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## Description of MRPP

### Permutation Methods (2001-01-01): 9-65 , January 01, 2001

Multiresponse permutation procedures (MRPP) are a class of permutation methods of one or more dimensions for distinguishing possible differences among two or more groups. To motivate MRPP, initially consider samples of independent and identically distributed univariate random variables of sizes n_{1}, ...,n_{g}, namely,
$$({y_{11}}, \cdots ,{y_{{n_1}1}}), \cdots ,({y_{1g}}, \cdots ,{y_{{n_g}g}}),$$
from *g* populations with cumulative distribution functions F^{1}(x), ...,F_{g}(x), respectively. For simplicity, suppose that population i is normal with mean μ_{i} and variance σ^{2} (i = 1, ...,g). This is the standard one-way classification model with *g* groups. In the classical test of a null hypothesis of no group differences, one tests H^{0}: μ^{1} = ... =μ^{g} versus H^{1}: μ^{i}≠μ^{j} for some i≠j using the *F* statistic given by
$$F = \frac{{M{S_{between}}}}{{M{S_{within}}}}$$
where
$$M{S_{between}} = M{S_{treatment}} = \frac{1}{{g - 1}}S{S_{between,}}$$
$$S{S_{between}} = \sum\limits_{i = 1}^g {{n_i}} {({\bar y_i} - \bar y)^2},$$

## Special methods of inventory by sampling if the population sets have approximately negative exponential distribution

### Trabajos de Estadistica (1959-02-01) 10: 19-29 , February 01, 1959

## Data Analysis

### International Encyclopedia of Statistical Science (2011-01-01): 331-334 , January 01, 2011

## Gauss-Hermite Quadrature Approximation for Estimation in Generalised Linear Mixed Models

### Computational Statistics (2003-03-01) 18: 57-78 , March 01, 2003

### Summary

This paper provides a unified algorithm to explicitly calculate the maximum likelihood estimates of parameters in a general setting of generalised linear mixed models (GLMMs) in terms of Gauss-Hermite quadration approximation. The score function and observed information matrix are expressed explicitly as analytically closed forms so that Newton-Raphson algorithm can be applied straightforwardly. Compared with some existing methods, this approach can produce more accurate estimates of the fixed effects and variance components in GLMMs, and can serve as a basis of assessing existing approximations in GLMMs. A simulation study and practical example analysis are provided to illustrate this point.

## Optimale Planung eines Kovarianzanalyse- und eines Intraclass Regressions-Experiments

### Metrika (1984-12-01) 31: 361-378 , December 01, 1984

### Summary

The modeling and design of general experiments with qualitative and quantitative factors of influence is presented and discussed. A complete and ready to apply characterization of concrete optimal designs and their operational characteristics are given for the two basic models of analysis of covariance and of intra class regression under different experiment constraints.

## Front Matter - Digitised Optical Sky Surveys

### Digitised Optical Sky Surveys (1992-01-01): 174 , January 01, 1992

## Online Statistics Education

### International Encyclopedia of Statistical Science (2011-01-01): 1018-1020 , January 01, 2011

## Ejercicios propuestos

### Trabajos de Estadistica y de Investigacion Operativa (1977-02-01) 28: 147-154 , February 01, 1977

## Optimal Mixture Designs for Estimation of Natural Parameters in Scheffé’s Model Under Constrained Factor Space

### Optimal Mixture Experiments (2014-01-01) 1028: 63-73 , January 01, 2014

Most of the studies on mixture experiments assume that the experimental region is the whole simplex. However, experimentation at the vertices of the simplex is generally not meaningful. One may, therefore, restrict the experiment to a subset of the simplex. In this chapter, an ellipsoid within the simplex is used as the experimental region, and Kiefer optimal designs are determined for both linear and quadratic models due to Scheffé.

## Numerical Solution of Stochastic Differential Equations in Finance

### Handbook of Computational Finance (2012-01-01): 529-550 , January 01, 2012

This chapter is an introduction and survey of numerical solution methods for stochastic differential equations. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial systems. We include a review of fundamental concepts, a description of elementary numerical methods and the concepts of convergence and order for stochastic differential equation solvers. In the remainder of the chapter we describe applications of SDE solvers to Monte-Carlo sampling for financial pricing of derivatives. Monte-Carlo simulation can be computationally inefficient in its basic form, and so we explore some common methods for fostering efficiency by variance reduction and the use of quasi-random numbers. In addition, we briefly discuss the extension of SDE solvers to coupled systems driven by correlated noise, which is applicable to multiple asset markets.