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When the model has been estimated over all available data with none held back, the MSPE of the model over the entire population of mostly unobserved data can be estimated as follows.
The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled).
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.
The maximum sustainable yield is usually higher than the optimum sustainable yield and maximum economic yield. MSY is extensively used for fisheries management . Unlike the logistic ( Schaefer ) model, [ 1 ] MSY has been refined in most modern fisheries models and occurs at around 30% of the unexploited population size.
The concept of maximum sustainable yield (MSY) has been used in fisheries science and fisheries management for more than a century. Originally developed and popularized by Fedor Baranov early in the 1900s as the "theory of fishing," it is often credited with laying the foundation for the modern understanding of the population dynamics of fisheries. [1]
The modified Dietz method [1] [2] [3] is a measure of the ex post (i.e. historical) performance of an investment portfolio in the presence of external flows. (External flows are movements of value such as transfers of cash, securities or other instruments in or out of the portfolio, with no equal simultaneous movement of value in the opposite direction, and which are not income from the ...
The earliest reference to a similar formula appears to be Armstrong (1985, p. 348), where it is called "adjusted MAPE" and is defined without the absolute values in the denominator. It was later discussed, modified, and re-proposed by Flores (1986).
It usually corresponds to an effort level lower than that of maximum sustainable yield. In environmental science , optimum sustainable yield is the largest economical yield of a renewable resource achievable over a long time period without decreasing the ability of the population or its environment to support the continuation of this level of ...