A jackknife variance estimator for unequal probability sampling

The jackknife method is often used for variance estimation in sample surveys but has only been developed for a limited class of sampling designs.We propose a jackknife variance estimator which is defined for any without-replacement unequal probability sampling design. We demonstrate design consistency of this estimator for a broad class of point estimators. A Monte Carlo study shows how the proposed estimator may improve on existing estimators.

A simple variance formula for population size estimators by conditioning

This note considers the variance estimation for population size estimators based on capture–recapture experiments. Whereas a diversity of estimators of the population size has been suggested, the question of estimating the associated variances is less frequently addressed. This note points out that the technique of conditioning can be applied here successfully which also allows us to identify sources of variation: the variance due to estimation of the model parameters and the binomial variance due to sampling n units from a population of size N. It is applied to estimators typically used in capture–recapture experiments in continuous time including the estimators of Zelterman and Chao and improves upon previously used variance estimators. In addition, knowledge of the variances associated with the estimators by Zelterman and Chao allows the suggestion of a new estimator as the weighted sum of the two. The decomposition of the variance into the two sources allows also a new understanding of how resampling techniques like the Bootstrap could be used appropriately. Finally, the sample size question for capture–recapture experiments is addressed. Since the variance of population size estimators increases with the sample size, it is suggested to use relative measures such as the observed-to-hidden ratio or the completeness of identification proportion for approaching the question of sample size choice.

Modelo de covariância bayesiana para seleção de protfólios de investimentos

The portfolio theory is a field of study devoted to investigate the decision-making by investors of resources. The purpose of this process is to reduce risk through diversification and thus guarantee a return. Nevertheless, the classical Mean-Variance has been criticized regarding its parameters and it is observed that the use of variance and covariance has sensitivity to the market and parameter estimation. In order to reduce the estimation errors, the Bayesian models have more flexibility in modeling, capable of insert quantitative and qualitative parameters about the behavior of the market as a way of reducing errors. Observing this, the present study aimed to formulate a new matrix model using Bayesian inference as a way to replace the covariance in the MV model, called MCB - Covariance Bayesian model. To evaluate the model, some hypotheses were analyzed using the method ex post facto and sensitivity analysis. The benchmarks used as reference were: (1) the classical Mean Variance, (2) the Bovespa index's market, and (3) in addition 94 investment funds. The returns earned during the period May 2002 to December 2009 demonstrated the superiority of MCB in relation to the classical model MV and the Bovespa Index, but taking a little more diversifiable risk that the MV. The robust analysis of the model, considering the time horizon, found returns near the Bovespa index, taking less risk than the market. Finally, in relation to the index of Mao, the model showed satisfactory, return and risk, especially in longer maturities. Some considerations were made, as well as suggestions for further work

Survey estimation and marginal effects in Stata

Stata is a general purpose software package that has become popular among various disciplines such as epidemiology, economics, or social sciences. Users like Stata for its scientific approach, its robustness and reliability, and the ease with which its functionality can be extended by user written programs. In this talk I will first give a brief overview of the functionality of Stata and then discuss two specific features: survey estimation and predictive margins/marginal effects. Most surveys are based on complex samples that contain multiple sampling stages, are stratified or clustered, and feature unequal selection probabilities. Standard estimators can produce misleading results in such samples unless the peculiarities of the sampling plan are taken into account. Stata offers survey statistics for complex samples for a wide variety of estimators and supports several variance estimation procedures such as linearization, jackknife, and balanced repeated replication (see Kreuter and Valliant, 2007, Stata Journal 7: 1-21). In the talk I will illustrate these features using applied examples and I will also show how user written commands can be adapted to support complex samples. Complex can also be the models we fit to our data, making it difficult to interpret them, especially in case of nonlinear or non-additive models (Mood, 2010, European Sociological Review 26: 67-82). Stata provides a number of highly useful commands to make results of such models accessible by computing and displaying predictive margins and marginal effects. In my talk I will discuss these commands provide various examples demonstrating their use.

