Approximating bayesian inference by weighted likelihood

The author proposes to use weighted likelihood to approximate Bayesian inference when no external or prior information is available. He proposes a weighted likelihood estimator that minimizes the empirical Bayes risk under relative entropy loss. He discusses connections among the weighted likelihood, empirical Bayes and James‐Stein estimators. Both simulated and real data sets are used for illustration purposes.     

Rate of strong uniform convergence of k-NN density estimates

Let f_n(x) be the univariate k-nearest neighbor (k-NN) density estimate proposed by Loftsgaarden and Quesenberry (1965). By using similar techniques as in Bahadur's representation of sample quantiles (1966), and by the recent results on the oscillation of empirical processes by Stute (1982), we derive the rate of strong uniform convergence of f_n(x) on some suitably chosen interval J_δ. Some comparison with the kernel estimates is given, as well as the choice of the bandwidth sequence relative to the sample size.     

Density estimation for samples satisfying a certain absolute regularity condition

Let {ξ_i} be an absolutely regular sequence of identically distributed random variables having common density function f(x). Let H_k(x,y) (k=1, 2,…) be a sequence of Borel-measurable functions and f_n(x)=n^?1(H_n(x,ξ₁)+…+H_n(x,ξ_n)) the empirical density function. In this paper, the asymptotic property of the probability P(sup_x|f_n(x)?f(x)|>ε) (n→∞) is studied.     

刘邦施行过楚爵制己有实证

刘邦施行过楚爵制己有实证朱绍侯二十级军功爵制是秦汉政权共行的爵位制度。《汉书》卷十九《百官公卿表》有明确的记载：“爵一级曰公士、二上造、三簪、四不更、五大夫、六官大夫、七公大夫、八公乘、九五大夫、十左庶长、十一右庶长、十二左更、十三中更、十四右更、十...     

Nonparametric curve estimation with missing data: A general empirical process approach

A general nonparametric imputation procedure, based on kernel regression, is proposed to estimate points as well as set- and function-indexed parameters when the data are missing at random (MAR). The proposed method works by imputing a specific function of a missing value (and not the missing value itself), where the form of this specific function is dictated by the parameter of interest. Both single and multiple imputations are considered. The associated empirical processes provide the right tool to study the uniform convergence properties of the resulting estimators. Our estimators include, as special cases, the imputation estimator of the mean, the estimator of the distribution function proposed by Cheng and Chu [1996. Kernel estimation of distribution functions and quantiles with missing data. Statist. Sinica 6, 63–78], imputation estimators of a marginal density, and imputation estimators of regression functions.     

Tests for the multivariate two-sample problem based on empirical probability measures

Nonparametric tests are proposed for the equality of two unknown p-variate distributions. Empirical probability measures are defined from samples from the two distributions and used to construct test statistics as the supremum of the absolute differences between empirical probabilities, the supremum being taken over all possible events. The test statistics are truly multivariate in not requiring the artificial ranking of multivariate observations, and they are distribution-free in the general p-variate case. Asymptotic null distributions are obtained. Powers of the proposed tests and a competitor are examined by Monte Carlo techniques.     

A Note on an Unbiased Test of Homogeneity of Variances

A necessary and sufficient condition for unbiasedness of the test of homogeneity of variances in normal samples is derived in a convenient form. In the case of two samples, it is shown that Bartlett's test is the only unbiased test of homogeneity of variances. A simple alternative proof of the unbiasedness of Bartlett's test in the general case is also provided.     

Minimax subset selection for the multinomial distribution

Let (X₁,…,X_k) be a multinomial vector with unknown cell probabilities (p₁,?,p_k). A subset of the cells is to be selected in a way so that the cell associated with the smallest cell probability is included in the selected subset with a preassigned probability, P¹. Suppose the loss is measured by the size of the selected subset, S. Using linear programming techniques, selection rules can be constructed which are minimax with respect to S in the class of rules which satisfy the P¹-condition. In some situations, the rule constructed by this method is the rule proposed by Nagel (1970). Similar techniques also work for selection in terms of the largest cell probability.     

科学语境中的实在层次及其转化

在人类的知识中,科学是公认的对自然现象的描述、解释和预言的最好方式。为了解释显现于我们经验之中的现象,现代科学继承了古老哲学中现象与实在二分的运思方式。基于实在概念的三个层次或含义的划分,我们就能够清楚看到,科学理论中基于经验实在而悬设的理论实在同时也是对经验的超越,是人类力图在思维中把握本体实在的尝试。随着科学的进步,这种理论实在会得到不断修正和完善而逐渐趋近本体实在,从而使“物自体”从不知变为可知。     

Managing Multiple Facets of Risk in New Product Alliances*

The trend of forming alliances to develop new products continues; however, many of these new product alliances fail. As such we explore how key risk types intrinsic in new product alliances, performance, relational, and knowledge appropriation risks, influence alliance success. Further, we theorize that different alliance governance mechanisms can reduce the negative impact of risks on alliance success. To disentangle possible heterogeneous factors across firms that may affect the interplay of risk assessments and the use of governance mechanisms, we employ latent class regression analysis on survey data collected from 128 new product alliance firms and find support for a two‐regime solution. Longer alliance relationships and lower technological turbulence are factors for some firms (regime one), while the opposite are factors for other firms (regime two). These two regimes show different patterns in the interplay of risk assessments and governance for alliance success. Our theory and results support viewing risk as a multiple‐factor concept and by understanding the different impacts of the risk types in new product alliances and how governance mechanisms mitigate such effects, we aid managers' decision making regarding the balance of contractual versus normative governance in new product alliances. Understanding the heterogeneous factors inherent in these complex relationships enables managers to understand the conditions in which various governance mechanisms promote new product alliance success.