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Index tracking mainly focuses on replicating or tracking the performance of a financial index which is also a popular passive portfolio management strategy. The classical methods often considerthe full replication consisted of all asserts of an index. However, the full replication often suffers from small and illiquid positions and high cost as the number of asserts increasing. Thus, the investors intend to purchase sparse portfolios. In stock markets, besides, there are still apparently existing group effects among stocks. This paper proposes the nonnegative sparse group lasso method for model selection and estimation to grouped variables without overlapping. We provide almost necessary and sufficient conditions for the variable selection and estimation consistency of the method in finite dimensional group cases. To get the solutions of the model, we derive a computational method based on coordinate decent algorithm. To track the index, the nonnegative sparse group lasso outperforms other current methods with group effects such as nonnegativeelastic net, according to tracking error.
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In this paper, we propose distribution-free mixed exponentially weighted moving average-cumulative sum (EWMA-CUSUM) and mixed cumulative sum -- exponentially weighted moving average (CUSUM-EWMA) control charts based on the Ansari-Bradley test for detecting process scale without any distributional assumption of the underlying quality process. The performances of the proposed charts are measured in terms of average run-length and some other performance indexes. The effect of sample size in phase I and phase II on phase II of the proposed charts is also investigated. The application of the new chart is illustrated by real data examples.
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We apply the empirical likelihood technique to propose a new class of estimators of the error variance in linear models. It is shown that the proposed estimators are asymptotically normally distributed with asymptotic variances not greater than that of the usual estimators of the error variance. And the closed forms of the asymptotic variances of the estimators are presented.
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By the empirical analysis of the open data on COVID-19 in the America, this paper proposes a stochastic dynamic infection model for the regions in America during the pandemic period of COVID-19. To solve when to ``open'' or ``restrict'' the economic and social activities, we construct a multi-regional optimal prevention and control switching Nash equilibrium strategy based on maximizing the expected utility with mean-field interactions. Then, we consider the infection population model for the representative region and solve the corresponding optimal prevention and control switching strategy under the infinite number of regions. Meanwhile, we prove that this strategy is an $\epsilon$-Nash equilibrium for finite regions when the number of regions tends to infinity. By comparing and analyzing the optimal switching boundaries under different process states, we will give specific suggestions on when and how to adjust the prevention
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In this paper, the compound binomial risk model is extended by involving the random premium income with Markov property and random dividend strategy. By the method of generating function, the recursive formula and initial values for the expected penalty functions with different initial states are obtained. Finally, some values of the ruin probability that change with the initial value and dividend barrier are shown in a numerical example.
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In fields of sociology, psychology, ecology, insurance, medicine and epidemiology, count data are often collected for specific studies. While count data without zero-category or with excess zeros arise quite frequently, a series of zero-truncated and zero-inflated models were soon developed to analyze these kinds of data, such as zero-truncated/inflated Poisson distribution and zero-truncated/inflated negative binomial distribution. It is necessary to make statistical inferences on unknown parameters when fitting data by these models. Existing studies merely focus on one of these models. In this paper, based on the stochastic representations of zero-truncated and zero-inflated distributions proposed in recent years, we construct a general method to obtain the maximum likelihood estimates of parameters under a unified framework, and make a review on familiar discrete distributions. Moreover, zero-adjusted models are further proposed to extend the applications, aiming to provide researchers appropriate and convenient methods in count data analyses. All methods are demonstrated by simulation studies and two real data analyses.
