Context: Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In applying statistics to, e.g., a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments., An experiment is a procedure carried out to support, refute, or validate a hypothesis. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated. Experiments vary greatly in goal and scale, but always rely on repeatable procedure and logical analysis of the results. There also exists natural experimental studies., Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384322 B.C.), though "analysis" as a formal concept is a relatively recent development., In statistics , a generalized additive model ( GAM ) is a generalized linear model in which the linear predictor depends linearly on unknown smooth functions of some predictor variables , and interest focuses on inference about these smooth functions . GAMs were originally developed by Trevor Hastie and Robert Tibshirani to blend properties of generalized linear models with additive models . The model relates a univariate response variable , Y , to some predictor variables , xi. An exponential family distribution is specified for Y ( for example normal , binomial or Poisson distributions ) along with a link function g ( for example the identity or log functions ) relating the expected value of Y to the predictor variables via a structure such as g ( \ operatorname ( E ) ( Y ) ) = \ beta_0 + f_1 ( x_1 ) + f_2 ( x_2 ) + \ cdots + f_m ( x_m ) . \ , \ ! The functions fi ( xi ) may be functions with a specified parametric form ( for example a polynomial , or a coefficient depending on the levels of a factor variable ) or may be specified non-parametrically , or semi-parametrically , simply as ' smooth functions ' , to be estimated by non-parametric means . So a typical GAM might use a scatterplot smoothing function , such as a locally weighted mean , for f1 ( x1 ) , and then use a factor model for f2 ( x2 ) . This flexibility to allow non-parametric fits with relaxed assumptions on the actual relationship between response and predictor , provides the potential for better fits to data than purely parametric models , but arguably with some loss of interpretability ., In statistics, a population is a set of similar items or events which is of interest for some question or experiment. A statistical population can be a group of actually existing objects (e.g. the set of all stars within the Milky Way galaxy) or a hypothetical and potentially infinite group of objects conceived as a generalization from experience (e.g. the set of all possible hands in a game of poker). A common aim of statistical analysis is to produce information about some chosen population., Debt, AIDS, Trade, Africa (DATA) was a multinational non-government organization founded in January 2002 in London by U2's Bono along with Bobby Shriver and activists from the Jubilee 2000 Drop the Debt campaign., A statistical model is a class of mathematical model, which embodies a set of assumptions concerning the generation of some sample data, and similar data from a larger population. A statistical model represents, often in considerably idealized form, the data-generating process., In statistics, multicollinearity (also collinearity) is a phenomenon in which two or more predictor variables in a multiple regression model are highly correlated, meaning that one can be linearly predicted from the others with a substantial degree of accuracy. In this situation the coefficient estimates of the multiple regression may change erratically in response to small changes in the model or the data. Multicollinearity does not reduce the predictive power or reliability of the model as a whole, at least within the sample data set; it only affects calculations regarding individual predictors. That is, a multiple regression model with correlated predictors can indicate how well the entire bundle of predictors predicts the outcome variable, but it may not give valid results about any individual predictor, or about which predictors are redundant with respect to others., The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces (often with hundreds or thousands of dimensions) that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience.
The expression was coined by Richard E. Bellman when considering problems in dynamic optimization., Nonparametric regression is a category of regression analysis in which the predictor does not take a predetermined form but is constructed according to information derived from the data. Nonparametric regression requires larger sample sizes than regression based on parametric models because the data must supply the model structure as well as the model estimates., Model selection is the task of selecting a statistical model from a set of candidate models, given data. In the simplest cases, a pre-existing set of data is considered. However, the task can also involve the design of experiments such that the data collected is well-suited to the problem of model selection. Given candidate models of similar predictive or explanatory power, the simplest model is most likely to be the best choice., A statistic (singular) or sample statistic is a single measure of some attribute of a sample (e.g., its arithmetic mean value). It is calculated by applying a function (statistical algorithm) to the values of the items of the sample, which are known together as a set of data., In statistics and machine learning, one of the most common tasks is to fit a "model" to a set of training data, so as to be able to make reliable predictions on general untrained data. In overfitting, a statistical model describes random error or noise instead of the underlying relationship. Overfitting occurs when a model is excessively complex, such as having too many parameters relative to the number of observations. A model that has been overfit has poor predictive performance, as it overreacts to minor fluctuations in the training data., In statistics, an additive model (AM) is a nonparametric regression method. It was suggested by Jerome H. Friedman and Werner Stuetzle (1981) and is an essential part of the ACE algorithm. The "AM" uses a one-dimensional smoother to build a restricted class of nonparametric regression models. Because of this, it is less affected by the curse of dimensionality than e.g. a "p"-dimensional smoother. Furthermore, the "AM" is more flexible than a standard linear model, while being more interpretable than a general regression surface at the cost of approximation errors. Problems with "AM" include model selection, overfitting, and multicollinearity., In statistics, the generalized linear model (GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a "link function" and by allowing the magnitude of the variance of each measurement to be a function of its predicted value., Subject: generalized additive model, Relation: instance_of, Options: (A) ace (B) approximation (C) attribute (D) category (E) change (F) class (G) concept (H) country (I) crystal (J) data (K) degree (L) drop (M) error (N) experiment (O) function (P) galaxy (Q) game (R) generation (S) government (T) group (U) group of objects (V) information (W) machine (X) machine learning (Y) mathematical model (Z) mathematics ([) may (\) method (]) model (^) noise (_) ordinary (`) performance (a) process (b) scale (c) single (d) space (e) standard (f) statistic (g) statistical model (h) statistics (i) structure (j) three (k) trade (l) training (m) two (n) understanding (o) value (p) variable
Output: statistical model