Statistical Inferences for Lomax Distribution Based on Record Values (Bayesian and Classical)

A maximum likelihood estimation (MLE) based on records is obtained and a proper prior distribution to attain a Bayes estimation (both informative and non-informative) based on records for quadratic loss and squared error loss functions is also calculated. The study considers the shortest confidence interval and Highest Posterior Distribution confidence interval based on records, and using Mean Square Error MSE criteria for point estimation and length criteria for interval estimation, their appropriateness to each other is examined

Model selection criteria and quadratic discrimination in ARMA and SETAR time series models

We show that analyzing model selection in ARMA time series models as a quadratic discrimination problem provides a unifying approach for deriving model selection criteria. Also this approach suggest a different definition of expected likelihood that the one proposed by Akaike. This approach leads to including a correction term in the criteria which does not modify their large sample performance but can produce significant improvement in the performance of the criteria in small samples. Thus we propose a family of criteria which generalizes the commonly used model selection criteria. These ideas can be extended to self exciting autoregressive models (SETAR) and we generalize the proposed approach for these non linear time series models. A Monte-Carlo study shows that this family improves the finite sample performance of criteria such as AIC, corrected AIC and BIC, for ARMA models, and AIC, corrected AIC, BIC and some cross-validation criteria for SETAR models. In particular, for small and medium sample size the frequency of selecting the true model improves for the consistent criteria and the root mean square error of prediction improves for the efficient criteria. These results are obtained for both linear ARMA models and SETAR models in which we assume that the threshold and the parameters are unknown

MODEL SELECTION CRITERIA AND QUADRATIC DISCRIMINATION IN ARMA AND SETAR TIME SERIES MODELS

We show that analyzing model selection in ARMA time series models as a quadratic discrimination problem provides a unifying approach for deriving model selection criteria. Also this approach suggest a different definition of expected likelihood that the one proposed by Akaike. This approach leads to including a correction term in the criteria which does not modify their large sample performance but can produce significant improvement in the performance of the criteria in small samples. Thus we propose a family of criteria which generalizes the commonly used model selection criteria. These ideas can be extended to self exciting autoregressive models (SETAR) and we generalize the proposed approach for these non linear time series models. A Monte-Carlo study shows that this family improves the finite sample performance of criteria such as AIC, corrected AIC and BIC, for ARMA models, and AIC, corrected AIC, BIC and some cross-validation criteria for SETAR models. In particular, for small and medium sample size the frequency of selecting the true model improves for the consistent criteria and the root mean square error of prediction improves for the efficient criteria. These results are obtained for both linear ARMA models and SETAR models in which we assume that the threshold and the parameters are unknown.

Adaptive Batch Size Selection in Active Learning for Regression

Training supervised machine learning models requires labeled examples. A judicious choice of examples is helpful when there is a significant cost associated with assigning labels. This dissertation aims to improve upon a promising extant method - Batch-mode Expected Model Change Maximization (B-EMCM) method - for selecting examples to be labeled for regression problems. Specifically, it aims to develop and evaluate alternate strategies for adaptively selecting batch size in B-EMCM, named adaptive B-EMCM (AB-EMCM). By determining the cumulative error that occurs from the estimation of the stochastic gradient descent, a stop criteria for each iteration of the batch can be specified to ensure that selected candidates are the most beneficial to model learning. This new methodology is compared to B-EMCM using mean absolute error and root mean square error over ten iterations using benchmark machine learning data sets. Using multiple data sets and metrics across all methods, one of the variations of ABEMCM, that uses the max bound of the accumulated error (AB-EMCM Max), showed the best results for an adaptive batch approach. It achieved better root mean squared error (RMSE) and mean absolute error (MAE) than the other adaptive and nonadaptive batch methods while reaching the result in nearly the same number of iterations as the non-adaptive batch methods

Bid design for non-parametric contingent valuation with a single bounded dichotomous choice format

This paper examines how the number of different bids used in a dichotomous choice contingent valuation exercise influences the non-parametric estimation of the mean willingness to pay. This task has been undertaken by several simulation experiments that combine different non-parametric procedures, number of bids, bid distribution, sample sizes, and willingness to pay distributions over the simulated population. The criteria used to analyze the effect of the number of bids in each experiment are (1) the mean square error of the differences between the actual and estimated mean maximum willingness to pay, and (2) an equality test between actual and estimated mean willingness to pay. The main conclusion is that it is advisable to use a larger number of distinct bids than currently practiced for the non-parametric procedures.non-parametric methods, bid design, Contingent valuation method, Monte Carlo simulation

