Shahjahan Khan | University of Southern Queensland (original) (raw)

Papers by Shahjahan Khan

Journal of Mathematics and Statistics, 2021

Bi-directional Grid Constrained (BGC) Stochastic Processes (BGCSP) become more constrained the fu... more Bi-directional Grid Constrained (BGC) Stochastic Processes (BGCSP) become more constrained the further they drift away from the origin or time axis are examined here. As they drift further away from the time axis, then the greater the likelihood of stopping, as if by two hidden reflective barriers. The theory of BGCSP is applied to a trading environment in which long and short trading is available. The stochastic differential equation of the Grid Trading Problem (GTP) is proposed, proved and its solution is simulated to derive new findings that can lead to further research in this area and the reduction of risk in portfolio management.

Weather and Climate Extremes, 2018

An agricultural producer's crop yield and the subsequent farming revenues are affected by many co... more An agricultural producer's crop yield and the subsequent farming revenues are affected by many complex factors, including price fluctuations, government policy and climate (e.g., rainfall and temperature) extremes. Geographical diversification is identified as a potential farmer adaptation and decision support tool that could assist producers to reduce unfavourable financial impacts due to the variabilities in crop price and yield, associated with climate variations. There has been limited research performed on the effectiveness of this strategy. This paper proposes a new statistical approach to investigate whether the geographical spread of wheat farm portfolios across three climate broad-acre (i.e., rain-fed) zones could potentially reduce financial risks for producers in the Australian agro-ecological zones. A suite of popular and statistically robust tools applied in the financial sector based on the well-established statistical theories, comprised of the Conditional Value-at-Risk (CVaR) and the joint copula models were employed to evaluate the effectiveness geographical diversification. CVaR is utilised to benchmark the losses (i.e., the downside risk), while the copula function is employed to model the joint distribution among marginal returns (i.e., profit in each zone). The mean-CVaR optimisations indicate that geographical diversification could be a feasible agricultural risk management approach for wheat farm portfolio managers in achieving their optimised expected returns while controlling the risks (i.e., target levels of risk). Further, in this study, the copula-based mean-CVaR model is seen to better simulate extreme losses compared to the conventional multivariate-normal models, which underestimate the minimum risk levels at a given target of expected return. Among the suite of tested copula-based models, the vine copula in this study is found to be a superior in capturing the tail dependencies compared to the other multivariate copula models investigated. The present study provides innovative solutions to agricultural risk management with advanced statistical models using Australia as a case study region, also with broader implications to other regions where farming revenues may be optimized through copula-statistical models.

Surgical laparoscopy, endoscopy & percutaneous techniques, 2016

Laparoscopic Roux-en-Y gastric bypass (LRYGB) and laparoscopic vertical sleeve gastrectomy (LVSG)... more Laparoscopic Roux-en-Y gastric bypass (LRYGB) and laparoscopic vertical sleeve gastrectomy (LVSG), have been proposed as cost-effective strategies to manage obesity-related chronic disease. The objectives of this meta-analysis and systematic review were to analyze the "late postoperative complication rate (>30 days)" for these 2 procedures. Randomized controlled trials (RCTs) published between 2000 and 2015 comparing the late complication rates, that is, >30 days following LVSG and LRYGB in adult population (ie, 16 y and above) were selected from PubMed, Medline, Embase, Science Citation Index, Current Contents, and the Cochrane database. The outcome variables analyzed included mortality rate, major and minor complications, and interventions required for their management and readmission rates. Random effects model was used to calculate the effect size of both binary and continuous data. Heterogeneity among the outcome variables of these trials was determined by the C...

Bi-Directional Grid Constrained (BGC) stochastic processes (BGCSPs) constrain the random movement... more Bi-Directional Grid Constrained (BGC) stochastic processes (BGCSPs) constrain the random movement toward the origin steadily more and more, the further they deviate from the origin, rather than all at once imposing reflective barriers, as does the well-established theory of Itô diffusions with such reflective barriers. We identify that BGCSPs are a variant rather than a special case of the multi-skew Brownian motion (M-SBM). This is because they have their own complexities, such as the barriers being hidden (not known in advance) and not necessarily constant over time. We provide a M-SBM theoretical framework and also a simulation framework to elaborate deeper properties of BGCSPs. The simulation framework is then applied by generating numerous simulations of the constrained paths and the results are analysed. BGCSPs have applications in finance and indeed many other fields requiring graduated constraining, from both above and below the initial position.

IEEE Access

This work involved human subjects or animals in its research. Approval of all ethical and experim... more This work involved human subjects or animals in its research. Approval of all ethical and experimental procedures and protocols was granted by the USQ Ethics Committee under Ethics Approval No. H18REA236.

