[6] **viXra:1211.0132 [pdf]**
*submitted on 2012-11-22 08:37:01*

**Authors:** Sergio Arciniegas-Alarcón, Marisol García-Peña, Carlos Tadeu dos Santos Dias

**Comments:** 7 Pages. Paper in portuguese

The aim of this work was the study of prediction errors associated with four imputation methods applied to solve the problem of unbalance in experiments with genotype×environment (G×E) interaction. A simulation study was carried out based on four complete matrices of real data obtained in trials of interaction G×E of pea, cotton, beans and eucalyptus, respectively. The simulation of unbalance was done with random withdrawal of 10, 20 and 40% in each matrix. The prediction errors were found using cross-validation and were tested in classic intervals of
95% for missing data. For data imputation, algorithms were considered using models of additive effects without interaction and model estimates of additive effects with multiplicative interaction based on robust submodels. In general, the best prediction errors were obtained after imputation through an additive model without interaction.

**Category:** Statistics

[5] **viXra:1211.0131 [pdf]**
*submitted on 2012-11-22 08:15:53*

**Authors:** Sergio Arciniegas-Alarcón;, Carlos Tadeu dos Santos Dias

**Comments:** 7 Pages. Paper in portuguese

The objective of this work was to evaluate the convenience of defining the number of multiplicative components of additive main effect and multiplicative interaction models (AMMI) in genotype x enviroment interaction experiments in cotton with imputed or unbalanced data. A simulation study was carried out based on a matrix of real seed-cotton productivity data obtained in trials with genotype x environment interaction carried out with 15 genotypes at 27 locations in Brazil. The simulation was made with random withdrawals of 10, 20 and 30% of the data. The optimal number of multiplicative components for the AMMI model was determined using the Cornelius test and the likelihood ratio test onto the matrix completed by imputation. A correction based on the data missing in the Cornelius procedure was proposed for testing the hypothesis when the analysis is made from averages and the repetitions are not available. For data imputation, the methods considered used robust submodels, alternating least squares and multiple imputation. For analysis of unbalanced experiments, it is advisable to choose the number of multiplicative components of the AMMI model only from the observed information and to make the classical estimation of parameters based on the matrices completed by imputation.

**Category:** Statistics

[4] **viXra:1211.0129 [pdf]**
*submitted on 2012-11-21 13:18:47*

**Authors:** Shyam S Chandramouli

**Comments:** 10 Pages.

Many decision making problems that arise in Finance, Economics, Inventory etc. can be formulated as Markov Decision Problems (MDPs)
and solved using Dynamic Programming techniques. Further, to mitigate the statistical errors in estimating the underlying transition matrix or to exercise optimal control under adverserial setup led to the study of robust formulations of the same problems in Ghaoui and Nilim~\cite{ghaoui} and Iyengar~\cite{garud}. In this work, we study the computational methodologies to develop and validate feasible control policies for the Robust Dynamic Programming Problem. In terms of developing control policies, the current work can be seen as generalizing the existing literature on Approximate Dynamic Programming (ADP) to its robust counterpart. The work also generalizes the Information Relaxation and Dual approach of Brown, Smith and Sun~\cite{bss} to robust multi period problems. While discussing this framework we approach it both from a discrete control perspective and also as a set of conditional continous measures as in Ghaoui and Nilim~\cite{ghaoui} and Iyengar~\cite{garud}. We show numerical experiments on applications like ... In a nutshell, we expand the gamut of problems that the dual approach
can handle in terms of developing tight bounds on the value function.

**Category:** Statistics

[3] **viXra:1211.0127 [pdf]**
*submitted on 2012-11-21 10:29:40*

**Authors:** Shyam S Chandramouli

**Comments:** 22 Pages.

In this current work, we generalize the recent Pathwise Optimization approach of Desai et al.~\cite{desai2010pathwise} to Multiple stopping problems.
The approach also minimizes the dual bound as in Desai et al.~\cite{desai2010pathwise} to find the best approximation architecture for the Multiple
stopping problem. Though, we establish the convexity of the dual operator, in this setting as well, we cannot directly take advantage of this property
because of the computational issues that arise due to the combinatorial nature of the problem. Hence, we deviate from the pure martingale dual approach
to \emph{marginal} dual approach of Meinshausen and Hambly~\cite{meinshausenhambly2004} and solve each such optimal stopping problem in the framework of
Desai et al.~\cite{desai2010pathwise}. Though, this Pathwise Optimization approach as generalized to the Multiple stopping problem is computationally
intensive, we highlight that it can produce superior dual and primal bounds in certain settings.

**Category:** Statistics

[2] **viXra:1211.0113 [pdf]**
*submitted on 2012-11-19 13:56:24*

**Authors:** Stephen Crowley

**Comments:** 2 Pages.

Maximum likelihood estimation of the negative binomial distribution via numerical
methods is discussed.

**Category:** Statistics

[1] **viXra:1211.0094 [pdf]**
*replaced on 2013-01-30 12:59:09*

**Authors:** Stephen Crowley

**Comments:** 41 Pages.

Definitions from the theory of point processes are recalled. Models of intensity function parametrization and maximum likelihood estimation from data are explored. Closed-form log-likelihood expressions are given for the (exponential) Hawkes (univariate and multivariate) process, Autoregressive Conditional Duration(ACD), with both exponential and Weibull distributed errors, and a hybrid model combining the ACD and the exponential Hawkes models. Formulas are also derived, however without the elegant recursions of the exponential kernels, for kernels of the Weibull and Gamma type and comparison of the Weibullfit vs exponential kernel fits viaQQand probability plots are provided. The additional complexity of the Hawkes-Weibull or the ACD-Hawkes appears to not be worth the tradeoff. Diurnal, or daily, adjustment of the deterministic predictable part of the intensity variation via piecewise polynomial splines is discussed. Data from the symbol SPY on three different electronic markets is used to estimate model parameters and generate illustrative plots. The parameters were estimated without diurnal adjustments, a repeat of the analysis with adjustments is due in a future version of this article. The connection of the Hawkes process to quantum theory is briefly mentioned. Prediction of the next point of a Hawkes process is briefly discussed and a closed-form expression in terms of the Lambert W function for the standard exponential kernel with P=1 is calculated.

**Category:** Statistics