In practice, it often occurs that some covariates of interest are not measured because of various reasons, but there may exist some auxiliary information available. In this case, an issue of interest is how to make use of the available auxiliary information for statistical analysis. This paper discusses statistical inference problems in the context of current status data arising from an additive hazards model with auxiliary covariates. An empirical log-likelihood ratio statistic for the regression parameter vector is defined and its limiting distribution is shown to be a standard chi-squared distribution. A profile empirical log-likelihood ratio statistic for a sub-vector of the parameters and its asymptotic distribution are also studied. To assess the finite sample performance of the proposed methods, simulation studies are implemented and simulation results show that the methods work well.
"Classical" optimization problems depending on a probability measure belong mostly to nonlinear deterministic optimization problems that are, from the numerical point of view, relatively complicated. On the other hand, these problems fulfil very often assumptions giving a possibility to replace the "underlying" probability measure by an empirical one to obtain "good" empirical estimates of the optimal value and the optimal solution. Convergence rate of these estimates have been studied mostly for "underlying" probability measures with suitable (thin) tails. However, it is known that probability distributions with heavy tails better correspond to many economic problems. The paper focuses on distributions with finite first moments and heavy tails. The introduced assertions are based on the stability results corresponding to the Wasserstein metric with an "underlying" L1 norm and empirical quantiles convergence.
This work concentrates on a novel method for empirical estimation
of generalization ability of neural networks. Given a set of training (and testing) data, one can choose a network architecture (nurnber of layers, number of neurons in each layer etc.), an initialization method, and a learning algorithrn to obtain a network. One measure of the performance of a trained network is how dosely its actual output approximates the desired output for an input that it has never seen before. Current methods provide a “number” that indicates the estimation of the generalization ability of the network. However, this number provides no further inforrnation to understand the contributing factors when the generalization ability is not very good. The method proposed uses a number of parameters to define the generalization ability. A set of the values of these parameters provide an estimate of the generalization ability. In addition, the value of each pararneter indicates the contribution of such factors as network architecture, initialization method, training data set, etc. Furthermore, a method has been developed to verify the validity of the estimated values of the parameters.
The index of regularity of a measure was introduced by Beirlant, Berlinet and Biau \cite{bbb} to solve practical problems in nearest neighbour density estimation such as removing bias or selecting the number of neighbours. These authors proved the weak consistency of an estimator based on the nearest neighbour density estimator. In this paper, we study an empirical version of the regularity index and give sufficient conditions for its weak and strong convergence without assuming absolute continuity or other global properties of the underlying measure.
The article reflects on influential views of the mind that come from cognitive science and seem to undermine the traditional philosophical view that the mind is simply unified and transparent to itself. Specifical y, the modularity thesis is presented, along with its important modifications and criticisms, suggesting that the apparent unity can be ascribed only to higher cognition, if at all. Various theories of why the mind seems to be unified while being composed of autonomous modules are discussed. The overview results in the conclusion that our linguistic capacity plays a prominent role in the unity of the mind., Článek reflektuje vlivné pohledy na mysl, které pocházejí z kognitivní vědy a zdánlivě podkopávají tradiční filosofický názor, že mysl je jednoduše sjednocená a transparentní. Specifická y, modulační práce je představena, spolu s jeho důležitými modifikacemi a kritiky, navrhnout, že zdánlivá jednota může být připisována jen k vyššímu poznání, jestliže vůbec. Diskutovány jsou různé teorie, proč se mysl zdá být sjednocená, zatímco jsou složeny z autonomních modulů. Výsledkem je závěr, že naše jazykové schopnosti hrají v jednotě mysli významnou roli., and Martin Vraný
Sunītā Jain´s short stories discussed in this article deal with the life of Indians in the United States. Usually the question is raised as to what a particular character has gained and lost in the new environment. The writer´s attention focuses on the experiences and feelings of the characters, on their perception of the environment, not on the environment itself. In a way, she warns her readers,: the independence and individuality that many of her characters have won are similar to loneliness.
Based on the data series of the annual reference crop evapotranspiration (ET0) and the amount of irrigation water (IR) from 1970 to 2013 in the Luhun irrigation district, the joint probability distribution of ET0 and IR is established using the Gumbel-Hougaard copula function. Subsequently, the joint probability, the conditional joint probability, and the conditional return period of rich−poor encounter situations of ET0 and IR are analysed. The results show that: (1) For the joint probabilities of rich−poor encounter situations of ET0 and IR, the asynchronous encounter probability is slightly larger than the synchronous encounter probability. (2) When IR is in rich state or ET0 is in poor state, the conditional joint probability is larger, and the conditional return period is smaller. (3) For a certain design frequency of ET0, if the design frequency decreases, the conditional joint probability of the amount of irrigation water will decrease, therefore the encounter probability of them will decrease. (4) For a certain design frequency of the amount of irrigation water, if the design frequency decreases, the conditional joint probability of ET0 will increase, thus the encounter probability of them will increase.