On the difference between gauss-markov and least squares estimates

For the usual full rank univariate least squares regression model y = XB + e, E(e) = 0, E(ee) = A, the equality of the estimates occurs when B-B^* = (XA^?1X)^?1XA^-1y-(XX)^?1Xy = 0. A necessary and sufficient condition for this equality is that A has some N - k + 1 roots equal where N is the rank of A and k is the rank of X.     

结合改进卷积神经网络和最小二乘法的颅骨性别鉴定

颅骨性别鉴定在法医学和颅骨面貌复原等领域具有重要研究意义和应用价值,针对传统颅骨性别鉴定需要专家参与且主观性强、计算机辅助方法需要人工标定特征点等问题,本文提出了结合改进卷积神经网络和最小二乘法的颅骨性别鉴定方法。首先,获取三维颅骨模型多角度颅骨图像,利用改进的卷积神经网络计算每个样本的每张图像属于男性和女性的概率;其次,基于概率均值采用最小二乘法计算每张图像对性别鉴定的权重;最后,利用上述步骤得到的最优参数构造决策函数,通过决策值完成颅骨性别鉴定。本文方法抛弃了繁琐的手动测量,对完整颅骨的性别鉴定正确率高达94.4%,对不完整颅骨的性别鉴定正确率高达87.5%,能够获得较好的颅骨性别鉴定性能。     

Prediction of functionally important sites from protein sequences using sparse kernel least squares classifiers

Identification of functionally important sites (FIS) in proteins is a critical problem and can have profound importance where protein structural information is limited. Machine learning techniques have been very useful in successful classification of many important biological problems. In this paper, we adopt the sparse kernel least squares classifiers (SKLSC) approach for classification and/or prediction of FIS using protein sequence derived features. The SKLSC algorithm was applied to 5435 FIS that have been extracted from 312 reliable alignments for a wide range of protein families. We obtained 68.28% sensitivity and 68.66% specificity for training dataset and 65.34% sensitivity and 66.88% specificity for testing dataset. Further, large scale benchmarking study using alignments of 101 protein families containing 1899 FIS showed that our method achieved an average ∼70% sensitivity in predicting different types of FIS, such as active sites, metal, ligand or protein binding sites. Our findings also indicate that active sites and metal binding sites are comparably easier to predict compared to the ligand and protein binding sites. Despite moderate success, our results suggest the usefulness and potential of SKLSC approach in prediction of FIS using only protein sequence derived information.     

Monotone spline‐based least squares estimation for panel count data with informative observation times

This article discusses the statistical analysis of panel count data when the underlying recurrent event process and observation process may be correlated. For the recurrent event process, we propose a new class of semiparametric mean models that allows for the interaction between the observation history and covariates. For inference on the model parameters, a monotone spline‐based least squares estimation approach is developed, and the resulting estimators are consistent and asymptotically normal. In particular, our new approach does not rely on the model specification of the observation process. The proposed inference procedure performs well through simulation studies, and it is illustrated by the analysis of bladder tumor data.     

Confidence regions and hypothesis tests for topologies using generalized least squares

A confidence region for topologies is a data-dependent set of topologies that, with high probability, can be expected to contain the true topology. Because of the connection between confidence regions and hypothesis tests, implicitly or explicitly, the construction of confidence regions for topologies is a component of many phylogenetic studies. Existing methods for constructing confidence regions, however, often give conflicting results. The Shimodaira-Hasegawa test seems too conservative, including too many topologies, whereas the other commonly used method, the Swofford-Olsen-Waddell-Hillis test, tends to give confidence regions with too few topologies. Confidence regions are constructed here based on a generalized least squares test statistic. The methodology described is computationally inexpensive and broadly applicable to maximum likelihood distances. Assuming the model used to construct the distances is correct, the coverage probabilities are correct with large numbers of sites.     

Evaluation of the Best Linear Unbiased Prediction in Mixed Linear Models with Estimated Variance Components by Means of the MSE of Prediction and the Genetic Selection Differential

Prediction in mixed linear models by Henderson 's (1972) BLUP (Best Linear Unbiased Prediction) requires knowledge of the underlying variance/covariance components to have the property ‘best’. In breeding value prediction these parameters are not known, generally. They have to be replaced by estimations and BLUP becomes estimated BLUP (EBLUP). The aim of this investigation was the evaluation of EBLUP with help of a designed simulation experiment. Criteria used for the evaluation were the mean squared error (MSE) and the (genetic) selection differential (GSD). Besides, an idea of the overestimation of the accuracy of EBLUP by the naive MSE approximation based on the MSE formulas of BLUP with variance component estimations instead of unknown parameters is given.     

A comparison of neural networks and partial least squares for deconvoluting fluorescence spectra

This article compares backpropagation neural networks (BNN) with partial least squares (PLS) techniques in terms of their ability to deconvolute fluorescence spectra. Both actual experimental and simulated spectral data are studied for 2 binary systems. These systems consist of mixtures of tryptophan and tyrosine, and NADH and tryptophan over a total concentration range of 10(-7) to 10(-4) M. It is shown that BNN is superior to PLS for both systems.