Non-random shuffling strategies in blackjack

Numerous playing and betting strategies for the game of twenty-one have been computed assuming the deck or decks are randomly shuffled. In practice, dealers do not spend the time necessary (it takes too long) to completely randomly shuffle the decks used. Hence, there is information not only from the current round of play, but potentially from the previous round of play. We present a model for a non-random shuffle and assert ways in which this information can be used. Rules are derived using a normal approximation which updates the current strategies utilizing information from a non-random shuffle.     

The generalized fluctuation test: A unifying view

In this paper, a general principle of constructing tests for parameter constancy without assuming a specific alternative is introduced. A unified asymptotic result is established to analyze this class of tests. As applications, tests based on the range of recursive and moving estimates are considered, and their asymptotic distributions are characterized analytically. Our simulations show that different tests have quite different behavior under various alternatives and that no test uniformly dominates the other tests.     

Testing Parameter Constancy in Unit Root Autoregressive Models Against Multiple Continuous Structural Changes

This article considers tests for logistic smooth transition autoregressive (LSTAR) models accommodating multiple time dependent transitions between regimes when the data generating process is a random walk. The asymptotic null distributions of the tests, in contrast to the standard results in Lin and Teräsvirta (1994 Lin , C. F. J. , Teräsvirta , T. ( 1994 ). Testing the constancy of regression parameters against continuous structural change . Journal of Econometrics 62 : 211 – 228 .[Crossref], [Web of Science ®] , [Google Scholar]), are nonstandard. Monte Carlo experiments reveal that the tests have modest size distortions and satisfactory power against LSTAR models with multiple smooth breaks. The tests are applied to Swedish unemployment rates and the hysteresis hypothesis is over-turned in favour of an LSTAR model with two transitions between extreme regimes.     

伊壁鸠鲁的"哲学治疗"解析

公元前三、四世纪,希腊城邦瓦解,人们处在苦难的乱世之中,极度没有安全感。宗教、饥饿、死亡威胁着人们,恐惧笼罩着人们。伊壁鸠鲁的原子论哲学论证了世界不是神创的,不会灭亡;个人是自由的,友谊能增进安全感;适度能解决匮乏,让人快乐;死亡不可怕。它像一剂良药给苦难的人们带去了幸福快乐的希望。     

非圆柱体车削的进给运动分析

分析了车削非圆柱体径向进给运动的振动特性、速度特性、加速度特性。论述在满足这些特性的前提下如何提高工件转速和加工质量 ,以及非圆截面柱体零件的设计、加工工艺的制定、设备的选择等方面应注意的问题     

Of Physics and Factory Physics

The “Principle of Least Action" is the foundational principle of fundamental physics. Application of this principle to the supply chain naturally results in an “uncertainty principle” linking variation in production to variation in net‐inventory. The model also provides an easy means of determining the stationary distribution of net‐inventory for a variety of control strategies. The formalism results in a control strategy that outperforms commonly used control methods.     

Nonstationary Binary Choice

This paper develops an asymptotic theory for time series binary choice models with nonstationary explanatory variables generated as integrated processes. Both logit and probit models are covered. The maximum likelihood (ML) estimator is consistent but a new phenomenon arises in its limit distribution theory. The estimator consists of a mixture of two components, one of which is parallel to and the other orthogonal to the direction of the true parameter vector, with the latter being the principal component. The ML estimator is shown to converge at a rate of n^3/4 along its principal component but has the slower rate of n^1/4 convergence in all other directions. This is the first instance known to the authors of multiple convergence rates in models where the regressors have the same (full rank) stochastic order and where the parameters appear in linear forms of these regressors. It is a consequence of the fact that the estimating equations involve nonlinear integrable transformations of linear forms of integrated processes as well as polynomials in these processes, and the asymptotic behavior of these elements is quite different. The limit distribution of the ML estimator is derived and is shown to be a mixture of two mixed normal distributions with mixing variates that are dependent upon Brownian local time as well as Brownian motion. It is further shown that the sample proportion of binary choices follows an arc sine law and therefore spends most of its time in the neighborhood of zero or unity. The result has implications for policy decision making that involves binary choices and where the decisions depend on economic fundamentals that involve stochastic trends. Our limit theory shows that, in such conditions, policy is likely to manifest streams of little intervention or intensive intervention.