Non Linear Blind Source Separation Using Different Optimization Techniques

The Independent Component Analysis technique has been used in Blind Source separation of non linear mixtures. The project involves the blind source separation of a non linear mixture of signals based on their mutual independence as the evaluation criteria. The linear mixer is modeled by the Fast ICA algorithm while the Non linear mixer is modeled by an odd polynomial function whose parameters are updated by four separate optimization techniques which are Particle Swarm Optimization, Real coded Genetic Algorithm, Binary Genetic Algorithm and Bacterial Foraging Optimization. The separated mixture outputs of each case was studied and the mean square error in each case was compared giving an idea of the effectiveness of each optimization technique

Stochastic comparisons of stratied sampling techniques for some Monte Carlo estimators

We compare estimators of the (essential) supremum and the integral of a function "f" defined on a measurable space when "f" may be observed at a sample of points in its domain, possibly with error. The estimators compared vary in their levels of stratification of the domain, with the result that more refined stratification is better with respect to dierent criteria. The emphasis is on criteria related to stochastic orders. For example, rather than compare estimators of the integral of "f" by their variances (for unbiased estimators), or mean square error, we attempt the stronger comparison of convex order when possible. For the supremum the criterion is based on the stochastic order of estimators. For some of the results no regularity assumptions for "f" are needed, while for others we assume that "f" is monotone on an appropriate domain. Along the way we prove convex order inequalities that are of interest "per se".We compare estimators of the (essential) supremum and the integral of a function "f" defined on a measurable space when "f" may be observed at a sample of points in its domain, possibly with error. The estimators compared vary in their levels of stratification of the domain, with the result that more refined stratification is better with respect to dierent criteria. The emphasis is on criteria related to stochastic orders. For example, rather than compare estimators of the integral of "f" by their variances (for unbiased estimators), or mean square error, we attempt the stronger comparison of convex order when possible. For the supremum the criterion is based on the stochastic order of estimators. For some of the results no regularity assumptions for "f" are needed, while for others we assume that "f" is monotone on an appropriate domain. Along the way we prove convex order inequalities that are of interest "per se".Non-Refereed Working Papers / of national relevance onl

Endogeneity in Panel Data Models with Time-Varying and Time-Fixed Regressors: To IV or not IV?

We analyse the problem of parameter inconsistency in panel data econometrics due to the correlation of exogenous variables with the error term.A common solution in this setting is to use Instrumental-Variable (IV) estimation in the spirit of Hausman-Taylor (1981). However, some potential shortcomings of the latter approach recently gave rise to the use of non-IV two-step estimators. Given their growing number of empirical applications, we aim to systematically compare the performance of IV and non-IV approaches in the presence of time-fixed variables and right hand side endogeneity using Monte Carlo simulations, where we explicitly control for the problem of IV selection in the Hausman-Taylor case. The simulation results show that the Hausman- Taylor model with perfect-knowledge about the underlying data structure (instrument orthogonality) has on average the smallest bias. However, compared to the empirically relevant specification with imperfect-knowledge and instruments chosen by statistical criteria, the non-IV rival performs equally well or even better especially in terms of estimating variable coefficients for timefixed regressors. Moreover, the non-IV method tends to have a smaller root mean square error (rmse) than both Hausman-Taylor models with perfect and imperfect knowledge about the underlying correlation between r.h.s variables and residual term.This indicates that it is generally more efficient.The results are roughly robust for various combinations in the time and cross-section dimension of the data.Endogeneity, instrumental variables, two-step estimators, Monte Carlo simulations

Applying Soft Computing Approaches to Predict Defect Density in Software Product Releases: An Empirical Study

There is non-linear relationship between software metrics and defects, which results to a complex mapping. Therefore, to focus on the defect density area, it is a critical business requirement of effective and practical approach, which can help find the defect density in software releases. Soft computing provides a better platform to solve the non-linear and complex mapping problem. The aim of this paper is to formulate, build, evaluate, validate and compare two main sections of soft computing, fuzzy logic and artificial neural network approaches in prediction of defect density of subsequent software product releases. In this research, these two approaches are formulated and applied to predict the existence of a defect in file of software release. Both approaches have also been validated against various releases of two commercial software product release data sets. The validation criteria include mean absolute error, root mean square error and graphical analysis. The analysis of the study shows that artificial neural network provides better results compared to Fuzzy Inference System; but applicability of best approach depends on the data availability and the quantum of data