A New Horizon of Statistics: Two Abstracts at 2011 JSM

A New Horizon of Statistics:
Ligong Chen’s Two Abstracts for 2011 JSM 

A New Horizon of Statistics:
The Definition of Self-weight for Continuous Variattribute
(=Continuous Random Variabloe, CRV) 

Ligong Chen, MD, MPH; Yongmei Chen, MD, MPH 

[Abstract for 2011 Joint Statistical Meetings in Miami]
Abstract Numbber is 300638
The Section is the General Methodology
The Session number is 43
Date: July 31, 2011
Presenter is Yongmei Chen 

A CRV X and its n random points x_i can be expressed in X{x_i}(i=1,2,…,n). We define a point-to-point differentiality D_j(j=i) with its range R_X for x_i as D_j{d_ij}=|X-x_i|/R_X and a similarity S_j{s_ij}=1-D_j{d_ij}. A product V{v_i} of the sum of D_j and the sum of S_j will be a real measure in a range R_V. We define a relative contribution C{c_i}=1-[V-min(V)]/R_V as an unbiased self-weight for the X{x_i} to the E(X). Then, we will have a convex-concave self-weight curve, which looks like a normal curve if the X is normal. Based on examining two properties of sample size n, we tried to unify the definitions of the weighted and non-weighted basic statistics, in which the degree of freedom may be defined as the sum of weights minus the self-weighted mean of the weight. These unified definitions in Statistics can be used to substitute various optimizations in advanced statistical methodological constructions. We also tried to infer the representativeness of arithmetical mean and propose a self-weighted t-test for the microarray data analysis to obtain a purely random variable P-value in multiple tests. A sample illustration and a series of simulations have shown that the new algorithms are extremely accurate and robust. 

A Basic Conceptual System of Statistics and
Several Universal Random Measures 

Ligong Chen, MD, MPH 

[Abstract for 2011 Joint Statistical Meetings in Miami]
Abstract Numbber is 302952
The Section is the General Methodology
The Session number is 43
Date: July 31, 2011
Presenter is Ligong Chen 

This paper tried to contribute a rigorous and feasible conceptual system by adding some new concepts and adjusting the connotations of several existing concepts in the Probability Theory. A main change is to define "sample space" as the sample itself and add a concept "scale space" to replace the Kolmogorov's sample space. Thus, a "measurable space" is a space in which every point is measurable over a defined scale space, and a "probability space" will be defined over a complete sample space with its scale space. These additions and adjustments are useful and necessary for eliminating all confusions in the current system. It will neither cause a significant impact to the system nor violate the laws of the Theory of Set in Mathematics but may bring us a clearer and better understanding on the whole system. This paper was also an attempt to directly introduce the basic concepts of the Probability Theory into Statistics so that we will have a better logical system to help the methodological construction in Statistics. It then further discussed the fundamentals of Statistics based on the new conceptual system and suggests several important random measurements as universal definitions. 

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The relevant information about the two abstracts has been sent out to the following email addresses with a personal explanation: 

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Hello, everyone, 

These are Liogng Chen and Yongmei Chen, a couple of biostatistician in medical education background in China. We are trying to contact you since this is an exciting time for us because we have known that we are successful in our 100% confidence. 

We have finished our submission of two mutually linked abstracts to the Joint Statistical Meetings this year. This is a complete new idea for describing continuous random variable by constructing a so-called “self-weight” for a single continuous random variable with its all sampling information. We will have a different weighting value for every point, especially the points at both tails will tend to be weighted to 0, the points around the unknown expectation will tend to be weighted to 1, thus we will have a self-weight curve, which looks like a distribution curve, for example normal or skewed curve, and the expectation will be estimated always at the peak of the self-weight curve for any concave distribution. Therefore, we believe that this is a new horizon of Statistics since it will bring us a complete new sight over the whole body of Statistics. We also believe that the so-called non-parametric methods, for example, the rank sum test, will go to its history. All methods in Statistics will be parametric for sufficiently utilizing all information in a sample without any loss or degradation. In addition, all the current advanced methodologies constructed with the so-called “optimization” will be reconstructed with the self-weighted expectation as a criterion since any optimization takes a random correspondence rather than an expected one. 

The links to the two newest abstracts are blow: 

The first one is for defining the self-weight. The complete mathematical algorithm for the self-weight is in the abstract. It is actually very simple, and everyone can realize it in SAS or any statistical software.  It is a wonderful idea from a deep philosophical thinking.
http://www.amstat.org/meetings/jsm/2011/onlineprogram/AbstractDetails.cfm?abstractid=300638  

The second one is an attempt to rigorously reconstruct the basic conceptual system of Statistics, including several basic concepts in the Probability Theory.
http://www.amstat.org/meetings/jsm/2011/onlineprogram/AbstractDetails.cfm?abstractid=302952  

These new ideas were stimulated by 1) trying to improve and finalize our functionalized general trichotomic regression analysis (FGTRA) as well as some theoretical statements associated with the FGTRA proposed at the JSM 2007 and improved at the JSM 2009 (See the JSM proceedings of the two years), 2) for unifying all definitions of basic statistics, 3) for finding the best approach to substitute all “optimizations” when they are employed as a criterion in modeling; and 4) for eliminating a serious systematic error and decreasing the random error in the p-value measuring in the microarray data analysis, which is an ultra-dimensional analysis. However, the whole research was stimulated by Dr. Peter John Huber with his great speech spoken to the Institute of Mathematical Statistics of the Chinese Scientific Academy in November of 1997, in which he said “Statistics or even Mathematics may need an external strong power to push them go ahead!” I believed that the power could come from Philosophy rather than anything else when I was lucky to hear this speech mostly repeated by a Chinese academician in mathematical statistics, Dr. Xiru Chen, giving his own talk to the Department of Mathematics of Wuhan University in March of 1998. Another important stimulating source is Tukey’s idea about “optimization is danger (in random system).” in his great work “The future of data analysis” published in 1962. 

We would like to take this opportunity to share the newest achievement in Statistics for your further research career or routine jobs. It is too hard for us to go to this end. It has taken us more than 13 years. It almost destroyed our personal life as well as our whole family. However, we are very peaceful now and will do our routine jobs to our best. 

Thanks for all of your attention and time. 

Yours sincerely,
     Ligong Chen, MD, MPH
    Yongmei Chen, MD, MPH, MS