Optimality of Group Testing with Differential Misclassification

Group testing is a method that can be used to estimate the prevalence of rare infectious diseases,which can effectively save time and reduce costs compared to the method of random sampling.However,previous literature only demonstrated the optimality of group testing strategy while estimating prevalence under some strong assumptions.This article weakens the assumption of misclassification rate in the previous literature,considers the misclassification rate of the infected samples as a differentiable function of the pool size,and explores some optimal properties of group testing for estimating prevalence in the presence of differential misclassification conforming to this assumption.This article theoretically demonstrates that the group testing strategy performs better than the sample by sample procedure in estimating disease prevalence when the total number of sample pools is given or the size of the test population is determined.Numerical simulation experiments were conducted to evaluate the performance of group tests in estimating prevalence in the presence of dilution effect.

EMPIRICAL BAYES TEST PROBLEMS OF VARIANCE COMPONENTS IN RANDOM EFFECTS MODEL

Bayes decision rule of variance components for one-way random effects model is derived and empirical Bayes (EB) decision rules are constructed by kernel estimation method. Under suitable conditions, it is shown that the proposed EB decision rules are asymptotically optimal with convergence rates near O(n-1/2). Finally, an example concerning the main result is given.

LIMITING BEHAVIOR OF RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES

Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.

Strong Convergence of Empirical Distribution for a Class of Random Matrices

Let {vij}, i, j = 1, 2, …, be i.i.d, random variables with Ev11 = 0, Ev11^2 = 1 and a1 = （ai1,…, aiM） be random vectors with {aij} being i.i.d, random variables. Define XN =（x1,…, xk） and SN =XNXN^T,where xi=ai×si and si=1/√N（v1i,…, vN,i）^T. The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions.

CONSISTENCY OF LS ESTIMATOR IN SIMPLE LINEAR EV REGRESSION MODELS

Consistency of LS estimate of simple linear EV model is studied. It is shown that under some common assumptions of the model, both weak and strong consistency of the estimate are equivalent but it is not so for quadratic-mean consistency.

THE SUPERIORITY OF EMPIRICAL BAYES ESTIMATION OF PARAMETERS IN PARTITIONED NORMAL LINEAR MODEL

In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.

PRICES OF ASIAN OPTIONS UNDER STOCHASTIC INTEREST RATES

Asian options are the popular second generation derivative products and embedded in many structured notes to enhance upside performance.The embedded options,as a result,usually have a long duration.The movement of interest rates becomes more important in pricing such long-dated options.In this paper,the pricing of Asian options under stochastic interest rates is studied.Assuming Hull and White model for the interest rates,a closed-form formula for geometric-average options is derived.As a by-product,pricing formula is also given for plan-vanilla options under stochastic interest rates.

A NOTE ON ASYMPTOTIC BEHAVIOR FOR NEGATIVE DRIFT RANDOM WALK WITH DEPENDENT HEAVY-TAILED STEPS AND ITS APPLICATION TO RISK THEORY

In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process. Xn=-u＋∑j=-∞^∞ φn-jεj, where { ε, εn; -∞〈n〈＋∞} is a sequence of independent, identically distributed random variables with zero mean, u 〉 0 is a constant and the coefficients {φi; -∞〈i〈∞} satisfy 0〈 ∑j=-∞^∞ ｜jφj｜〈 ∞ . Under the conditions that the distribution function of ｜ε｜ has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{sup n≥0 （-qu＋∑j=-∞^∞ εj βnj）〉x} is discussed. Then the result is applied to ultimate ruin probability.

Strong Consistency of Kernel Regression Estimate

In this paper, regression function estimation from independent and identically distributed data is considered. We establish strong pointwise consistency of the famous Nadaraya-Watson estimator under weaker conditions which permit to apply kernels with unbounded support and even not integrable ones and provide a general approach for constructing strongly consistent kernel estimates of regression functions.

Estimating Gini Coefficient Based on Hurun Report and Poverty Line

Based on the review of various methods of estimating Gini coefficient, the paper applies a quintile rule to estimate Gini coefficient of rural areas, urban areas and the whole country using the grouped income data of urban and rural residents. Besides, the paper uses the curve-fitting method to roughly estimate Gini coefficient from eye-catching Hurun Rich List and the latest poverty line. The result shows that the estimation of Gini coefficient using quintile rule is small for both urban and rural area, while the value of the whole country is obviously larger, which is above the warning line of 0.4. It is indicated that the wealth gap mainly comes from the gap between urban and rural areas. On the other hand, the estimation of Gini coefficient using curve-fitting method is as large as more than 0.7, which implies that the wealth gap is?highlighted from the analysis of the lowest and highest part of the wealth distribution. All in all, China’s current gap between the poor and the rich is serious. The reform of the income distribution needs to speed up to ensure social harmony and stability.

LIMITING BEHAVIOR OF UNIFORM RECURSIVE TREES

The authors consider the limiting behavior of various branches in a uniform recursive tree with size growing to infinity. The limiting distribution of ξn,m, the number of branches with size m in a uniform recursive tree of order n, converges weakly to a Poisson distribution with parameter 1/m with convergence of all moments. The size of any large branch tends to infinity almost surely.

