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The use of a sequence of experiments, where the design of each may depend on the results of previous experiments, including the possible decision to stop experimenting, is within the scope of sequential analysis, a field that was pioneered [12] by Abraham Wald in the context of sequential tests of statistical hypotheses. [13]
Sequential analysis also has a connection to the problem of gambler's ruin that has been studied by, among others, Huygens in 1657. [12]Step detection is the process of finding abrupt changes in the mean level of a time series or signal.
Once it is suspected that only significant explanatory variables are left, then a more complicated design, such as a central composite design can be implemented to estimate a second-degree polynomial model, which is still only an approximation at best. However, the second-degree model can be used to optimize (maximize, minimize, or attain a ...
Sequential estimation is the core of many well known applications, such as the Viterbi decoder, convolutional codes, video compression or target tracking. Due to its state space representation, which is in most cases motivated by physical laws of motion, there is a direct link to control applications, which led to the use of the Kalman filter ...
The main approaches for stepwise regression are: Forward selection, which involves starting with no variables in the model, testing the addition of each variable using a chosen model fit criterion, adding the variable (if any) whose inclusion gives the most statistically significant improvement of the fit, and repeating this process until none improves the model to a statistically significant ...
In the examples listed above, a nuisance variable is a variable that is not the primary focus of the study but can affect the outcomes of the experiment. [3] They are considered potential sources of variability that, if not controlled or accounted for, may confound the interpretation between the independent and dependent variables .
The design matrix has dimension n-by-p, where n is the number of samples observed, and p is the number of variables measured in all samples. [4] [5]In this representation different rows typically represent different repetitions of an experiment, while columns represent different types of data (say, the results from particular probes).
where D indicates employment (D = 1 if the respondent is employed and D = 0 otherwise), Z is a vector of explanatory variables, is a vector of unknown parameters, and Φ is the cumulative distribution function of the standard normal distribution. Estimation of the model yields results that can be used to predict this employment probability for ...