自适应Smith预估极点配置自效正PI控制器

对具有大惯性、大纯时延、变参数的过程控制对象，提出了一种带有自适应Ｓｍｉｔｈ预估的极点配置的自效正ＰＩ控制方案，以１０ｔ／ｈ链条炉作为控制对象，通过数字仿真，并与常规 ＰＩ比较，证明了该方案比常规ＰＩ有更好的控制性能。     

The concept of risk unbiasedness in statistical prediction

This paper extends the concept of risk unbiasedness for applying to statistical prediction and nonstandard inference problems, by formalizing the idea that a risk unbiased predictor should be at least as close to the “true” predictant as to any “wrong” predictant, on the average. A novel aspect of our approach is measuring closeness between a predicted value and the predictant by a regret function, derived suitably from the given loss function. The general concept is more relevant than mean unbiasedness, especially for asymmetric loss functions. For squared error loss, we present a method for deriving best (minimum risk) risk unbiased predictors when the regression function is linear in a function of the parameters. We derive a Rao–Blackwell type result for a class of loss functions that includes squared error and LINEX losses as special cases. For location-scale families, we prove that if a unique best risk unbiased predictor exists, then it is equivariant. The concepts and results are illustrated with several examples. One interesting finding is that in some problems a best unbiased predictor does not exist, but a best risk unbiased predictor can be obtained. Thus, risk unbiasedness can be a useful tool for selecting a predictor.     

MULTI-STAGE KERNEL-BASED CONDITIONAL QUANTILE PREDICTION IN TIME SERIES

We present a multi-stage conditional quantile predictor for time series of Markovian structure. It is proved that at any quantile level, p ∈ (0, 1), the asymptotic mean squared error (MSE) of the new predictor is smaller than the single-stage conditional quantile predictor. A simulation study confirms this result in a small sample situation. Because the improvement by the proposed predictor increases for quantiles at the tails of the conditional distribution function, the multi-stage predictor can be used to compute better predictive intervals with smaller variability. Applying this predictor to the changes in the U.S. short-term interest rate, rather smooth out-of-sample predictive intervals are obtained.     

A NOTE ON VARIANCE ESTIMATION FOR THE GENERALIZED REGRESSION PREDICTOR

The generalized regression (GREG) predictor is used for estimating a finite population total when the study variable is well‐related to the auxiliary variable. In 1997, Chaudhuri & Roy provided an optimal estimator for the variance of the GREG predictor within a class of non‐homogeneous quadratic estimators (H) under a certain superpopulation model M. They also found an inequality concerning the expected variances of the estimators of the variance of the GREG predictor belonging to the class H under the model M. This paper shows that the derivation of the optimal estimator and relevant inequality, presented by Chaudhuri & Roy, are incorrect.     

New approaches to model-free dimension reduction for bivariate regression

Dimension reduction with bivariate responses, especially a mix of a continuous and categorical responses, can be of special interest. One immediate application is to regressions with censoring. In this paper, we propose two novel methods to reduce the dimension of the covariates of a bivariate regression via a model-free approach. Both methods enjoy a simple asymptotic chi-squared distribution for testing the dimension of the regression, and also allow us to test the contributions of the covariates easily without pre-specifying a parametric model. The new methods outperform the current one both in simulations and in analysis of a real data. The well-known PBC data are used to illustrate the application of our method to censored regression.     

Quantile Regression under Misspecification,with an Application to the U.S. Wage Structure

Quantile regression (QR) fits a linear model for conditional quantiles just as ordinary least squares (OLS) fits a linear model for conditional means. An attractive feature of OLS is that it gives the minimum mean‐squared error linear approximation to the conditional expectation function even when the linear model is misspecified. Empirical research using quantile regression with discrete covariates suggests that QR may have a similar property, but the exact nature of the linear approximation has remained elusive. In this paper, we show that QR minimizes a weighted mean‐squared error loss function for specification error. The weighting function is an average density of the dependent variable near the true conditional quantile. The weighted least squares interpretation of QR is used to derive an omitted variables bias formula and a partial quantile regression concept, similar to the relationship between partial regression and OLS. We also present asymptotic theory for the QR process under misspecification of the conditional quantile function. The approximation properties of QR are illustrated using wage data from the U.S. census. These results point to major changes in inequality from 1990 to 2000.     

SMALL AREA ESTIMATION USING SURVEY WEIGHTS WITH FUNCTIONAL MEASUREMENT ERROR IN THE COVARIATE

Nested error linear regression models using survey weights have been studied in small area estimation to obtain efficient model‐based and design‐consistent estimators of small area means. The covariates in these nested error linear regression models are not subject to measurement errors. In practical applications, however, there are many situations in which the covariates are subject to measurement errors. In this paper, we develop a nested error linear regression model with an area‐level covariate subject to functional measurement error. In particular, we propose a pseudo‐empirical Bayes (PEB) predictor to estimate small area means. This predictor borrows strength across areas through the model and makes use of the survey weights to preserve the design consistency as the area sample size increases. We also employ a jackknife method to estimate the mean squared prediction error (MSPE) of the PEB predictor. Finally, we report the results of a simulation study on the performance of our PEB predictor and associated jackknife MSPE estimator.     

Accurate Confidence Interval Estimation of Small Area Parameters Under the Fay–Herriot Model

Small area estimation has long been a popular and important research topic due to its growing demand in public and private sectors. We consider here the basic area level model, popularly known as the Fay–Herriot model. Although much of current research is predominantly focused on second order unbiased estimation of mean squared prediction errors, we concentrate on developing confidence intervals (CIs) for the small area means that are second order correct. The corrected CI can be readily implemented, because it only requires quantities that are already estimated as part of the mean squared error estimation. We extend the approach to a CI for the difference of two small area means. The findings are illustrated with a simulation study.     

Variance estimation in model assisted survey sampling

Two versions of Yates-Grundy type variance estimators are usually employed for large samples when estimating a survey population total by a generalized regression (Greg, in brief) predictor motivated by consideration of a linear regression model. Their two alternative modifications are developed so that the limiting values of the design expectations of the model expectations of variance estimators 'match' respectively the (I) model expectations of the Taylor approximation of the design variance of the Greg predictor and the (II) limiting value of the design expectation of the model expectation of the squared difference between the Greg predictor and the population total. The exercise is extended to yield modifications needed when randomized response (RR) is only available rather than direct response (DR) when one encounters sensitive issues demanding protection of privacy. A comparative study based on simulation is presented for illustration..     

Two-stage group-screening designs with equal prior probabilities and no errors in decisions

A discrete approach to group-screening designs in the sense of discontinuous variation in the sizes of group-factors is studied. The results obtained using the finite differences method are compared with Watson!s results obtained by assuming continuous variation. Conditions for two-stage designs to be more economic than the corresponding single-stage designs are also given.