PREDICTION INTERVALS FOR SUPPORT VECTOR MACHINE REGRESSION

ABSTRACT

The support vector machine (SVM), first developed by Vapnik and his group at AT&T Bell Laboratories, is being used as a new technique for regression and classification problems. In this paper we present an approach to estimating prediction intervals for SVM regression based on posterior predictive densities. Furthermore, the method is illustrated with a data example.     

Confidence Intervals for Gini's Diversity Measure and Shannon's Entropy Using Adjusted Proportions

Abstract

Asymptotic confidence intervals are given for two functions of multinomial outcome probabilities: Gini's diversity measure and Shannon's entropy. “Adjusted” proportions are used in all asymptotic mean and variance formulas, along with a possible logarithmic transformation. Exact confidence coefficients are computed in some cases. Monte Carlo simulation is used in other cases to compare actual coverages to nominal ones. Some recommendations are made.     

A note on the satterthwaite confidence interval for a variance

When using a Satterthwaite chi-squared approximation, it is generally thought that the approximation is satisfactory when it is applied to a positive linear combination of mean squares. In this note, we describe how the Williams - Tukey idea for getting a confidence interval for the among groups variance in a random one-way model can be incorporated into Satterthwaite’s procedure for getting a confidence interval for a variance. This adjusted Satterthwaite procedure insures that his chi-squared approximation is always applied to positive linear combinations of mean squares. A small simulation is included which suggests that the adjustment to the Satterthwaite procedure is effective.     

Shortest prediction intervals for the birnbaum-saunders distribution

Shortest prediction intervals for a future observation from the Birnbaum-Saunders distribution are obtained from both frequentist and Bayesian perspectives. Comparisons are made with alternative intervals obtained via inversion. Monte Carlo simulations are performed to assess the approximate intervals.     

Some inequalities in elementary special functions with applications to nonparametric statistical inference

Some inequalities are established in P₁(r, s) and P₁(r+1, s), where P₁(r, s) is the confidence coefficient of Wilks’ (1962) outer confidence interval (X_(r) X_(s)) for the quantile interval (ξ_p1, ξ_p2). An inequality concerning incomplete beta functions is also presented and it is shown to be an improved version of one of Koti's (1989) inequalities.     

Multi-stage estimation of the common location parameter of several exponential distributions

The problem of constructing a confidence interval of ‘preassigned width and coverage probability’ considered by Costanza/ Hamdy and Son(1986) is further analyzed. Several multi-stage estimation procedures [ like, purely sequential, accelerated sequential and three-stage procedures ] are utilized to deal with the same estimation problem. The relative advantages and disadvantages of these procedures are discussed.     

Empirical bayes shrinkage estimation of reliability in the exponential distribution

In this paper we propose two empirical Bayes shrinkage estimators for the reliability of the exponential distribution and study their properties. Under the uniform prior distribution and the inverted gamma prior distribution these estimators are developed and compared with a preliminary test estimator and with a shrinkage testimator in terms of mean squared error. The proposed empirical Bayes shrinkage estimator under the inverted gamma prior distribution is shown to be preferable to the preliminary test estimator and the shrinkage testimator when the prior value of mean life is clsoe to the true mean life.     

Tolerance‐based error reduction in multi‐agent bioassays

Some degree of error is inevitable in multi‐agent bioassays regardless of design or measurement technology. Estimation error can be reduced post facto by exploiting the matrix partial ordering of the bioassay survival estimates. The standard method for this is order‐restricted regression (ORR). If the joint action of the bioassay agents admits a tolerance‐based interpretation, additional structure beyond matrix partial ordering is available, leading to a new method of error reduction. This tolerance‐based error reduction (TBER) procedure almost always outperforms ORR. Like ORR, TBER applies to complete factorial bioassay designs and, using weighting, to incomplete designs.