The estimation of the Pareto index in presence of covariate information is discussed. The Pareto index is modelled as a function of the explanatory variables and hence measures the tail heaviness of the conditional distribution of the response variable given this covariate information. The original response data are transformed in order to obtain generalized residuals, possessing a common Paret...

"Let Sn be an estimate of S in the linear model, Y. = x!S + e.. Define the -v 1 -11 residuals Yi xi~' let 0 < a < ~, and let ~ be the least squares estimate of S calculated after removing the observations with the [an] smallest and [an] largest residuals. By use of an asymptotic expansion, the limit distribution of "SL is found under certain regularity conditions. This distribution depends ~ he...

A number of circular regression models have been proposed in the literature. In recent years, there is a strong interest shown on the subject of outlier detection in circular regression. An outlier detection procedure can be developed by defining a new statistic in terms of the circular residuals. In this paper, we propose a new measure which transforms the circular residuals into linear measur...

This paper presents simple large sample prediction intervals for a future response Yf given a vector xf of predictors when the regression model has the form Yi = m(xi) + ei where m is a function of xi and the errors ei are iid. Intervals with correct asymptotic coverage and shortest asymptotic length can be made by applying the shorth estimator to the residuals. Since residuals underestimate th...

We consider the problem of testing subhypotheses in a heteroscedastic linear regression model. The proposed test statistics are based on the ranks of scaled residuals obtained under the null hypothesis. Any estimator that is n”2-consistent under the null hypothesis can be used to form the residuals. The error variances are estimated through a parametric model. This extends the theory of aligned...

The flow directions of the extracted drainage network are more random based on random flow model. Binary linear regression method is applied to calculate the residual value at every point, and then the normalized residuals are used to prune reasonably as the variables. The terrains are distinguished automatically according to the normalized residuals, and the local catchment area threshold is d...

Fractional regression hot deck imputation (FRHDI), suggested by J. K. Kim, imputes multiple values for each instance of a missing dependent variable. The imputed values are equal to the predicted value based on the fully observed cases plus multiple random residuals chosen from the set of empirical residuals. Fractional weights are chosen to enable variance estimation and to preserve the correl...

and ( j , δj) ⊥ ( `, δ`) (4.1c) for all j 6= `. The lengths of the vectors yj , β, and δj , respectively, are nj , r, and s. Like in all regression-type models, the explanatory variables X and Z are regarded as fixed variables, which can also be expressed by saying that the distributions of the random variables and δ are conditional onX andZ. The random variables and δ are also called the vecto...

In this essay we discuss how to test for symmetry of unobservable errors. Two easily computable test statistics based on the estimated regression residuals are developed. Alternatively, we consider various nonparametric procedures that have been proposed in the literature to test for symmetry of observations; they can be used in this framework replacing the unknown errors by well-behaved residu...

for all j 6= l. The lengths of the vectors yj , β, and δj , respectively, are nj , r, and s. Like in all regression-type models, the explanatory variables X and Z are regarded as fixed variables, which can also be expressed by saying that the distributions of the random variables ǫ and δ are conditional on X and Z. The random variables ǫ and δ are also called the vectors of residuals at levels ...