The prediction distribution of generalized geometric series distribution (GGSD) and of its trunca... more The prediction distribution of generalized geometric series distribution (GGSD) and of its truncated and size-biased forms is derived and studied under the non-informative and beta prior distributions. The prediction distributions for all the models are beta distribution, but the parameters of the prediction distributions depend on the choice of the prior distribution as well as the model under consideration.

The measurement errors problem is endemic in many econometric studies, and one of the oldest know... more The measurement errors problem is endemic in many econometric studies, and one of the oldest known statistical problems. Instrumental variable (IV) method is one of the popular solutions adopted to deal with the mismeasured variables in statistical and econometric analyses. This paper proposes an efficient IV estimator to the parameters of the simple regression model where both variables are subject to measurement errors. The proposed IV is defined using simple mathematical transformation of the manifest independent variable (mismeasured variable). The proposed method is straightforward, and easy to implement. The theoretical superiority of the proposed estimator over the existing IV based estimators due to Wald (1940), Bartlett (1949), and Durbin (1954) is established by analytical comparison and geometric expositions. Simulation based numerical comparisons of the proposed estimator with four different existing estimators are also included.

A score type test based on the M-estimation method for a linear regression model is more reliable... more A score type test based on the M-estimation method for a linear regression model is more reliable than the parametric based-test under mild departures from model assumptions, or when dataset has outliers. An R-function is developed for the score M-test, and applied to two real datasets to illustrate the procedure. The asymptotic power function of the M-test under a sequence of (contiguous) local alternatives is derived. Through computation of power function from simulated data, the M-test is compared with its alternatives, the Student's ttt and Wilcoxon's rank tests. Graphical illustration of the asymptotic power of the M-test is provided for randomly generated data from the normal, Laplace, Cauchy, and logistic distributions.

This paper introduces a new weighted geometric mean (WG) estimator to fit regression line when bo... more This paper introduces a new weighted geometric mean (WG) estimator to fit regression line when both the response and explanatory variables are subject to measurement errors. The proposed estimator is based on the mathematical relationship between the vertical and orthogonal distances of the observed points and the regression line (cf. Saqr and Khan, 2012). It minimizes the orthogonal distance of the observed points from the unfitted line. The WG estimator is less sensitive to the ratio of error variances. It is a better alternative than the currently used geometric mean (GM) and OLS-bisector estimators. Extensive simulation results show that the proposed WG estimator is much more stable than the geometric mean and OLS-bisector estimators. The mean absolute error of the WG estimator is consistently smaller than the geometric mean and OLS-bisector estimators.

summary This paper deflnes the preliminary test estimator (PTE) of the univariate normal mean und... more summary This paper deflnes the preliminary test estimator (PTE) of the univariate normal mean under the original as well as the Edgeworth size corrected Wald (W), likelihood ratio (LR) and Lagrange multiplier (LM) tests. The bias and mean squared error (MSE) functions of the estimators are derived. The con∞icts among the biases and the MSEs of the PTEs under the three original and the size corrected tests have been obtained. It is found that instead of the original W, LR and LM tests, the use of the Edgeworth size corrected W, LR and LM tests in the formation of the PTEs reduces the con∞ict among the biases and MSEs of the estimators remarkably.

Journal of Probability and Statistics, 2021

Bidirectional Grid Constrained (BGC) stochastic processes (BGCSPs) are constrained Itô diffusions... more Bidirectional Grid Constrained (BGC) stochastic processes (BGCSPs) are constrained Itô diffusions with the property that the further they drift away from the origin, the more the resistance to movement in that direction they undergo. The underlying characteristics of the BGC parameter Ψ X t , t are investigated by examining its geometric properties. The most appropriate convex form for Ψ , that is, the parabolic cylinder is identified after extensive simulation of various possible forms. The formula for the resulting hidden reflective barrier(s) is determined by comparing it with the simpler Ornstein–Uhlenbeck process (OUP). Applications of BGCSP arise when a series of semipermeable barriers are present, such as regulating interest rates and chemical reactions under concentration gradients, which gives rise to two hidden reflective barriers.

Risk Governance and Control: Financial Markets and Institutions, 2020

Whilst the gambler’s ruin problem (GRP) is based on martingales and the established probability t... more Whilst the gambler’s ruin problem (GRP) is based on martingales and the established probability theory proves that the GRP is a doomed strategy, this research details how the semimartingale framework is required for the grid trading problem (GTP) of financial markets, especially foreign exchange (FX) markets. As banks and financial institutions have the requirement to hedge their FX exposure, the GTP can help provide a framework for greater automation of the hedging process and help forecast which hedge scenarios to avoid. Two theorems are adapted from GRP to GTP and prove that grid trading, whilst still subject to the risk of ruin, has the ability to generate significantly more profitable returns in the short term. This is also supported by extensive simulation and distributional analysis. We introduce two absorption barriers, one at zero balance (ruin) and one at a specified profit target. This extends the traditional GRP and the GTP further by deriving both the probability of rui...

