Errors-in-variables data processing including essential weighting of mapped path-oriented deviations with normal component discrimination

• US 7,930,146 B2
• Filed: 05/23/2007
• Issued: 04/19/2011
• Est. Priority Date: 05/23/2007
• Status: Expired due to Fees

• Current Assignee: Larry S. Chandler
• Original Assignee: Larry S. Chandler
• Inventors: Chandler, Larry S.
• Primary Examiner(s): Cosimano; Edward R
• Application Number:
  US11/802,553
• Publication Number:
  US 20080294371A1
• Time in Patent Office: 1,427 Days
• Field of Search: 702/1, 702/33, 702/34, 702/66, 702/127, 702/179, 702/180, 702/181, 702/182, 702/183, 702/187, 702/188, 702/189, 702/57
• US Class Current: 702/189
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04

Abstract

Representations of data inversions are generated by alternate forms of maximum likelihood estimating which are rendered in correspondence with dependent coordinate mappings of path-oriented displacements. The dependent coordinate mappings are alternately considered to represent either path coincident deviations, path-oriented data-point projections. Normal displacements are rendered in normalized coordinates as a shortest distance between respective data samples and successive fitting function approximations. Deficiencies in representing likelihood as related to nonlinearities and heterogeneous precision are compensated by essential weighting of respectively mapped path-oriented displacements.

Claims

1. A process for errors in variables reduction data processing in an automated data processing system comprising a processor, and input device, and an output device for outputting to display and/or memory in order to obtain corrected fitting parameters for a fitting function;

said process comprising;

a) inputting into said processor a raw database comprised of observation sampling measurement data points;

b) programming said processor with a fitting function comprising fitting parameters and which represents an expected locus of said data points;

c) selecting a reduction deviation expression for said data points;

d) inputting estimated preliminary values of said fitting parameters for said fitting function based on said data points;

e) thereafter using said programmed processor;

determining dependent component deviations for said plurality of data points as the deviation of each respective data point from the fitting function along its respective variable coordinates;

subjecting the data points to reduction deviation to determine a reduction deviation value for each of said plurality of data points;

determining a skew ratio for each data point as a ratio of the dependent component deviation divided by the reduction deviation;

determining a weight factor for each of said data points from the reduction deviation values thereof, the fitting parameters of the fitting function, and the respective skew ratios; and

determining optimized values for the fitting parameters from the sum of products of the weight factors and the squares of the reduction deviations of the respective data points;

f) reiterating step e) using the optimized fitting parameters from the preceding interation in the fitting function until the optimized fitting parameters converge or approach a limit; and

g) thereafter outputting the successive iterations of the fitting parameters for the fitting function as a corrected database of sampling data points.

2. A process as claimed in claim 1, wherein the selected reduction deviation is a transverse reduction deviation.

3. A process as claimed in claim 1, wherein the preliminary values of said fitting parameters are generated using a maximum likelihood estimator.

4. A process as claimed in claim 1, wherein the data points are subjected to common regression in which each variable of the data point is alternately set as a dependent variable and is included in a common sum of addends comprising weighted squares of reduction derivatives.

5. A process a claimed in claim 1, wherein the reduction deviation expression is selected from the group consisting of:

6. A process as claimed in claim 1, wherein the successive iterations of the fitting parameters are outputted as a locus of corrected fitting parameters for the fitting function.

7. A process as claimed in claim 1, wherein said weight factor is an essential weight factor comprising the product of a tailored weight factor and the square of the skew ratio divided by the variability of the dependent component deviation.

8. A process as claimed in claim 7, wherein the dependent component deviation variability is an estimated sampling variability of the dependent component sampling measurement.

9. A process as claimed in claim 7, wherein the dependent component deviation variability is an estimate of variability which is determined from sample measurement of the associated independent variables and their respective measurement variabilities as related to successive estimates for said fitting parameters.

10. A process as claimed in claim 9, wherein the dependent component deviation variability is equal to the sum of the products of independent variable variabilities multiplied by squares of the derivatives or partial derivatives of the dependent variable taken with respect to the respective independent variables.

11. A process as claimed in claim 7 wherein said tailored weight factor is computed for a dependent variable of a data point by taking the square root of the sum of the squares of the derivatives or partial derivatives of all independent variables of that data point.

12. A process as claimed in claim 11, wherein each data point is subjected to common regression in which each variable of the data point is alternately set to be the dependent variable.