Application of stellar photometry to the analysis of microarray images

Improvements in the analysis of microarray images are critical for accurately quantifying gene expression levels. The acquisition of accurate spot intensities directly influences the results and interpretation of statistical analyses. This dissertation discusses the implementation of a novel approach to the analysis of cDNA microarray images. We use a stellar photometric model, the Moffat function, to quantify microarray spots from nylon microarray images. The inherent flexibility of the Moffat shape model makes it ideal for quantifying microarray spots. We apply our novel approach to a Wilms' tumor microarray study and compare our results with a fixed-circle segmentation approach for spot quantification. Our results suggest that different spot feature extraction methods can have an impact on the ability of statistical methods to identify differentially expressed genes. We also used the Moffat function to simulate a series of microarray images under various experimental conditions. These simulations were used to validate the performance of various statistical methods for identifying differentially expressed genes. Our simulation results indicate that tests taking into account the dependency between mean spot intensity and variance estimation, such as the smoothened t-test, can better identify differentially expressed genes, especially when the number of replicates and mean fold change are low. The analysis of the simulations also showed that overall, a rank sum test (Mann-Whitney) performed well at identifying differentially expressed genes. Previous work has suggested the strengths of nonparametric approaches for identifying differentially expressed genes. We also show that multivariate approaches, such as hierarchical and k-means cluster analysis along with principal components analysis, are only effective at classifying samples when replicate numbers and mean fold change are high. Finally, we show how our stellar shape model approach can be extended to the analysis of 2D-gel images by adapting the Moffat function to take into account the elliptical nature of spots in such images. Our results indicate that stellar shape models offer a previously unexplored approach for the quantification of 2D-gel spots. ^

Elección de la duración del viaje vacacional: una aproximación con modelos de recuento

La duración del viaje vacacional es una decisión del turista con unas implicaciones fundamentales para las organizaciones turísticas, pero que ha recibido una escasa atención por la literatura. Además, los escasos estudios se han centrado en los destinos costeros, cuando el turismo de interior se está erigiendo como una alternativa importante en algunos países. El presente trabajo analiza los factores determinantes de la elección temporal del viaje turístico, distinguiendo el tipo de destino elegido -costa e interior-, y proponiendo varias hipótesis acerca de la influencia de las características de los individuos relacionadas con el destino, de las restricciones personales y de las características sociodemográficas. La metodología aplicada estima, como novedad en este tipo de decisiones, un Modelo Binomial Negativo Truncado que evita los sesgos de estimación de los modelos de regresión y el supuesto restrictivo de igualdad media-varianza del Modelo de Poisson. La aplicación empírica realizada en España sobre una muestra de 1.600 individuos permite concluir, por un lado, que el Modelo Binomial Negativo es más adecuado que el de Poisson para realizar este tipo de análisis. Por otro lado, las dimensiones determinantes de la duración del viaje vacacional son, para ambos destinos, el alojamiento en hotel y apartamento propio, las restricciones temporales, la edad del turista y la forma de organizar el viaje; mientras que el tamaño de la ciudad de residencia y el atributo “precios baratos” es un aspecto diferencial de la costa; y el alojamiento en apartamentos alquilados lo es de los destinos de interior.

Estimating conditional volatility with neural networks

It is well known that one of the obstacles to effective forecasting of exchange rates is heteroscedasticity (non-stationary conditional variance). The autoregressive conditional heteroscedastic (ARCH) model and its variants have been used to estimate a time dependent variance for many financial time series. However, such models are essentially linear in form and we can ask whether a non-linear model for variance can improve results just as non-linear models (such as neural networks) for the mean have done. In this paper we consider two neural network models for variance estimation. Mixture Density Networks (Bishop 1994, Nix and Weigend 1994) combine a Multi-Layer Perceptron (MLP) and a mixture model to estimate the conditional data density. They are trained using a maximum likelihood approach. However, it is known that maximum likelihood estimates are biased and lead to a systematic under-estimate of variance. More recently, a Bayesian approach to parameter estimation has been developed (Bishop and Qazaz 1996) that shows promise in removing the maximum likelihood bias. However, up to now, this model has not been used for time series prediction. Here we compare these algorithms with two other models to provide benchmark results: a linear model (from the ARIMA family), and a conventional neural network trained with a sum-of-squares error function (which estimates the conditional mean of the time series with a constant variance noise model). This comparison is carried out on daily exchange rate data for five currencies.

