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Winsorizing
Winsorizing or winsorization is the transformation of statistics by limiting extreme values in the statistical data to reduce the effect of possibly spurious outliers. It is named after the engineer-turned-biostatistician Charles P. Winsor (1895–1951). The effect is the same as clipping in signal processing. The distribution of many statistics can be heavily influenced by outliers. A typical strategy is to set all outliers to a specified percentile of the data; for example, a 90% winsorization would see all data below the 5th percentile set to the 5th percentile, and data above the 95th percentile set to the 95th percentile. Winsorized estimators are usually more robust to outliers than their more standard forms, although there are alternatives, such as trimming, that will achieve a similar effect. Example Consider the data set consisting of: : (N = 20, mean = 101.5) The data below the 5th percentile lies between −40 and −5, while the data above the 95th percentile lies b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Winsor
Charles Paine Winsor (June 19, 1895 – April 4, 1951) was an American engineer, physiologist and biostatistician. Winsor was born in Boston to Frederick Winsor and Mary Anna Lee Winsor in 1895. He studied at Harvard University where he obtained 2 degrees (AB and SB) in engineering. From 1921 to 1927 he worked as an engineer at the New England Telephone and Telegraph Company. His interest in biology made him switch career and he moved to Baltimore to work for Raymond Pearl, and he returned to Harvard to finish his PhD in 1935 in general physiology under W. J. Crozier. Following this, from 1938 to 1941 he worked at the Statistical Laboratory at Iowa State College as Assistant Professor of mathematics. During the war he worked at Princeton University under a contract from the Office of Scientific Research and Development. Following the war, in 1946 he went back to Baltimore and become Assistant Professor of Biostatistics in the School of Hygiene and Public Health, Johns Hopkins U ... [...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] |
Outliers
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistic
A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis. The average (or mean) of sample values is a statistic. The term statistic is used both for the function and for the value of the function on a given sample. When a statistic is being used for a specific purpose, it may be referred to by a name indicating its purpose. When a statistic is used for estimating a population parameter, the statistic is called an '' estimator''. A population parameter is any characteristic of a population under study, but when it is not feasible to directly measure the value of a population parameter, statistical methods are used to infer the likely value of the parameter on the basis of a statistic computed from a sample taken from the population. For example, the sample mean is an unbiased estimato ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truncated Mean
A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves the calculation of the mean after discarding given parts of a probability distribution or sample at the high and low end, and typically discarding an equal amount of both. This number of points to be discarded is usually given as a percentage of the total number of points, but may also be given as a fixed number of points. For most statistical applications, 5 to 25 percent of the ends are discarded. For example, given a set of 8 points, trimming by 12.5% would discard the minimum and maximum value in the sample: the smallest and largest values, and would compute the mean of the remaining 6 points. The 25% trimmed mean (when the lowest 25% and the highest 25% are discarded) is known as the interquartile mean. The median can be regarded as a fully truncated mean and is most robust. As with other trimmed estimators, the main advantage of the trimmed mean is robu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Data Transformation
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 experim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematical Statistics
The ''Annals of Mathematical Statistics'' was a peer-reviewed statistics journal published by the Institute of Mathematical Statistics from 1930 to 1972. It was superseded by the ''Annals of Statistics'' and the '' Annals of Probability''. In 1938, Samuel Wilks became editor-in-chief of the ''Annals'' and recruited a remarkable editorial staff: Fisher, Neyman, Cramér, Hotelling, Egon Pearson, Georges Darmois, Allen T. Craig, Deming, von Mises, H. L. Rietz, and Shewhart Walter Andrew Shewhart (pronounced like "shoe-heart"; March 18, 1891 – March 11, 1967) was an American physicist, engineer and statistician, sometimes known as the ''father of statistical quality control'' and also related to the Shewhart cycl .... References {{reflist External links Annals of Mathematical Statistics at Project Euclid Statistics journals Probability journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robust Regression
In robust statistics, robust regression seeks to overcome some limitations of traditional regression analysis. A regression analysis models the relationship between one or more independent variables and a dependent variable. Standard types of regression, such as ordinary least squares, have favourable properties if their underlying assumptions are true, but can give misleading results otherwise (i.e. are not robust to assumption violations). Robust regression methods are designed to limit the effect that violations of assumptions by the underlying data-generating process have on regression estimates. For example, least squares estimates for regression models are highly sensitive to outliers: an outlier with twice the error magnitude of a typical observation contributes four (two squared) times as much to the squared error loss, and therefore has more leverage over the regression estimates. The Huber loss function is a robust alternative to standard square error loss that redu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Huber Loss
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), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stock Indexes
In finance, a stock index, or stock market index, is an index that measures a stock market, or a subset of the stock market, that helps investors compare current stock price levels with past prices to calculate market performance. Two of the primary criteria of an index are that it is ''investable'' and ''transparent'': The methods of its construction are specified. Investors can invest in a stock market index by buying an index fund, which are structured as either a mutual fund or an exchange-traded fund, and "track" an index. The difference between an index fund's performance and the index, if any, is called '' tracking error''. For a list of major stock market indices, see List of stock market indices. Types of indices by weighting method Stock market indices could be segmented by their index weight methodology, or the rules on how stocks are allocated in the index, independent of its stock coverage. For example, the S&P 500 and the S&P 500 Equal Weight both covers the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Survey Methodology
Survey methodology is "the study of survey methods". As a field of applied statistics concentrating on human-research surveys, survey methodology studies the sampling of individual units from a population and associated techniques of survey data collection, such as questionnaire construction and methods for improving the number and accuracy of responses to surveys. Survey methodology targets instruments or procedures that ask one or more questions that may or may not be answered. Researchers carry out statistical surveys with a view towards making statistical inferences about the population being studied; such inferences depend strongly on the survey questions used. Polls about public opinion, public-health surveys, market-research surveys, government surveys and censuses all exemplify quantitative research that uses survey methodology to answer questions about a population. Although censuses do not include a "sample", they do include other aspects of survey methodolog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
