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Redescending M-estimator
In statistics, redescending M-estimators are ''Ψ''-type M-estimators which have ''ψ'' functions that are non-decreasing near the origin, but decreasing toward 0 far from the origin. Their ''ψ'' functions can be chosen to redescend smoothly to zero, so that they usually satisfy ''ψ''(''x'') = 0 for all x with , ''x'', > ''r'', where ''r'' is referred to as the minimum rejection point. Due to these properties of the ''ψ'' function, these kinds of estimators are very efficient, have a high breakdown point and, unlike other outlier rejection techniques, they do not suffer from a masking effect. They are efficient because they completely reject gross outliers, and do not completely ignore moderately large outliers (like median). Advantages Redescending M-estimators have high breakdown points (close to 0.5), and their ''Ψ'' function can be chosen to redescend smoothly to 0. This means that moderately large outliers are not ignored completely, and greatly improves the efficiency ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
M-estimator
In statistics, M-estimators are a broad class of extremum estimators for which the objective function is a sample average. Both non-linear least squares and maximum likelihood estimation are special cases of M-estimators. The definition of M-estimators was motivated by robust statistics, which contributed new types of M-estimators. The statistical procedure of evaluating an M-estimator on a data set is called M-estimation. 48 samples of robust M-estimators can be found in a recent review study. More generally, an M-estimator may be defined to be a zero of an estimating function. This estimating function is often the derivative of another statistical function. For example, a maximum-likelihood estimate is the point where the derivative of the likelihood function with respect to the parameter is zero; thus, a maximum-likelihood estimator is a critical point of the score function. In many applications, such M-estimators can be thought of as estimating characteristics of the pop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Outlier Rejection Technique
In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are sometimes excluded from the data set. An outlier can be an indication of exciting possibility, but can also cause serious problems in statistical analyses. Outliers can occur by chance in any distribution, but they can indicate novel behaviour or structures in the data-set, measurement error, or that the population has a heavy-tailed distribution. In the case of measurement error, one wishes to discard them or use statistics that are robust to outliers, while in the case of heavy-tailed distributions, they indicate that the distribution has high skewness and that one should be very cautious in using tools or intuitions that assume a normal distribution. A frequent cause of outliers is a mixture of two distributions, which may be two dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robust Statistics
Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal. Robust statistical methods have been developed for many common problems, such as estimating location, scale, and regression parameters. One motivation is to produce statistical methods that are not unduly affected by outliers. Another motivation is to provide methods with good performance when there are small departures from a parametric distribution. For example, robust methods work well for mixtures of two normal distributions with different standard deviations; under this model, non-robust methods like a t-test work poorly. Introduction Robust statistics seek to provide methods that emulate popular statistical methods, but which are not unduly affected by outliers or other small departures from model assumptions. In statistics, classical estimation methods rely heavily on assumptions which are often not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Huber Loss Function
Huber is a German-language surname. It derives from the German word ''Hube'' meaning hide, a unit of land a farmer might possess, granting them the status of a free tenant. It is in the top ten most common surnames in the German-speaking world, especially in Austria and Switzerland where it is the surname of approximately 0.3% of the population. Variants arising from varying dialectal pronunciation of the surname include Hueber, Hüber, Huemer, Humer, Haumer, Huebner and (anglicized) Hoover. People with the surname Huber A *Adam Huber (born 1987), American actor and model. *Alexander Huber (born 1968), German climber and mountaineer *Alexander Huber (football) (born 1985), German football player * Alyson Huber (born 1972), Californian legislator elected to the State Assembly in 2008 *Anja Huber (born 1983), German skeleton racer *Anke Huber (born 1974), German tennis player *Anthony Huber (born 1994), killed in the Kenosha unrest shooting B *Bruno Huber (1930–1999), Swis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauchy Distribution
The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution f(x; x_0,\gamma) is the distribution of the -intercept of a ray issuing from (x_0,\gamma) with a uniformly distributed angle. It is also the distribution of the ratio of two independent normally distributed random variables with mean zero. The Cauchy distribution is often used in statistics as the canonical example of a " pathological" distribution since both its expected value and its variance are undefined (but see below). The Cauchy distribution does not have finite moments of order greater than or equal to one; only fractional absolute moments exist., Chapter 16. The Cauchy distribution has no moment generating function. In mathematics, it is closely related to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hampel
Hampel is a German surname. Notable people with the surname include: *Anton Joseph Hampel (1710–1771), German classical horn player *Armin-Paul Hampel (born 1957), German politician * Desiderius Hampel (1895–1981), Croatian SS general *Felicity Hampel (born 1955), Australian lawyer and judge *George Hampel (other), multiple people *Gunter Hampel (born 1937), German musician and composer *Jarosław Hampel (born 1982), Polish motorcycle speedway rider *József Hampel (1849–1913), Hungarian archaeologist * Olaf Hampel (born 1965), German bobsledder *Oliver Hampel (born 1985), German footballer *Otto and Elise Hampel (died 1943), German activists *Paul William Hampel, Russian spy See also *Hampl *Hempel *Hample Hample is a surname. Notable people with the surname include: *Dale Hample (born 1949), American academic *Judy Hample Judy Gayle Hample was an American academic administrator. She is the former chancellor of the Pennsylvania State System of Hig ... {{surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tukey
John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distribution, the Tukey test of additivity, and the Teichmüller–Tukey lemma all bear his name. He is also credited with coining the term ' bit' and the first published use of the word ' software'. Biography Tukey was born in New Bedford, Massachusetts in 1915, to a Latin teacher father and a private tutor. He was mainly taught by his mother and attended regular classes only for certain subjects like French. Tukey obtained a BA in 1936 and MSc in 1937 in chemistry, from Brown University, before moving to Princeton University, where in 1939 he received a PhD in mathematics after completing a doctoral dissertation titled "On denumerability in topology". During World War II, Tukey worked at the Fire Control Research Office and collaborated wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrew
Andrew is the English form of a given name common in many countries. In the 1990s, it was among the top ten most popular names given to boys in English-speaking countries. "Andrew" is frequently shortened to "Andy" or "Drew". The word is derived from the el, Ἀνδρέας, ''Andreas'', itself related to grc, ἀνήρ/ἀνδρός ''aner/andros'', "man" (as opposed to "woman"), thus meaning "manly" and, as consequence, "brave", "strong", "courageous", and "warrior". In the King James Bible, the Greek "Ἀνδρέας" is translated as Andrew. Popularity Australia In 2000, the name Andrew was the second most popular name in Australia. In 1999, it was the 19th most common name, while in 1940, it was the 31st most common name. Andrew was the first most popular name given to boys in the Northern Territory in 2003 to 2015 and continuing. In Victoria, Andrew was the first most popular name for a boy in the 1970s. Canada Andrew was the 20th most popular name chosen for male ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
