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In mathematics, particularly in dynamical systems, the Hilbert–Arnold problem is an unsolved problem concerning the estimation of limit cycles.It asks whether in a generic finite-parameter family of smooth vector fields on a sphere with a compact parameter base, the number of limit cycles is uniformly bounded across all parameter values.
An example is shown on the left. The parameter space has just two elements and each point on the graph corresponds to the risk of a decision rule: the x-coordinate is the risk when the parameter is and the y-coordinate is the risk when the parameter is . In this decision problem, the minimax estimator lies on a line segment connecting two ...
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.
If the parameter space Θ is compact and there is a limiting function Q 0 (θ) such that: ^ converges to Q 0 (θ) in probability uniformly over Θ, and the function Q 0 (θ) is continuous and has a unique maximum at θ = θ 0 then ^ is consistent for θ 0. [1]
MINQUE is a theory alongside other estimation methods in estimation theory, such as the method of moments or maximum likelihood estimation. Similar to the theory of best linear unbiased estimation , MINQUE is specifically concerned with linear regression models. [ 1 ]
The primary application of the Levenberg–Marquardt algorithm is in the least-squares curve fitting problem: given a set of empirical pairs (,) of independent and dependent variables, find the parameters of the model curve (,) so that the sum of the squares of the deviations () is minimized:
The ECF apparently made its debut in page 342 of the classical textbook of Cramér (1946), [1] and then as part of the auxiliary tools for density estimation in Parzen (1962). [2] Nearly a decade later the ECF features as the main object of research in two separate lines of application: In Press (1972) [ 3 ] for parameter estimation and in ...
In econometrics and statistics, the generalized method of moments (GMM) is a generic method for estimating parameters in statistical models.Usually it is applied in the context of semiparametric models, where the parameter of interest is finite-dimensional, whereas the full shape of the data's distribution function may not be known, and therefore maximum likelihood estimation is not applicable.