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In statistics, the method of moments is a method of estimation of population parameters.The same principle is used to derive higher moments like skewness and kurtosis. It starts by expressing the population moments (i.e., the expected values of powers of the random variable under consideration) as functions of the parameters of interest.
Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data.
This is due to the fact that the intersection between sets of parameter vectors that are consistent with the i th data bar is empty. To be robust with respect to outliers, we generally characterize the set of parameter vectors that are consistent with all data bars except q of them. This is possible using the notion of q-relaxed intersection.
A given regression method will ultimately provide an estimate of , usually denoted ^ to distinguish the estimate from the true (unknown) parameter value that generated the data. Using this estimate, the researcher can then use the fitted value ^ = (, ^) for prediction or to assess the accuracy of the model in explaining the data.
Conversely, if we know the value of the latent variables , we can find an estimate of the parameters fairly easily, typically by simply grouping the observed data points according to the value of the associated latent variable and averaging the values, or some function of the values, of the points in each group.
In order to still use the Box–Jenkins approach, one could difference the series and then estimate models such as ARIMA, given that many commonly used time series (e.g. in economics) appear to be stationary in first differences. Forecasts from such a model will still reflect cycles and seasonality that are present in the data.
A Newey–West estimator is used in statistics and econometrics to provide an estimate of the covariance matrix of the parameters of a regression-type model where the standard assumptions of regression analysis do not apply. [1] It was devised by Whitney K. Newey and Kenneth D. West in 1987, although there are a number of later variants.
A "parameter" is to a population as a "statistic" is to a sample; that is to say, a parameter describes the true value calculated from the full population (such as the population mean), whereas a statistic is an estimated measurement of the parameter based on a sample (such as the sample mean).