Liquidity and portfolio optimisation

This thesis presents research within empirical financial economics with focus on liquidity and portfolio optimisation in the stock market. The discussion on liquidity is focused on measurement issues, including TAQ data processing and measurement of systematic liquidity factors (FSO). Furthermore, a framework for treatment of the two topics in combination is provided. The liquidity part of the thesis gives a conceptual background to liquidity and discusses several different approaches to liquidity measurement. It contributes to liquidity measurement by providing detailed guidelines on the data processing needed for applying TAQ data to liquidity research. The main focus, however, is the derivation of systematic liquidity factors. The principal component approach to systematic liquidity measurement is refined by the introduction of moving and expanding estimation windows, allowing for time-varying liquidity co-variances between stocks. Under several liability specifications, this improves the ability to explain stock liquidity and returns, as compared to static window PCA and market average approximations of systematic liquidity. The highest ability to explain stock returns is obtained when using inventory cost as a liquidity measure and a moving window PCA as the systematic liquidity derivation technique. Systematic factors of this setting also have a strong ability in explaining a cross-sectional liquidity variation. Portfolio optimisation in the FSO framework is tested in two empirical studies. These contribute to the assessment of FSO by expanding the applicability to stock indexes and individual stocks, by considering a wide selection of utility function specifications, and by showing explicitly how the full-scale optimum can be identified using either grid search or the heuristic search algorithm of differential evolution. The studies show that relative to mean-variance portfolios, FSO performs well in these settings and that the computational expense can be mitigated dramatically by application of differential evolution.

Econometric models in foreign exchange market

According to the significance of the econometric models in foreign exchange market, the purpose of this research is to give a closer examination on some important issues in this area. The research covers exchange rate pass-through into import prices, liquidity risk and expected returns in the currency market, and the common risk factors in currency markets. Firstly, with the significant of the exchange rate pass-through in financial economics, the first empirical chapter studies on the degree of exchange rate pass-through into import in emerging economies and developed countries in panel evidences for comparison covering the time period of 1970-2009. The pooled mean group estimation (PMGE) is used for the estimation to investigate the short run coefficients and error variance. In general, the results present that the import prices are affected positively, though incompletely, by the exchange rate. Secondly, the following study addresses the question whether there is a relationship between cross-sectional differences in foreign exchange returns and the sensitivities of the returns to fluctuations in liquidity, known as liquidity beta, by using a unique dataset of weekly order flow. Finally, the last study is in keeping with the study of Lustig, Roussanov and Verdelhan (2011), which shows that the large co-movement among exchange rates of different currencies can explain a risk-based view of exchange rate determination. The exploration on identifying a slope factor in exchange rate changes is brought up. The study initially constructs monthly portfolios of currencies, which are sorted on the basis of their forward discounts. The lowest interest rate currencies are contained in the first portfolio and the highest interest rate currencies are in the last. The results performs that portfolios with higher forward discounts incline to contain higher real interest rates in overall by considering the first portfolio and the last portfolio though the fluctuation occurs.

