Neyman-Pearson classification has been studied in several articles before. But they all proceeded in the classes of indicator functions with indicator function as the loss function, which make the calculation to be di...Neyman-Pearson classification has been studied in several articles before. But they all proceeded in the classes of indicator functions with indicator function as the loss function, which make the calculation to be difficult. This paper investigates Neyman- Pearson classification with convex loss function in the arbitrary class of real measurable functions. A general condition is given under which Neyman-Pearson classification with convex loss function has the same classifier as that with indicator loss function. We give analysis to NP-ERM with convex loss function and prove it＇s performance guarantees. An example of complexity penalty pair about convex loss function risk in terms of Rademacher averages is studied, which produces a tight PAC bound of the NP-ERM with convex loss function.展开更多
The partial sums of basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several transformation and summation formulae for well-poised, quadratic, cubic and quartic q...The partial sums of basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several transformation and summation formulae for well-poised, quadratic, cubic and quartic q-series are established.展开更多
Neyman-Pearson（NP） criterion is one of the most important ways in hypothesis testing. It is also a criterion for classification. This paper addresses the problem of bounding the estimation error of NP classification...Neyman-Pearson（NP） criterion is one of the most important ways in hypothesis testing. It is also a criterion for classification. This paper addresses the problem of bounding the estimation error of NP classification, in terms of Rademacher averages. We investigate the behavior of the global and local Rademacher averages, and present new NP classification error bounds which are based on the localized averages, and indicate how the estimation error can be estimated without a priori knowledge of the class at hand.展开更多
For the two side truncated distribution family: dPθ(x) = f(x;θ1θ2)I(θ≤ x≤θ2)dx, where θ=(θ1,θ2),θ < θ2,chen & Fu studied one side asymptotic efficiency of the estimator for parameter hation g(θ) =...For the two side truncated distribution family: dPθ(x) = f(x;θ1θ2)I(θ≤ x≤θ2)dx, where θ=(θ1,θ2),θ < θ2,chen & Fu studied one side asymptotic efficiency of the estimator for parameter hation g(θ) = c1θ1 + C2θ2, they pointed out that when c1c2≥0, there exist one side asymptotic efficient estimators for g(θ); when c1c2 < 0, the estimator they proposed is not asymptotically efficient. Then they put forward a question: Is there any other asymptotically efficient estimator for g(θ) when c1c2 <0? In this paper, we study this problem, we prove that when the distribution under consideration is uniform distribution with location and scale parameters, there does not exist one side asymptotically efficient estimators for the scale parameter.展开更多
The stability of testing hypotheses is discussed.Differing from the usual tests measured by Neyman-Pearson lemma,the regret and correction of the tests are considered.After the decision is made based on the observatio...The stability of testing hypotheses is discussed.Differing from the usual tests measured by Neyman-Pearson lemma,the regret and correction of the tests are considered.After the decision is made based on the observations X1,X2,...,Xn,one more piece of datum Xn+1 is picked and the test is done again in the same way but based on X1,X2,...,Xn,Xn+1.There are three situations;(i) The previous decision is right but the new decision is wrong; (ii) the previous decision is wrong but the new decision is right; (iii) both of them are right or both of them are wrong.Of course,it is desired that the probability of the occurrence of (i) is as small as possible and the probability of the occurrence of (ii) is as large as possible.Since the sample size is sometimes not chosen very precisely after the type Ⅰ error and the type Ⅱ error are determined in practice,it seems more urgent to consider the above problem.Some optimal plans are also given.展开更多
基金This is a Plenary Report on the International Symposium on Approximation Theory and Remote SensingApplications held in Kunming, China in April 2006Supported in part by NSF of China under grants 10571010 , 10171007 and Startup Grant for Doctoral Researchof Beijing University of Technology
文摘Neyman-Pearson classification has been studied in several articles before. But they all proceeded in the classes of indicator functions with indicator function as the loss function, which make the calculation to be difficult. This paper investigates Neyman- Pearson classification with convex loss function in the arbitrary class of real measurable functions. A general condition is given under which Neyman-Pearson classification with convex loss function has the same classifier as that with indicator loss function. We give analysis to NP-ERM with convex loss function and prove it＇s performance guarantees. An example of complexity penalty pair about convex loss function risk in terms of Rademacher averages is studied, which produces a tight PAC bound of the NP-ERM with convex loss function.
基金supported by National Natural Science Foundation for the Youth (Grant No. 10801026)
文摘The partial sums of basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several transformation and summation formulae for well-poised, quadratic, cubic and quartic q-series are established.
基金Research supported in part by NSF of China under Grant Nos. 10801004, 10871015supported in part by Startup Grant for Doctoral Research of Beijing University of Technology
文摘Neyman-Pearson（NP） criterion is one of the most important ways in hypothesis testing. It is also a criterion for classification. This paper addresses the problem of bounding the estimation error of NP classification, in terms of Rademacher averages. We investigate the behavior of the global and local Rademacher averages, and present new NP classification error bounds which are based on the localized averages, and indicate how the estimation error can be estimated without a priori knowledge of the class at hand.
文摘For the two side truncated distribution family: dPθ(x) = f(x;θ1θ2)I(θ≤ x≤θ2)dx, where θ=(θ1,θ2),θ < θ2,chen & Fu studied one side asymptotic efficiency of the estimator for parameter hation g(θ) = c1θ1 + C2θ2, they pointed out that when c1c2≥0, there exist one side asymptotic efficient estimators for g(θ); when c1c2 < 0, the estimator they proposed is not asymptotically efficient. Then they put forward a question: Is there any other asymptotically efficient estimator for g(θ) when c1c2 <0? In this paper, we study this problem, we prove that when the distribution under consideration is uniform distribution with location and scale parameters, there does not exist one side asymptotically efficient estimators for the scale parameter.
基金Project supported by the National Natural Science Foundation of China and the Doctoral Programme Foundation.
文摘The stability of testing hypotheses is discussed.Differing from the usual tests measured by Neyman-Pearson lemma,the regret and correction of the tests are considered.After the decision is made based on the observations X1,X2,...,Xn,one more piece of datum Xn+1 is picked and the test is done again in the same way but based on X1,X2,...,Xn,Xn+1.There are three situations;(i) The previous decision is right but the new decision is wrong; (ii) the previous decision is wrong but the new decision is right; (iii) both of them are right or both of them are wrong.Of course,it is desired that the probability of the occurrence of (i) is as small as possible and the probability of the occurrence of (ii) is as large as possible.Since the sample size is sometimes not chosen very precisely after the type Ⅰ error and the type Ⅱ error are determined in practice,it seems more urgent to consider the above problem.Some optimal plans are also given.
