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Homogeneity can be studied to several degrees of complexity. For example, considerations of homoscedasticity examine how much the variability of data-values changes throughout a dataset. However, questions of homogeneity apply to all aspects of the statistical distributions, including the location parameter
In fact, statistical inference in high dimensions is intrinsically hard, a phenomenon known as the curse of dimensionality, and it can be shown that no estimator can do better in a worst-case sense without additional information (see Example 15.10 [2]). Nevertheless, the situation in high-dimensional statistics may not be hopeless when the data ...
Data envelopment analysis provides efficiency coefficients similar to those obtained by multivariate analysis without any distributional assumption. KNNs classify the unseen instance based on the K points in the training set which are nearest to it. A support vector machine (with a Gaussian kernel) is a nonparametric large-margin classifier.
One of the best-known examples of Simpson's paradox comes from a study of gender bias among graduate school admissions to University of California, Berkeley.The admission figures for the fall of 1973 showed that men applying were more likely than women to be admitted, and the difference was so large that it was unlikely to be due to chance.
Difference in differences (DID [1] or DD [2]) is a statistical technique used in econometrics and quantitative research in the social sciences that attempts to mimic an experimental research design using observational study data, by studying the differential effect of a treatment on a 'treatment group' versus a 'control group' in a natural experiment. [3]
Use an orthogonal representation of the data. [12] Poorly-written statistical software will sometimes fail to converge to a correct representation when variables are strongly correlated. However, it is still possible to rewrite the regression to use only uncorrelated variables by performing a change of basis .
For example, when working with time series and other types of sequential data, it is common to difference the data to improve stationarity. If data generated by a random vector X are observed as vectors X i of observations with covariance matrix Σ, a linear transformation can be used to decorrelate the data.
Statistical bias exists in numerous stages of the data collection and analysis process, including: the source of the data, the methods used to collect the data, the estimator chosen, and the methods used to analyze the data. Data analysts can take various measures at each stage of the process to reduce the impact of statistical bias in their ...