Weighted Loss Functions for Set Estimation and Testing Hypotheses

Hypotheses testing as a fuzzy set estimation problem

For many scientific experiments computing a p-value is the standard method for reporting the outcome. It is a simple way of summarizing the information in the data. One theoretical justification for p-values is the Neyman-Pearson theory of hypotheses testing. However the decision making focus of this theory does not correspond well with the desire, in most scientific experiments, for a simple a...

Testing fuzzy hypotheses with vague data

The problem of testing fuzzy hypotheses in the presence of vague data is considered. A new method based on the necessity index of strict dominance (NSD) is suggested. An example hoe to apply the proposed test in statistical quality control is shown.

Fitting nature's basic functions. II. Estimating uncertainties and testing hypotheses

E(∈) = 0, E(∈∈ T) = Σ 2. (1) Here, y is an m-vector of measurements, α* is an n-vector of unknown parameters (with n ≤ m), Φ is the m × n least-squares matrix (with linearly independent columns that do not depend on α*), and ∈ is an m-vector of random errors with expected value 0 and m × m positive definite variance matrix Σ 2. When Σ 2 is not known, we usually assume that Σ 2 = σ 2

Estimation of Scale Parameter in a Subfamily of Exponential Family with Weighted Balanced Loss Function

Suppose x1,x2, x3, ..., xn is a random sample of size n  from a distribution with pdf...[To continue please click here]

An iterative approach for estimation of efficiency by weighted distance