Sohail Chand

On tuning parameter selection of lasso-type methods - a monte carlo study

In regression analysis, variable selection is a challenging task. Over the last decade, the lasso-type methods have become popular method for variable selection due to their property of shrinking some of the model coefficients to exactly zero. Theory says that lasso-type methods are able to do consistent variable selection but it is hard to achieve this property in practice. This consistent variable selection highly depends on the right choice of the tuning parameter. In this paper, we show that selection of tuning parameter by cross validation almost always fail to achieve consistent variable selection. We have also shown that lasso-type methods with a BIC-type tuning parameter selector, under certain conditions, can do the consistent variable selection. We have also made a novel suggestion for choosing the value of Cn, a weight on estimated model size, in BIC. Our results show that with this choice of Cn, the lasso-type methods can do consistent variable selection.In regression analysis, variable selection is a challenging task. Over the last decade, the lasso-type methods have become popular method for variable selection due to their property of shrinking some of the model coefficients to exactly zero. Theory says that lasso-type methods are able to do consistent variable selection but it is hard to achieve this property in practice. This consistent variable selection highly depends on the right choice of the tuning parameter. In this paper, we show that selection of tuning parameter by cross validation almost always fail to achieve consistent variable selection. We have also shown that lasso-type methods with a BIC-type tuning parameter selector, under certain conditions, can do the consistent variable selection. We have also made a novel suggestion for choosing the value of Cn, a weight on estimated model size, in BIC. Our results show that with this choice of Cn, the lasso-type methods can do consistent variable selection.

Mixed Portmanteau Test for Diagnostic Checking of Time Series Models

Model criticism is an important stage of model building and thus goodness of fit tests provides a set of tools for diagnostic checking of the fitted model. Several tests are suggested in literature for diagnostic checking. These tests use autocorrelation or partial autocorrelation in the residuals to criticize the adequacy of fitted model. The main idea underlying these portmanteau tests is to identify if there is any dependence structure which is yet unexplained by the fitted model. In this paper, we suggest mixed portmanteau tests based on autocorrelation and partial autocorrelation functions of the residuals. We derived the asymptotic distribution of the mixture test and studied its size and power using Monte Carlo simulations.

Geostatistical cokriging and multivariate statistical methods to evaluate groundwater salinization in Faisalabad, Pakistan

In the present study, multivariate techniques and geostatistical cokriging were used to look into the groundwater salinization of district Faisalabad. The groundwater condition of district Faisalabad has become miserable because of the rapid increase in population, industrial wastes, and agrochemical application. As a result, majority of the people do not have access to pure drinking water and, consequently, polluted water is causing many deaths per year. A number of 220 water samples based on instructions of World Health Organization (WHO) were taken from four main sources such as hand pump, injector pump, tube well, and water supply. All samples were tested for 12 water quality parameters and summary statistics were calculated to compare the water quality parameters with WHO permissible limits. Initially, correlation matrix was constructed to evaluate the most significant parameters and later on used principal component analysis (PCA) to select those parameters causing maximum variation. Dendrogram based on cluster analysis conveyed same sort of information as delivered by PCA. First, factor of PCA contributed 41.6% of total variation. Six water quality parameters such as sulfate, calcium, total dissolved solids, sodium, chloride, and magnesium were found to be most alarming because all of these have factor loadings greater than 75%. Cross-variogram based on cokriging showed spatial dependence as well as positive pairwise spatial correlation among all parameters. The prediction maps highlighted the most dangerous and health hazard areas; therefore, may be very helpful for water management agencies to target those high-risk areas. It was found that the area with east latitude 31.0°–31.4° and north longitude 72.8°–73.2° is most alarming zone.

Predicting the spatial distribution of sulfate concentration in groundwater of Jampur-Pakistan using geostatistical methods

AbstractIn this study, we investigate the spatial distribution of sulfate concentration in groundwater of tehsil Jampur, Pakistan using geostatistical techniques. Sulfate concentration in drinking water causes chronic diseases like stomach disorder, diarrhea, laxative effects, and food poisoning in human beings, particularly in infants. First, 30 water samples were collected with their spatial coordinates to evaluate the spatial variation and distribution of sulfate concentration in groundwater of tehsil Jampur. Then, we evaluated the assumptions of normality and autocorrelation in the spatial data and used Matern covariance model to assess the correlation structure of response variable (random field). Furthermore, we applied ordinary least square and weighted least square to estimate the variogram parameters. Two interpolation methods, Ordinary Kriging and Bayesian Kriging were used to predict the unmonitored locations within the studied domain. Performance of the interpolation methods was assessed throu...

SPATIAL MODELING OF FIELD VARIABILITY IN IMPROVING THE POTENCY OF VARIETAL CONTRAST

*In this paper, large wheat varietal experiment was comparatively studied and analyzed through classical ANOVA and latest spatial modeling approach. Spatial modeling technique captures the trend of field variability which consequently results in an unbiased varietal contrast and considerable improvement in precision of underlying experiment. An experiment based on the layout of alpha lattice design with 24 wheat varieties replicated three times was conducted for the purpose of varietal comparison. Post blocking technique was used to re-analyze the experiment using RCBD which was actually conducted using the layout of alpha design. Variogram used to capture the spatial dependence between neighboring wheat field plots which suggests serial correlation among adjacent plots. Run test was also carried out to know the pattern of variation in underlying experiment. Linear mixed spatial model was used as novel statistical method for modeling all possible sources of variation present in field trial thus get significant results using spatial modeling approach in reduction of Standard Error of Difference (SED) as compared to traditional ANOVA. Three main sources of variations were tried to capture during spatial modeling. Among five different proposed spatial and non spatial models, the best model was the row-column spatial model with a first-order spatial auto-regressive correlated error process which detains two way variability of the experiment.