Asymptotic Normality of Multi-Dimension Quasi Maximum Likelihood Estimate in Generalized Linear Models withAdaptive Design

We study the quasi likelihood equation in Generalized Linear Models（GLM） with adaptive design ∑（i=1）^n xi（yi-h（x＇iβ））=0, where yi is a q=vector, and xi is a p×q random matrix. Under some assumptions, it is shown that the Quasi- Likelihood equation for the GLM has a solution which is asymptotic normal.

Proteomics in Discovery of Hepatocellular Carcinoma Biomarkers

Objective： To discover new proteomic biomarkers of hepatocellular carcinoma. Methods： Surface enhanced laser desorption/ionization time-of-flight （SELDI-TOF） mass spectrometry was used to discover biomarkers for differentiating hepatocellular carcinoma and chronic liver disease. A population of 50 patients with hepatocellular carcinoma and 33 patients with chronic liver disease was studied. Results： Twelve proteomic biomarkers of hepatocellular carcinoma were detected in this study. Three proteomic biomarkers were highly expressed in hepatocellular carcinoma and nine proteomic biomarkers were highly expressed in chronic liver disease. The most valuable proteomic biomarker with m/z=11498 had no similar diagnostic value as α-fetoprotein. Conclusion： Some of the twelve proteomic biomarkers may become new biomarkers of hepatocellular carcinoma.

On the behavior of the product of independent random variables

For two independent non-negative random variables X and Y, we treat X as the initial variable of major importance and Y as a modifier (such as the interest rate of a portfolio).Stability in the tail behaviors of the product compared with that of the original variable X is of practical interests. In this paper, we study the tail behaviors of the product XY when the distribution of X belongs to the classes L and S, respectively. Under appropriate conditions, we show that the distribution of the product XY is in the same class as X when X belongs to class L or S, in other words, classes L and S are stable under some mild conditions on the distribution of Y. We also show that if the distribution of X is in class L(γ) (γ＞ 0) and continuous, then the product XY is in L if and only if Y is unbounded.

equivalent conditions of complete convergence for m-dimensional products of iid random variables and application to strong law of large numbers

Under very weak condition 0 × r(f) ↑ ∞, t→ ∞, we obtain a series of equivalent conditions of complete convergence for maxima of m-dimensional products of iid random variables, which provide a useful tool for researching this class of questions. Some results on strong law of large numbers are given such that our results are much stronger than the corresponding result of Gadidov’s.

WEIGHTED LASSO ESTIMATES FOR SPARSE LOGISTIC REGRESSION:NON-ASYMPTOTIC PROPERTIES WITH MEASUREMENT ERRORS

For high-dimensional models with a focus on classification performance,the?1-penalized logistic regression is becoming important and popular.However,the Lasso estimates could be problematic when penalties of different coefficients are all the same and not related to the data.We propose two types of weighted Lasso estimates,depending upon covariates determined by the Mc Diarmid inequality.Given sample size n and a dimension of covariates p,the finite sample behavior of our proposed method with a diverging number of predictors is illustrated by non-asymptotic oracle inequalities such as the?1-estimation error and the squared prediction error of the unknown parameters.We compare the performance of our method with that of former weighted estimates on simulated data,then apply it to do real data analysis.

One-sided empirical Bayes test for location parameter in Gamma distribution

In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤ δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.

DYNAMIC VALUATION OF OPTIONS ON NON-TRADED ASSETS AND TRADING STRATEGIES

This paper investigates the pricing of options written on non-traded assets and trading strategies for the stock and option in an exponential utility maximization framework.Under the assumption that the option can be continuously traded without friction just as the stock,a dynamic relationship between their optimal positions is derived by using the stochastic dynamic programming techniques.The dynamic option pricing equations are also established.In particular,the properties of the associated solutions are discussed and their explicit representations are demonstrated via the Feynman-Kac formula.This paper further compares the dynamic option price to the existing price notions,such as the marginal price and indifference price.

The limiting theorems of random quadratic forms and their application

The strong convergence and convergence rate of the random quadratic formss1T(S1S1T)ms1 and s1T(SST)ms1 are set up. The application of these results in wireless communication is given. Simulation results are presented.

Distribution Approximation of Shrinkage Estimate in Censored Regression Model via Randomly Weighting Method

Censored regression("Tobit") model is a special case of limited dependent variable regression model, and plays an important role in econometrics. Based on this model, all kinds of methods for variable or group variable selection have been developed and the corresponding shrinkage parameter estimates are widely studied. However, asymptotic distributions of the shrinkage estimates involve unknown nuisance parameters,such as density function of error term. To avoid estimating nuisance parameters, this paper presents a randomly weighting method to approximate to the asymptotic distribution of the shrinkage estimate. A computation procedure of random approximation is provided and asymptotic properties of the randomly weighting estimates are also obtained. The proposed methods are evaluated with extensively numerical studies and a women labor supply example.