Investment Management and Financial Innovations, 2020

Bi-Directional Grid Constrained (BGC) trading strategies have never been studied academically unt... more Bi-Directional Grid Constrained (BGC) trading strategies have never been studied academically until now, are relatively new in the world of financial markets and have the ability to out-perform many other trading algorithms in the short term but will almost surely ruin an investment account in the long term. Whilst the Gambler’s Ruin Problem (GRP) is based on martingales and the established probability theory proves that the GRP is a doomed strategy, this research details how the semimartingale framework is required to solve the grid trading problem (GTP), i.e. a form of BGC financial markets strategies, and how it can deliver greater return on investment (ROI) for the same level of risk. A novel theorem of GTP is derived, proving that grid trading, whilst still subject to the risk of ruin, has the ability to generate significantly more profitable returns in the short term. This is also supported by extensive simulation and distributional analysis. These results not only can be stud...

Journal of Statistical Theory and Applications, 2019

The data generated by many factorial experiments are analyzed by linear regression models. Often ... more The data generated by many factorial experiments are analyzed by linear regression models. Often the higher order interaction terms of such models are negligible (e.g., R. Mead, The Design of Experiments, Cambridge University Press, Cambridge, 1988, p. 368) although there is uncertainty around it. This kind of nonsample prior information (NSPI) can be presented by null hypotheses (cf. T.A. Bancroft, Ann. Math. Stat. 15 (1944), 190 204), and its uncertainty removed through appropriate statistical test. Depending on the level of the NSPI the unrestricted, restricted, and pretest (PTT) tests are defined. The sampling distributions of test statistics and power functions of the three tests are derived. The graphical and analytical comparisons of powers reveal that the PTT dominates over the other tests.

Applied Mathematics & Information Sciences, 2016

In the age of evidence based decision making through a systematic review of the literature, stati... more In the age of evidence based decision making through a systematic review of the literature, statistical meta-analysis has been extensively used to synthesise published summary data on a particular topic of interest from a number of independent studies in order to make credible and scientifically valid conclusions. The main objective is to estimate the common effect size as a pooled statistic for any selected outcome variables from the relevant data. There are several issues concerning the quality and type of the published summary statistics and inherent heterogeneity among the estimates of the effect size across the studies. This paper covers several estimators of the common effect size and some of their major impacts in meta-analysis through redistribution of weights to the individual studies. Some examples from recent literature on cancer research studies are used to illustrate the alternative estimators and discuss their usefulness in analysing data from randomised controlled trials in medicine.

In presence of an uncertain prior information about the slope parameter, the estimation of the in... more In presence of an uncertain prior information about the slope parameter, the estimation of the intercept of a simple regression model with a multivariate Student- t error distribution is investigated. The unrestricted, restricted and preliminary test maximum likelihood estimators are deflned. The expressions for the bias and the mean square error of the three estimators are provided and the relative e-ciencies are analysed. A maximin criterion is established, and graphs and tables are con- structed for difierent number of degrees of freedom (D.F.) as well as sample sizes. These tables of relative e-ciencies can be used to determine a proper choice of the signiflcance level of the preliminary test which in turn determines the choice of the estimator.

This paper proposes a new method of improved meta analysis to combine relative risk for both homo... more This paper proposes a new method of improved meta analysis to combine relative risk for both homogeneous and heterogeneous set of studies. The standard meta analyses don't give any conclusive result when the effects of heterogenous studies are combined. The proposed improved meta analysis uses the predicted relative risk, and chi-square test to check the heterogeneity of the effects. Confidence intervals for the relative risks obtained via improved method concentrate more towards the value of the pooled estimate than that of the standard meta analysis. Exclusion of identified studies with outliers from the analysis brings the results of the remaining studies closer to the pooled estimate. An illustration shows that the new method improves the results and provide conclusive estimate of the relative risk.

The paper obtains two Stein-type estimators of the mean vector of a multivariate Student-t popula... more The paper obtains two Stein-type estimators of the mean vector of a multivariate Student-t population with unknown shape parameter based on two random samples from populations having common but unknown covariance matrix by using the preliminary test approach to shrinkage estimation. The properties of the shrinkage and the positive rule shrinkage estimators are investigated in terms of bias and the quadratic risk criteria. The relative performances of the estimators, and dominance over the usual maximum likelihood estimator are discussed. Comparisons of the estimators for the multivariate normal model are also included under different conditions. The uniform dominance of the positive rule shrinkage estimator over the shrinkage and maximum likelihood estimator is established.

Emerging technologies are being used increasingly to improve the communication and quality of ins... more Emerging technologies are being used increasingly to improve the communication and quality of instruction in the statistics classroom. Whereas a decade ago the move commenced away from blackboard writing with chalk towards computer assisted lecture ...