Student’s t-test for scale mixture errors
نویسنده
چکیده
Generalized t-tests are constructed under weaker than normal conditions. In the first part of this paper we assume only the symmetry (around zero) of the error distribution (i). In the second part we assume that the error distribution is a Gaussian scale mixture (ii). The optimal (smallest) critical values can be computed from generalizations of Student’s cumulative distribution function (cdf), tn(x). The cdf’s of the generalized t-test statistics are denoted by (i) tSn(x) and (ii) t G n (x), resp. As the sample size n → ∞ we get the counterparts of the standard normal cdf Φ(x): (i) Φ(x) := limn→∞ tSn(x), and (ii) Φ(x) := limn→∞ tGn (x). Explicit formulae are given for the underlying new cdf’s. For example Φ(x) = Φ(x) iff |x| ≥ √ 3. Thus the classical 95% confidence interval for the unknown expected value of Gaussian distributions covers the center of symmetry with at least 95% probability for Gaussian scale mixture distributions. On the other hand, the 90% quantile of Φ is 4 √ 3/5 = 1.385 · · · > Φ(0.9) = 1.282 . . . .
منابع مشابه
Student's t Distribution based Estimation of Distribution Algorithms for Derivative-free Global Optimization
In this paper, we are concerned with a branch of evolutionary algorithms termed estimation of distribution (EDA), which has been successfully used to tackle derivative-free global optimization problems. For existent EDA algorithms, it is a common practice to use a Gaussian distribution or a mixture of Gaussian components to represent the statistical property of available promising solutions fou...
متن کاملReal-timeVideoSegmentation Using Student'stMixture Model
Mixture models for video segmentation have mainly revolved around Gaussian distributions for a long time due to their simplicity and applicability. In this work, we propose a novel real-time video segmentation algorithm based on Student’s t mixture model. Though, Student’s t-distribution has been used for image segmentation by applying Expectation Maximization (EM) algorithm, the same technique...
متن کاملBayesian analysis of robust Poisson geometric process model using heavy-tailed distributions
We propose a robust Poisson geometric process model with heavy-tailed distributions to cope with the problem of outliers as it may lead to an overestimation of mean and variance resulting in inaccurate interpretations of the situations. Two heavy-tailed distributions namely Student’s t and exponential power distributions with different tailednesses and kurtoses are used and they are represented...
متن کاملSTUDENT’S t-TEST WITHOUT SYMMETRY CONDITIONS
An explicit representation of an arbitrary zero-mean distribution as the mixture of (at-most-)two-point zero-mean distributions is given. Based in this representation, tests for (i) asymmetry patterns and (ii) for location without symmetry conditions can be constructed. Exact inequalities implying conservative properties of such tests are presented. These developments extend results established...
متن کاملGeometric convergence of the Haar PX-DA algorithm for the Bayesian multivariate regression model with Student t errors
We consider Bayesian analysis of data from multivariate linear regression models whose errors have a distribution that is a scale mixture of normals. Such models are used to analyze data on financial returns, which are notoriously heavy-tailed. Let π denote the intractable posterior density that results when this regression model is combined with the standard non-informative prior on the unknow...
متن کامل