scispace - formally typeset
Topic

Mean squared error

About: Mean squared error is a(n) research topic. Over the lifetime, 20807 publication(s) have been published within this topic receiving 464068 citation(s). The topic is also known as: MSE.

...read more

Papers
More filters

Journal ArticleDOI
Arthur E. Hoerl1, Robert W. Kennard1Institutions (1)
01 Feb 2000-Technometrics
Abstract: In multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory, if not incorrect, if the prediction vectors are not orthogonal. Proposed is an estimation procedure based on adding small positive quantities to the diagonal of X′X. Introduced is the ridge trace, a method for showing in two dimensions the effects of nonorthogonality. It is then shown how to augment X′X to obtain biased estimates with smaller mean square error.

...read more

6,934 citations


Journal ArticleDOI
01 Jan 1973-
TL;DR: Two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space; in both cases, the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the least squarederror criterion function.

...read more

Abstract: Two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space. In both cases, the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the least squared error criterion function. In the first case, the range of T consists largely of ordinary (i.e. non-fuzzy) partitions of X and the associated iteration scheme is essentially the well known ISODATA process of Ball and Hall. However, in the second case, the range of T consists mainly of fuzzy partitions and the associated algorithm is new; when X consists of k compact well separated (CWS) clusters, Xi , this algorithm generates a limiting partition with membership functions which closely approximate the characteristic functions of the clusters Xi . However, when X is not the union of k CWS clusters, the limi...

...read more

5,261 citations


01 Jan 1973-
Abstract: Two fuzzy versions of the k-means optimal, least squared error partitioning problem are formulated for finite subsets X of a general inner product space. In both cases, the extremizing solutions are shown to be fixed points of a certain operator T on the class of fuzzy, k-partitions of X, and simple iteration of T provides an algorithm which has the descent property relative to the least squared error criterion function. In the first case, the range of T consists largely of ordinary (i.e. non-fuzzy) partitions of X and the associated iteration scheme is essentially the well known ISODATA process of Ball and Hall. However, in the second case, the range of T consists mainly of fuzzy partitions and the associated algorithm is new; when X consists of k compact well separated (CWS) clusters, Xi , this algorithm generates a limiting partition with membership functions which closely approximate the characteristic functions of the clusters Xi . However, when X is not the union of k CWS clusters, the limi...

...read more

5,254 citations


Journal ArticleDOI
Zhou Wang, Alan C. Bovik1Institutions (1)
TL;DR: Although the new index is mathematically defined and no human visual system model is explicitly employed, experiments on various image distortion types indicate that it performs significantly better than the widely used distortion metric mean squared error.

...read more

Abstract: We propose a new universal objective image quality index, which is easy to calculate and applicable to various image processing applications. Instead of using traditional error summation methods, the proposed index is designed by modeling any image distortion as a combination of three factors: loss of correlation, luminance distortion, and contrast distortion. Although the new index is mathematically defined and no human visual system model is explicitly employed, our experiments on various image distortion types indicate that it performs significantly better than the widely used distortion metric mean squared error. Demonstrative images and an efficient MATLAB implementation of the algorithm are available online at http://anchovy.ece.utexas.edu//spl sim/zwang/research/quality_index/demo.html.

...read more

4,687 citations


Journal ArticleDOI
01 May 1991-Econometrica
TL;DR: Using these results, data-dependent automatic bandwidth/lag truncation parameters are introduced and asymptotically optimal kernel/weighting scheme and bandwidth/agreement parameters are obtained.

...read more

Abstract: This paper is concerned with the estimation of covariance matrices in the presence of heteroskedasticity and autocorrelation of unknown forms. Currently available estimators that are designed for this context depend upon the choice of a lag truncation parameter and a weighting scheme. Results in the literature provide a condition on the growth rate of the lag truncation parameter as T \rightarrow \infty that is sufficient for consistency. No results are available, however, regarding the choice of lag truncation parameter for a fixed sample size, regarding data-dependent automatic lag truncation parameters, or regarding the choice of weighting scheme. In consequence, available estimators are not entirely operational and the relative merits of the estimators are unknown. This paper addresses these problems. The asymptotic truncated mean squared errors of estimators in a given class are determined and compared. Asymptotically optimal kernel/weighting scheme and bandwidth/lag truncation parameters are obtained using an asymptotic truncated mean squared error criterion. Using these results, data-dependent automatic bandwidth/lag truncation parameters are introduced. The finite sample properties of the estimators are analyzed via Monte Carlo simulation.

...read more

3,970 citations


Network Information
Related Topics (5)
Covariance matrix

24.4K papers, 653.2K citations

90% related
Statistical parameter

2.5K papers, 98.9K citations

90% related
Estimation theory

35.3K papers, 1M citations

90% related
Kernel density estimation

7K papers, 195.6K citations

89% related
Least squares

17.7K papers, 559K citations

89% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202239
20211,359
20201,258
20191,205
20181,096
20171,050

Top Attributes

Show by:

Topic's top 5 most impactful authors

Housila P. Singh

59 papers, 448 citations

Rajesh Singh

54 papers, 261 citations

Javid Shabbir

44 papers, 357 citations

Yonina C. Eldar

39 papers, 1.6K citations

Peter Hall

24 papers, 4.2K citations