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Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance,where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form,ANOVA provides a statistical test of whether two or more population means are equal,and therefore generalizes the t-test beyond two means. In other words,the ANOVA is used to test the difference between two or more means.
The following outline is provided as an overview of and topical guide to statistics:
Nonparametric statistics is the type of statistics that is not restricted by assumptions concerning the nature of the population from which a sample is drawn. This is opposed to parametric statistics,for which a problem is restricted a priori by assumptions concerning the specific distribution of the population and parameters. Nonparametric statistics is based on either not assuming a particular distribution or having a distribution specified but with the distribution's parameters not specified in advance. Nonparametric statistics can be used for descriptive statistics or statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are evidently violated.
In statistical modeling,regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables. The most common form of regression analysis is linear regression,in which one finds the line that most closely fits the data according to a specific mathematical criterion. For example,the method of ordinary least squares computes the unique line that minimizes the sum of squared differences between the true data and that line. For specific mathematical reasons,this allows the researcher to estimate the conditional expectation of the dependent variable when the independent variables take on a given set of values. Less common forms of regression use slightly different procedures to estimate alternative location parameters or estimate the conditional expectation across a broader collection of non-linear models.
Mathematical statistics is the application of probability theory,a branch of mathematics,to statistics,as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis,linear algebra,stochastic analysis,differential equations,and measure theory.
Truncated regression models are a class of models in which the sample has been truncated for certain ranges of the dependent variable. That means observations with values in the dependent variable below or above certain thresholds are systematically excluded from the sample. Therefore,whole observations are missing,so that neither the dependent nor the independent variable is known. This is in contrast to censored regression models where only the value of the dependent variable is clustered at a lower threshold,an upper threshold,or both,while the value for independent variables is available.
Joseph Michael Hilbe was an American statistician and philosopher,founding President of the International Astrostatistics Association(IAA) and one of the most prolific authors of books on statistical modeling in the early twenty-first century. Hilbe was an elected Fellow of the American Statistical Association as well as an elected member of the International Statistical Institute (ISI),for which he founded the ISI astrostatistics committee in 2009. Hilbe was also a Fellow of the Royal Statistical Society and Full Member of the American Astronomical Society.
Neil Shephard,FBA,is an econometrician,currently Frank B. Baird Jr.,Professor of Science in the Department of Economics and the Department of Statistics at Harvard University.
Jayanta Kumar Ghosh was an Indian statistician,an emeritus professor at Indian Statistical Institute and a professor of statistics at Purdue University.
Richard John Samworth is the Professor of Statistical Science and the Director of the Statistical Laboratory,University of Cambridge,and a Teaching Fellow of St John's College,Cambridge. He was educated at St John's College,Cambridge. His main research interests are in nonparametric and high-dimensional statistics. Particular topics include shape-constrained density estimation and other nonparametric function estimation problems,nonparametric classification,clustering and regression,the bootstrap and high-dimensional variable selection problems.
In statistics,one purpose for the analysis of variance (ANOVA) is to analyze differences in means between groups. The test statistic,F,assumes independence of observations,homogeneous variances,and population normality. ANOVA on ranks is a statistic designed for situations when the normality assumption has been violated.
Erik Gustav Elfving was a Finnish mathematician and statistician. He wrote pioneering works in mathematical statistics,especially on the design of experiments.
In non-parametric statistics,the Theil–Sen estimator is a method for robustly fitting a line to sample points in the plane by choosing the median of the slopes of all lines through pairs of points. It has also been called Sen's slope estimator,slope selection,the single median method,the Kendall robust line-fit method,and the Kendall–Theil robust line. It is named after Henri Theil and Pranab K. Sen,who published papers on this method in 1950 and 1968 respectively,and after Maurice Kendall because of its relation to the Kendall tau rank correlation coefficient.
Control functions are statistical methods to correct for endogeneity problems by modelling the endogeneity in the error term. The approach thereby differs in important ways from other models that try to account for the same econometric problem. Instrumental variables,for example,attempt to model the endogenous variable X as an often invertible model with respect to a relevant and exogenous instrument Z. Panel analysis uses special data properties to difference out unobserved heterogeneity that is assumed to be fixed over time.
Dorota Maria Dabrowska is a Polish statistician known for applying nonparametric statistics and semiparametric models to counting processes and survival analysis. Dabrowska's estimator,from her paper "Kaplan–Meier estimate on the plane" is a widely used tool for bivariate survival under random censoring.
Ingrid Van Keilegom is a Belgian statistician. She is a professor of operations research and business statistics at KU Leuven,and an extraordinary professor at the Universitécatholique de Louvain. Her research interests include survival analysis,observational error,econometrics,and nonparametric statistics.
Siddhartha Chib is an econometrician and statistician,the Harry C. Hartkopf Professor of Econometrics and Statistics at Washington University in St. Louis. His work is primarily in Bayesian statistics,econometrics,and Markov chain Monte Carlo methods.
Charles "Chuck" Joel Stone was an American statistician and mathematician.
References
- ↑ "Michael Akritas".
- 1 2 "Michael G. Akritas - CV" (PDF).
- ↑ "Fellows of the ASA". Archived from the original on 2019-04-25. Retrieved 2019-11-18.
- ↑ "Honored IMS Fellows".
- ↑ "George G. Roussas".
- ↑ "Richard A. Johnson".
- ↑ "Statistical Consulting Center for Astronomy".
- ↑ "About ISNPS".
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