Age estimation in common sole Solea solea larvae: validation of daily increments and evaluation of a pattern recognition technique

Close similarities have been found between the otoliths of sea-caught and laboratory-reared larvae of the common sole Solea solea (L.), given appropriate temperatures and nourishment of the latter. But from hatching to mouth formation. and during metamorphosis, sole otoliths have proven difficult to read because the increments may be less regular and low contrast. In this study, the growth increments in otoliths of larvae reared at 12 degrees C were counted by light microscopy to test the hypothesis of daily deposition, with some results verified using scanning electron microscopy (SEM), and by image analysis in order to compare the reliability of the 2 methods in age estimation. Age was first estimated (in days posthatch) from light micrographs of whole mounted otoliths. Counts were initiated from the increment formed at the time of month opening (Day 4). The average incremental deposition rate was consistent with the daily hypothesis. However, the light-micrograph readings tended to underestimate the mean ages of the larvae. Errors were probably associated with the low-contrast increments: those deposited after the mouth formation during the transition to first feeding, and those deposited from the onset of eye migration (about 20 d posthatch) during metamorphosis. SEM failed to resolve these low-contrast areas accurately because of poor etching. A method using image analysis was applied to a subsample of micrograph-counted otoliths. The image analysis was supported by an algorithm of pattern recognition (Growth Demodulation Algorithm, GDA). On each otolith, the GDA method integrated the growth pattern of these larval otoliths to averaged data from different radial profiles, in order to demodulate the exponential trend of the signal before spectral analysis (Fast Fourier Transformation, FFT). This second method both allowed more precise designation of increments, particularly for low-contrast areas, and more accurate readings but increased error in mean age estimation. The variability is probably due to a still rough perception of otolith increments by the GDA method, counting being achieved through a theoretical exponential pattern and mean estimates being given by FFT. Although this error variability was greater than expected, the method provides for improvement in both speed and accuracy in otolith readings.

Avaliação de métodos de estimação da variância em amostras complexas

A necessidade de conhecer uma população impulsiona um processo de recolha e análise de informação. Usualmente é muito difícil ou impossível estudar a totalidade da população, daí a importância do estudo com recurso a amostras. Conceber um estudo por amostragem é um processo complexo, desde antes da recolha dos dados até a fase de análise dos mesmos. Na maior parte dos estudos utilizam-se combinações de vários métodos probabilísticos de amostragem para seleção de uma amostra, que se pretende representativa da população, denominado delineamento de amostragem complexo. O conhecimento dos erros de amostragem é necessário à correta interpretação dos resultados de inquéritos e à avaliação dos seus planos de amostragem. Em amostras complexas, têm sido usadas aproximações ajustadas à natureza complexa do plano da amostra para a estimação da variância, sendo as mais utilizadas: o método de linearização Taylor e as técnicas de reamostragem e replicação. O principal objetivo deste trabalho é avaliar o desempenho dos estimadores usuais da variância em amostras complexas. Inspirado num conjunto de dados reais foram geradas três populações com características distintas, das quais foram sorteadas amostras com diferentes delineamentos de amostragem, na expectativa de obter alguma indicação sobre em que situações se deve optar por cada um dos estimadores da variância. Com base nos resultados obtidos, podemos concluir que o desempenho dos estimadores da variância da média amostral de Taylor, Jacknife e Bootstrap varia com o tipo de delineamento e população. De um modo geral, o estimador de Bootstrap é o menos preciso e em delineamentos estratificados os estimadores de Taylor e Jackknife fornecem os mesmos resultados; Evaluation of variance estimation methods in complex samples ABSTRACT: The need to know a population drives a process of collecting and analyzing information. Usually is to hard or even impossible to study the whole population, hence the importance of sampling. Framing a study by sampling is a complex process, from before the data collection until the data analysis. Many studies have used combinations of various probabilistic sampling methods for selecting a representative sample of the population, calling it complex sampling design. Knowledge of sampling errors is essential for correct interpretation of the survey results and evaluation of the sampling plans. In complex samples to estimate the variance has been approaches adjusted to the complex nature of the sample plane. The most common are: the linearization method of Taylor and techniques of resampling and replication. The main objective of this study is to evaluate the performance of usual estimators of the variance in complex samples. Inspired on real data we will generate three populations with distinct characteristics. From this populations will be drawn samples using different sampling designs. In the end we intend to get some lights about in which situations we should opt for each one of the variance estimators. Our results show that the performance of the variance estimators of sample mean Taylor, Jacknife and Bootstrap varies with the design and population. In general, the Bootstrap estimator is less precise and in stratified design Taylor and Jackknife estimators provide the same results.

