Estimation of location parameter within pre-specified error bound with second-order efficient two-stage procedure

This paper develops a general approach for constructing a confidence interval for a parameter of interest with a specified confidence coefficient and a specified width. This is done assuming known a positive lower bound for the unknown nuisance parameter and independence of suitable statistics. Under mild conditions, we develop a modified two-stage procedure which enjoys attractive optimality properties including a second-order efficiency property and asymptotic consistency property. We extend this work for finding a confidence interval for the location parameter of the inverse Gaussian distribution. As an illustration, we developed a modified mean absolute deviation-based procedure in the supplementary section for finding a fixed-width confidence interval for the normal mean.

Functional SAC model: With application to spatial econometrics

Spatial autoregressive combined (SAC) models have been widely studied in the literature for the analysis of spatial data in various areas such as geography, economics, demography, regional sciences. This is a linear model with scalar response and scalar explanatory variables which allows for spatial interactions in the dependent variables and the disturbances. In this work we extend this modeling approach from scalar to functional covariate. The parameters of the model are estimated via the maximum likelihood estimation method. A simulation study is conducted to evaluate the performance of the proposed methodology. As an illustration, the model is used to establish the relationship between unemployment and illiteracy in Senegal.

Estimating the Gini index for heavy-tailed income distributions

In the present paper, we define and study one of the most popular indices which measures the inequality of capital incomes, known as the Gini index. We construct a semiparametric estimator for the Gini index in case of heavy-tailed income distributions and we establish its asymptotic distribution and derive bounds of confidence. We explore the performance of the confidence bounds in a simulation study and draw conclusions about capital incomes in some income distributions.

Regularisation in discrete survival models: A comparison of lasso and gradient boosting

We present the results of a simulation study performed to compare the accuracy of a lasso-type penalization method and gradient boosting in estimating the baseline hazard function and covariate parameters in discrete survival models. The mean square error results reveal that the lasso-type algorithm performs better in recovering the baseline hazard and covariate parameters. In particular, gradient boosting underestimates the sizes of the parameters and also has a high false positive rate. Similar results are obtained in an application to real-life data.

Contextual batting and bowling in limited overs cricket

Cricket is a sport for which many batting and bowling statistics have been proposed. However, a feature of cricket is that the level of aggressiveness adopted by batsmen is dependent on match circumstances. It is therefore relevant to consider these circumstances when evaluating batting and bowling performances. This paper considers batting performance in the second innings of limited overs cricket when a target has been set. The runs required, the number of overs completed and the wickets taken are relevant in assessing the batting performance. We produce a visualization for second innings batting which describes how a batsman performs under different circumstances. The visualization is then reduced to a single statistic "clutch batting" which can be used to compare batsmen. An analogous approach is then provided for bowlers based on the symmetry between batting and bowling, and we define the statistic "clutch bowling".

A generic test for the similarity of spatial data

Two spatial data sets are considered to be similar if they originate from the same stochastic process in terms of their spatial structure. Many tests have been developed over recent years to test the similarity of certain types of spatial data, such as spatial point patterns, geostatistical data and images. This research proposes a generic spatial similarity test able to handle various types of spatial data, for example images (modelled spatially), point patterns, marked point patterns, geostatistical data and lattice patterns. A simulation study is done in order to test the method for each spatial data set. After the simulation study, it was concluded that the proposed spatial similarity test is not sensitive to the user-defined resolution of the pixel image representation. From the simulation study, the proposed spatial similarity test performs well on lattice data, some of the unmarked point patterns and the marked point patterns with discrete marks. We illustrate this test on property prices in the City of Cape Town and the City of Johannesburg, South Africa.