Unconditional analogues of Cochran–Mantel–Haenszel tests

The Cochran–Mantel–Haenszel tests are a suite of tests that are usually defined as conditional tests, tests that assume all marginal totals are known before sighting the data. Here unconditional analogues of these tests are defined for the more usual situation when the marginal totals are not known before sighting the data.     

Estimation of parameters of SDE driven by fractional Brownian motion with polynomial drift

ABSTRACT

Strongly consistent and asymptotically normal estimators of the Hurst index and volatility parameters of solutions of stochastic differential equations with polynomial drift are proposed. The estimators are based on discrete observations of the underlying processes.     

纽结的Homflypt多项式

介绍了一类重要的纽结不变量,即Honmflypt多项式,证明了两个环链的Homlypt多项式相等的必要条件是它们的环绕数相等。此外,研究了它同纽结Jones多项式和Vassiliev不变量之间的关系。     

Cumulative correspondence analysis using orthogonal polynomials

Taguchi's statistic has long been known to be a more appropriate measure of association of the dependence for ordinal variables compared to the Pearson chi-squared statistic. Therefore, there is some advantage in using Taguchi's statistic in the correspondence analysis context when a two-way contingency table consists at least of an ordinal categorical variable. The aim of this paper, considering the contingency table with two ordinal categorical variables, is to show a decomposition of Taguchi's index into linear, quadratic and higher-order components. This decomposition has been developed using Emerson's orthogonal polynomials. Moreover, two case studies to explain the methodology have been analyzed.     

A class of integral operators generated by random variables

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D. Rasch: Einführung in die mathematische Statistik - WahrscheinUcllkeitsrechnung und Grundlagen der mathematlsehan Statistlk. VEB Deutscher Verlag delr Wissenschaften, Berlin 1976, 371 S., 37 Abb., 46 'I'ab., 40,– M.

D. Rasch: Einführung in die muthematisehe Statlstik - II .Anweuduugen, VEB Deutscher Verlag der Wissenschaften, Berlin 1976.

Donald L. Snyder: Random Point Processes. -JohnWiley &; Sons, New York 1975,485 S.     

Bayesian variable selection approach to a Bernstein polynomial regression model with stochastic constraints

This paper provides a Bayesian estimation procedure for monotone regression models incorporating the monotone trend constraint subject to uncertainty. For monotone regression modeling with stochastic restrictions, we propose a Bayesian Bernstein polynomial regression model using two-stage hierarchical prior distributions based on a family of rectangle-screened multivariate Gaussian distributions extended from the work of Gurtis and Ghosh [7 S.M. Curtis and S.K. Ghosh, A variable selection approach to monotonic regression with Bernstein polynomials, J. Appl. Stat. 38 (2011), pp. 961–976. doi: 10.1080/02664761003692423[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. This approach reflects the uncertainty about the prior constraint, and thus proposes a regression model subject to monotone restriction with uncertainty. Based on the proposed model, we derive the posterior distributions for unknown parameters and present numerical schemes to generate posterior samples. We show the empirical performance of the proposed model based on synthetic data and real data applications and compare the performance to the Bernstein polynomial regression model of Curtis and Ghosh [7 S.M. Curtis and S.K. Ghosh, A variable selection approach to monotonic regression with Bernstein polynomials, J. Appl. Stat. 38 (2011), pp. 961–976. doi: 10.1080/02664761003692423[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] for the shape restriction with certainty. We illustrate the effectiveness of our proposed method that incorporates the uncertainty of the monotone trend and automatically adapts the regression function to the monotonicity, through empirical analysis with synthetic data and real data applications.     

Markov regime switching in mean and in fractional integration parameter

We propose a specific general Markov-regime switching estimation both in the long memory parameter d and the mean of a time series. We employ Viterbi algorithm that combines the Viterbi procedures in two state Markov-switching parameter estimation. It is well-known that existence of mean break and long memory in time series can be easily confused with each other in most cases. Thus, we aim at observing the deviation and interaction of mean and d estimates for different cases. A Monte Carlo experiment reveals that the finite sample performance of the proposed algorithm for a simple mixture model of Markov-switching mean and d changes with respect to the fractional integrating parameters and the mean values for the two regimes.     

Design two-level factorial experiments in blocks of size four

Recently, many researchers have devoted themselves to the investigation on the number of replicates needed for experiments in blocks of size two. In practice, experiments in blocks of size four might be more useful than those in blocks of size two. To estimate the main effects and two-factor interactions from a two-level factorial experiment in blocks, we might need many replicates. This article investigates designs with the least number of replicates for factorial experiments in blocks of size four. The methods to obtain such designs are presented.     

Decomposition of the main effects and interaction term by using orthogonal polynomials in multiple non symmetrical correspondence analysis

The multiple non symmetric correspondence analysis (MNSCA) is a useful technique for analyzing a two-way contingency table. In more complex cases, the predictor variables are more than one. In this paper, the MNSCA, along with the decomposition of the Gray–Williams Tau index, in main effects and interaction term, is used to analyze a contingency table with two predictor categorical variables and an ordinal response variable. The Multiple-Tau index is a measure of association that contains both main effects and interaction term. The main effects represent the change in the response variables due to the change in the level/categories of the predictor variables, considering the effects of their addition, while the interaction effect represents the combined effect of predictor categorical variables on the ordinal response variable. Moreover, for ordinal scale variables, we propose a further decomposition in order to check the existence of power components by using Emerson's orthogonal polynomials.