.6×10 +22.0%
2Tongji UniversityChina 51.319.8%3.5×8 +23.2%
3Lomonosov Moscow State UniversityRussia 34.17.4%7.0×9 -38.3%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Statistical and numerical algorithms, country by country

Is Statistical and numerical algorithms research growing?

Output in 2022-2025 was 4% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Statistical and numerical algorithms.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Statistical and numerical algorithms as a percentage of every work published that year, 0.0074% in 2024.

still counting0.010%0.020%0.030%Statistical and numerical algorithms0.0081% in 202519801990200020102020

Fractional works of Statistical and numerical algorithms over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Statistical and numerical algorithms10.3% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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