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Winsorising
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, values that are 'way outside' the bulk of the data. A typical strategy to account for, without eliminating altogether, these outlier values is to 'reset' outliers to a specified percentile (or an upper and lower percentile) of the data. For example, a 90% winsorization would see all data below the 5th percentile set to the 5th percentile, and all 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 (see below), that will achieve a similar effect. Examp ... [...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 d ... [...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 ro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robust Statistics
Robust statistics are statistics that maintain their properties even if the underlying distributional assumptions are incorrect. Robust Statistics, statistical methods have been developed for many common problems, such as estimating location parameter, location, scale parameter, scale, and regression coefficient, 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 statistics, 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 are not unduly affected by outliers or other small departures from Statistical assumption, model assumptions. In statistics, classical e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trimmed Estimator
In statistics, a trimmed estimator is an estimator derived from another estimator by excluding some of the extreme values, a process called truncation. This is generally done to obtain a more robust statistic, and the extreme values are considered outliers. Trimmed estimators also often have higher efficiency for mixture distributions, and heavy-tailed distributions than the corresponding untrimmed estimator, at the cost of lower efficiency for other distributions, such as the normal distribution. Given an estimator, the x% trimmed version is obtained by discarding the x% lowest or highest observations or on both end: it is a statistic on the ''middle'' of the data. For instance, the 5% trimmed mean is obtained by taking the mean of the 5% to 95% range. In some cases a trimmed estimator discards a fixed number of points (such as maximum and minimum) instead of a percentage. Examples The median is the most trimmed statistic (nominally 50%), as it discards all but the most centra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Censoring (statistics)
In statistics, censoring is a condition in which the Value (mathematics), value of a measurement or observation is only partially known. For example, suppose a study is conducted to measure the impact of a drug on mortality rate. In such a study, it may be known that an individual's age at death is ''at least'' 75 years (but may be more). Such a situation could occur if the individual withdrew from the study at age 75, or if the individual is currently alive at the age of 75. Censoring also occurs when a value occurs outside the range of a measuring instrument. For example, a bathroom scale might only measure up to 140 kg, after which it rolls over 0 and continues to count up from there. If a 160 kg individual is weighed using the scale, the observer would only know that the individual's weight is 20 modulo, mod 140 kg (in addition to 160kg, they could weigh 20kg, 300kg, 440kg, and so on). The problem of censored data, in which the observed value of some variable is partially kn ... [...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 (e.g., a calculation method of the average) and for the value of the function on a given sample (e.g., the result of the average calculation). 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 s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MSCI
MSCI Inc. (formerly Morgan Stanley Capital International) is an American finance company headquartered in New York City. MSCI is a global provider of equity, fixed income, real estate indices, multi-asset portfolio analysis tools, ESG and climate finance products. It operates the MSCI World, MSCI Emerging Markets, and MSCI All Country World (ACWI) indices, among others. The company is headquartered at 7 World Trade Center in Manhattan. Its business primarily consists of licensing its indices to index funds, such as exchange-traded funds (ETFs), which pay a fee of around 0.02 to 0.04 percent of the invested volume for the use of the index. funds worth over 16.5 trillion US$ were based on MSCI indices. History In 1968, Capital International published indices covering the global stock market for non-U.S. markets. In 1986, Morgan Stanley licensed the rights to the indices from Capital International and branded the indices as the Morgan Stanley Capital International (MSCI) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Data Transformation
Statistics (from German: ', "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. When census data (comprising every member of the target population) 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 experimental study involves taking measurements of the syst ... [...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 Egon Sharpe Pearson (11 August 1895 – 12 June 1980) was one of three children of Karl Pearson and Maria, née Sharpe, and, like his father, a British statistician. Career Pearson was educated at Winchester College and Trinity College ..., Georges Darmois, Allen T. Craig, Deming, von Mises, H. L. Rietz, and Shewhart. References External links ''Annals of Mathematical Statistics''at Project Euclid Statistics journals Probability journals {{statistics-journal-stub ... [...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 r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
