Minimax Predictor Research Articles

Linear minimax prediction of finite population regression coefficient under a balanced loss function

ABSTRACTUnder a balanced loss function, we investigate the minimax prediction of finite population regression coefficient in a superpopulation model with Gauss–Markov type errors. The linear minimax predictor (LMP) proved to be admissible in the class of homogeneous linear predictors is obtained. Under the balanced loss function, we further prove that LMP dominates the best linear unbiased predictor (BLUP) proposed by Bolfarine et al. [Bolfarine et al., Optimal prediction of the finite population regression coefficient. Sankhy. Ser. B. 56 (1994) 1–10] on certain conditions. Moreover, a numerical example is performed to illustrate the theoretical results.

Optimal and minimax prediction in multivariate normal populations under a balanced loss function

Abstract Under a balanced loss function, we investigate the optimal and minimax prediction of finite population regression coefficient in a general linear regression superpopulation model with normal errors. The best unbiased prediction (BUP) is obtained in the class of all unbiased predictors. The minimax predictor (MP) is also obtained in the class of all predictors. We prove that MP is unique in the class of all predictors and is better than BUP in a certain region of parameter space. Next, we give some conditions for optimality of the simple projection predictor (SPP) and prove that MP dominates SPP on certain occasions.

Robust Bayesian methodology with applications in credibility premium derivation and future claim size prediction

Robust Bayesian methodology deals with the problem of explaining uncertainty of the inputs (the prior, the model, and the loss function) and provides a breakthrough way to take into account the input’s variation. If the uncertainty is in terms of the prior knowledge, robust Bayesian analysis provides a way to consider the prior knowledge in terms of a class of priors \(\varGamma \) and derive some optimal rules. In this paper, we motivate utilizing robust Bayes methodology under the asymmetric general entropy loss function in insurance and pursue two main goals, namely (i) computing premiums and (ii) predicting a future claim size. To achieve the goals, we choose some classes of priors and deal with (i) Bayes and posterior regret gamma minimax premium computation, (ii) Bayes and posterior regret gamma minimax prediction of a future claim size under the general entropy loss. We also perform a prequential analysis and compare the performance of posterior regret gamma minimax predictors against the Bayes predictors.

Robust Bayesian prediction and estimation under a squared log error loss function

Robust Bayesian analysis is concerned with the problem of making decisions about some future observation or an unknown parameter, when the prior distribution belongs to a class Γ instead of being specified exactly. In this paper, the problem of robust Bayesian prediction and estimation under a squared log error loss function is considered. We find the posterior regret Γ -minimax predictor and estimator in a general class of distributions. Furthermore, we construct the conditional Γ -minimax, most stable and least sensitive prediction and estimation in a gamma model. A prequential analysis is carried out by using a simulation study to compare these predictors.

Minimax Prediction of the Empirical Distribution Function

Let X 1,…, X n be i.i.d. random variables from an unknown cumulative distribution function F defined on the real line ℝ. No assumptions are made on the unknown F. The problem is to predict the empirical distribution function of a future sample Y = (Y 1,…,Y m ) from the distribution function F on the basis of the observations X 1,…, X n . To solve the problem, a decision theoretic approach is used. In certain situations, when for example a weighted quadratic loss function is used in the prediction problem, the problem of finding the minimax predictor of the empirical distribution function can be reduced to the problem of minimax estimation of the cumulative distribution function F under a composite weighted quadratic loss function. In such a case, a general method of finding minimax predictors of is presented. The method is also useful when no equalizer rule is available. The problem of prediction considered refers also to prediction of the empirical lifetime distribution function and may have some practical significance. For example, the results enable to predict, under the minimax criterion, the number of devices (from among all the m ones) which will fail up to any fixed time t 0.

Minimax prediction under random sample size

A class of minimax predictors of random variables with multinomial or multivariate hypergeometric distribution is determined in the case when the sample size is assumed to be a random variable with an unknown distribution. It is also proved that the usual

Minimax Prediction for the Multinomial and Multivariate Hypergeometric Distributions

A problem of minimax prediction for the multinomial and multivariate hypergeometric distribution is considered. A class of minimax predictors is determined for estimating linear combinations of the unknown parameter and the random variable having the mult

Prediction in finite population under error-in-variables superpopulation models

In this paper we consider the optimal prediction of finite population total and variance under location model with measurement errors. Bayes predictors of population total and variance under a class of priors have been derived and a minimax predictor for population total has been obtained. Under regression superpopulation model with measurement errors, an optimal predictor of population total has been derived. A Bayesian approach for this model shows the linear regression predictor to be a Bayes predictor.

Bayes and minimax prediction in finite populations

We consider Bayesian and minimax prediction of some finite population quantities. The usual best linear unbiased predictor of the population total T is shown to be minimax under normality and the squared error loss function. A general Bayesian predictor is derived for the population variance S 2 y . A minimax predictor of S 2 y is presented for the location model. Bayes, minimax and best unbiased prediction is also considered for the finite population regression coefficient β N .

Minimax prediction in finite populations

In this paper, minimax predictors are considered for some population quantities of interest, under some specific superpopulation models. Minimax predictors are derived under a binomial superpopulation model. The well known ratio estimator is shown to be minimax under the usual simple regression normal model. Nonparametric minimax predictors are considered under some models. Some of the predictors considered also shown to be admis s ible.

Single‐parameter inference based on partial prior information

AbstractPartial specification of a prior distribution can be appealing to an analyst, but there is no conventional way to update a partial prior. In this paper, we show how a framework for Bayesian updating with data can be based on the Dirichlet(a) process. Within this framework, partial information predictors generalize standard minimax predictors and have interesting multiple‐point shrinkage properties. Approximations to partial‐information estimators for squared error loss are defined straightforwardly, and an estimate of the mean shrinks the sample mean. The proposed updating of the partial prior is a consequence of four natural requirements when the Dirichlet parameter a is continuous. Namely, the updated partial posterior should be calculable from knowledge of only the data and partial prior, it should be faithful to the full posterior distribution, it should assign positive probability to every observed event {X,}, and it should not assign probability to unobserved events not included in the partial prior specification.

Minimax Predictors for Signals Having a Bonded kth Derivative

Predictors are derived which minimize the maximum possible mean-squared prediction error for signals observed in white noise and having a bounded kth derivative. Expressions are given for the resulting worst-case error and a suboptimal solution is presented which, for the case k = 2, performs nearly as well as the optimal and is far easier to implement.