A Proof that Both the Bias and the Mean Square Error of the Two-Stage Least Squares Estimator are Monotonically Non-Increasing Functions of Sample Size

Econometrica ◽  
1976 ◽  
Vol 44 (2) ◽  
pp. 409 ◽  
Author(s):  
A. D. Owen
Keyword(s):  
Sample Size ◽  
Least Squares ◽  
Mean Square Error ◽  
Least Squares Estimator ◽  
Mean Square ◽  
Two Stage ◽  
The Mean ◽  
Two Stage Least Squares ◽  
Increasing Functions

IV.—On Least Squares and Linear Combination of Observations

1936 ◽  
Vol 55 ◽  
pp. 42-48 ◽  
Author(s):  
A. C. Aitken
Keyword(s):  
Least Squares ◽  
Linear Combination ◽  
Mean Square Error ◽  
Mean Square ◽  
Approximate Representation ◽  
Linear Combinations ◽  
The Mean ◽  
Image Position

In a series of papers W. F. Sheppard (1912, 1914) has considered the approximate representation of equidistant, equally weighted, and uncorrelated observations under the following assumptions:–(i) The data beingu1, u2, …, un, the representation is to be given by linear combinations(ii) The linear combinations are to be such as would reproduce any set of values that were already values of a polynomial of degree not higher than thekth.(iii) The sum of squared coefficientswhich measures the mean square error ofyi, is to be a minimum for each value ofi.

scholarly journals The VIF and MSE in Raise Regression

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 605 ◽  
Author(s):  
Román Salmerón Gómez ◽  
Ainara Rodríguez Sánchez ◽  
Catalina García García ◽  
José García Pérez
Keyword(s):  
Least Squares ◽  
Mean Square Error ◽  
Ordinary Least Squares ◽  
Least Squares Estimation ◽  
Mean Square ◽  
Variance Inflation Factor ◽  
Inflation Factor ◽  
The Mean

The raise regression has been proposed as an alternative to ordinary least squares estimation when a model presents collinearity. In order to analyze whether the problem has been mitigated, it is necessary to develop measures to detect collinearity after the application of the raise regression. This paper extends the concept of the variance inflation factor to be applied in a raise regression. The relevance of this extension is that it can be applied to determine the raising factor which allows an optimal application of this technique. The mean square error is also calculated since the raise regression provides a biased estimator. The results are illustrated by two empirical examples where the application of the raise estimator is compared to the application of the ridge and Lasso estimators that are commonly applied to estimate models with multicollinearity as an alternative to ordinary least squares.

scholarly journals Parameter Estimation of Inverse Rayleigh Distribution under Competing Risk Model for Masked data

2015 ◽  
Vol 20 (2) ◽  
pp. 122-127 ◽  
Author(s):  
M.S. Panwar ◽  
Bapat Akanshya Sudhir ◽  
Rashmi Bundel ◽  
Sanjeev K. Tomer
Keyword(s):  
Sample Size ◽  
Mean Square Error ◽  
Confidence Intervals ◽  
Risk Model ◽  
Life Time ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Mean Square ◽  
True Value ◽  
The Mean

This paper tries to derive maximum likelihood estimators (MLEs) for the parameters of the inverse Rayleigh distribution (IRD) when the observed data is masked. MLEs, asymptotic confidence intervals (ACIs) and boot-p confidence intervals (boot-p CIs) for the lifetime parameters have been discussed. The simulation illustrations provided that as the sample size increases the estimated value approaches to the true value, and the mean square error decreases with the increase in sample size, and mean square error increases with increase in level of masking, the ACIs are always symmetric and the boot-p CIs approaches to symmetry as the sample size increases whereas the mean life time due to the local spread of the disease is less than that due to the metastasis spread in case of real data set.Journal of Institute of Science and Technology, 2015, 20(2): 122-127

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