A practical approach for identifying expected solution performance and robustness in operations research applications

A practical approach for identifying solution robustness is proposed for situations where parameters are uncertain. The approach is based upon the interpretation of a probability density function (pdf) and the definition of three parameters that describe how significant changes in the performance of a solution are deemed to be. The pdf is constructed by interpreting the results of simulations. A minimum number of simulations are achieved by updating the mean, variance, skewness and kurtosis of the sample using computationally efficient recursive equations. When these criterions have converged then no further simulations are needed. A case study involving several no-intermediate storage flow shop scheduling problems demonstrates the effectiveness of the approach.

Blind steganalysis : a countermeasure for binary image steganography

In this paper, we propose a new blind steganalytic method to detect the presence of secret messages embedded in black and white images using the steganographic techniques. We start by extracting several sets of matrix, such as run length matrix, gap length matrix and pixel difference. We also apply characteristic function on these matrices to enhance their discriminative capabilities. Then we calculate the statistics which include mean, variance, kurtosis and skewness to form our feature sets. The presented empirical works demonstrate our proposed method can effectively detect three different types of steganography. This proves the universality of our proposed method as a blind steganalysis. In addition, the experimental results show our proposed method is capable of detecting small amount of the embedded message.

Performances of socially responsible investment and environmentally friendly funds

The socially responsible investment (SRI) funds performances remain inconclusive. Hence, more studies need to be conducted to determine if SRI funds systematically underperform or outperform conventional funds. This paper has employed dynamic mean-variance model using shortage function approach to evaluate the performance of SRI and Environmentally friendly funds (EF). Unlike the traditional methods, this approach estimates fund performance considering both the return and risk at the same time. The empirical results show that SRI funds outperformed conventional funds in EU and US. In addition, the results of EU are among the top-performing categories. EF do not perform as well as SRI, but perform in manners equal or superior to conventional funds. These results show statistically significant in some cases.

Decision support system for age-related macular degeneration using discrete wavelet transform

Age-related macular degeneration (AMD) affects the central vision and subsequently may lead to visual loss in people over 60 years of age. There is no permanent cure for AMD, but early detection and successive treatment may improve the visual acuity. AMD is mainly classified into dry and wet type; however, dry AMD is more common in aging population. AMD is characterized by drusen, yellow pigmentation, and neovascularization. These lesions are examined through visual inspection of retinal fundus images by ophthalmologists. It is laborious, time-consuming, and resource-intensive. Hence, in this study, we have proposed an automated AMD detection system using discrete wavelet transform (DWT) and feature ranking strategies. The first four-order statistical moments (mean, variance, skewness, and kurtosis), energy, entropy, and Gini index-based features are extracted from DWT coefficients. We have used five (t test, Kullback–Lieber Divergence (KLD), Chernoff Bound and Bhattacharyya Distance, receiver operating characteristics curve-based, and Wilcoxon) feature ranking strategies to identify optimal feature set. A set of supervised classifiers namely support vector machine (SVM), decision tree, k -nearest neighbor ( k -NN), Naive Bayes, and probabilistic neural network were used to evaluate the highest performance measure using minimum number of features in classifying normal and dry AMD classes. The proposed framework obtained an average accuracy of 93.70 %, sensitivity of 91.11 %, and specificity of 96.30 % using KLD ranking and SVM classifier. We have also formulated an AMD Risk Index using selected features to classify the normal and dry AMD classes using one number. The proposed system can be used to assist the clinicians and also for mass AMD screening programs.