ASSESSMENT OF LOCAL INFLUENCE IN MULTIVARIATE REGRESSION MODEL

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Recursive state and parameter estimation with applications in water resources

Hydrologic models, as well as measurements of hydrologic processes, are corrupted by noise. The Kalman filter is a convenient tool to estimate the true but unknown state of a hydrologic system. It is, however, difficult to specify the necessary error covariances. A procedure is proposed to estimate the error covariances recursively in a combined state and parameter filter. Applications of the procedure yield meaningful results for two hydrologic data series of very different character. A major benefit of the proposed algorithm seems to be its robustness against instability.  

多元协方差阵扰动模型岭估计的影响分析

本文研究了多元线性同归模型岭估计的影响分析问题.利用最小二乘估计方法,获得了多元协方差阵扰动模型与原模型参数阵之间的岭估计的一些关系式,给出了度量影响大小的基于岭估计的广义Cook距离.  

Multivariate regression model with constraints

The aim of the paper is to present explicit formulae for parameter estimators and confidence regions in multivariate regression model with different kind of constraints and to give some comments to it. The covariance matrix of observation is either totally known, or some unknown parameters of it must be estimated, or the covariance matrix is totally unknown. Supported by the Council of Czech Government J14/98: 153100011.  

基于时间序列的长沙市PM2.5的统计分析

通过对长沙市2015年AQI检测指标数值PM2.5与SO_2,NO_2,PM10,CO,O_3间相关性进行分析,得到PM2.5与SO_2,NO_2,PM10,CO间存在正相关关系,与O_3间为负相关关系.后建立自回归移动平均模型(ARMA)对长沙市2015年的PM2.5进行短期预测,得到最优模型为ARMA(3,2).最后对长沙治理PM2.5提出相关建议.  

西安市PM2.5相关因素多元回归分析模型

为了探索空气污染的主要因素，对空气污染监测指标 PM2.5与 AQI 中其他监测指标进行相关性分析，得到 PM2.5与 SO2、NO2、CO 呈正相关，与 O3和温度呈负相关，同时利用多元回归模型得到PM2.5与主因子的数量关系，给西安市 PM2.5防控提供参考意见.  

Some remarks to multivariate regression model

Some remarks to problems of point and interval estimation, testing and problems of outliers are presented in the case of multivariate regression model. This work was supported by the Council of Czech Government J14/98:153100011.  

Corrected versions of cross-validation criteria for selecting multivariate regression and growth curve models

This paper is concerned with cross-validation (CV) criteria for choice of models, which can be regarded as approximately unbiased estimators for two types of risk functions. One is AIC type of risk or equivalently the expected Kullback-Leibler distance between the distributions of observations under a candidate model and the true model. The other is based on the expected mean squared error of prediction. In this paper we study asymptotic properties of CV criteria for selecting multivariate regression models and growth curve models under the assumption that a candidate model includes the true model. Based on the results, we propose their corrected versions which are more nearly unbiased for their risks. Through numerical experiments, some tendency of the CV criteria will be also pointed.