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In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of ...
Quantile regression is a type of regression analysis used in statistics and econometrics. Whereas the method of least squares estimates the conditional mean of the response variable across values of the predictor variables, quantile regression estimates the conditional median (or other quantiles) of the response variable.
Standard method like Gauss elimination can be used to solve the matrix equation for .A more numerically stable method is provided by QR decomposition method. Since the matrix is a symmetric positive definite matrix, can be solved twice as fast with the Cholesky decomposition, while for large sparse systems conjugate gradient method is more effective.
An example application of the method of moments is to estimate polynomial probability density distributions. In this case, an approximating polynomial of order is defined on an interval [,]. The method of moments then yields a system of equations, whose solution involves the inversion of a Hankel matrix. [2]
The data set contains two outliers, which greatly influence the sample mean. (The sample mean need not be a consistent estimator for any population mean, because no mean needs to exist for a heavy-tailed distribution.) A well-defined and robust statistic for the central tendency is the sample median, which is consistent and median-unbiased for ...
The method of conditional probabilities replaces the random root-to-leaf walk in the random experiment by a deterministic root-to-leaf walk, where each step is chosen to inductively maintain the following invariant: the conditional probability of failure, given the current state, is less than 1.
In statistics, the Hodges–Lehmann estimator is a robust and nonparametric estimator of a population's location parameter.For populations that are symmetric about one median, such as the Gaussian or normal distribution or the Student t-distribution, the Hodges–Lehmann estimator is a consistent and median-unbiased estimate of the population median.
Once the sample mean is known, no further information about μ can be obtained from the sample itself. On the other hand, for an arbitrary distribution the median is not sufficient for the mean: even if the median of the sample is known, knowing the sample itself would provide further information about the population mean. For example, if the ...