A New Weighting Scheme in Weighted Markov Model for Predicting the Probability of Drought Episodes

Drought is a complex stochastic natural hazard caused by prolonged shortage of rainfall. Several environmental factors are involved in determining drought classes at the specific monitoring station. Therefore, efficient sequence processing techniques are required to explore and predict the periodic information about the various episodes of drought classes. In this study, we proposed a new weighting scheme to predict the probability of various drought classes under Weighted Markov Chain (WMC) model. We provide a standardized scheme of weights for ordinal sequences of drought classifications by normalizing squared weighted Cohen Kappa. Illustrations of the proposed scheme are given by including temporal ordinal data on drought classes determined by the standardized precipitation temperature index (SPTI). Experimental results show that the proposed weighting scheme for WMC model is sufficiently flexible to address actual changes in drought classifications by restructuring the transient behavior of a Markov chain. In summary, this paper proposes a new weighting scheme to improve the accuracy of the WMC, specifically in the field of hydrology

Robust kernel regression function with uncertain scale parameter for high dimensional ergodic data using k k -nearest neighbor estimation

In this paper, we consider a new method dealing with the problem of estimating the scoring function $\gamma_a$, with a constant $a$, in functional space and an unknown scale parameter under a nonparametric robust regression model. Based on the $k$ Nearest Neighbors ($k$NN) method, the primary objective is to prove the asymptotic normality aspect in the case of a stationary ergodic process of this estimator. We begin by establishing the almost certain convergence of a conditional distribution estimator. Then, we derive the almost certain convergence (with rate) of the conditional median (scale parameter estimator) and the asymptotic normality of the robust regression function, even when the scale parameter is unknown. Finally, the simulation and real-world data results reveal the consistency and superiority of our theoretical analysis in which the performance of the $k$NN estimator is comparable to that of the well-known kernel estimator, and it outperforms a nonparametric series (spline) estimator when there are irrelevant regressors

Characterization of regional hydrological drought using improved precipitation records under multi-auxiliary information

Drought is a complex natural hazard that has been recurrently occurred in many regions across the globe. Therefore, precise drought characterization and its regional monitoring are key challenges for advanced water management and hydrological research. In this research, we provided a novel method to improve annual average time series data for the Standardized Drought Index (SDI)-type drought monitoring tools. We proposed multi-auxiliary information-based estimation strategy that improves annual moving average/total precipitation time series records. Therefore, we incorporated a minimum and maximum temperature as auxiliary variables under multi-auxiliary regression estimator. In summary, this study propagates a new drought index named: the Precision-Weighted Standardized Precipitation Index (PWSDI). We evaluated the performance of PWSDI for 10 meteorological stations in Pakistan. We found that improved estimates of temporal precipitation time series are good candidates for modelling and monitoring hydrological drought at the regional settings under SDI procedure

Strong consistency rate in functional single index expectile model for spatial data

Analyzing the real impact of spatial dependency in financial time series data is crucial to financial risk management. It has been a challenging issue in the last decade. This is because most financial transactions are performed via the internet and the spatial dependency between different international stock markets is not standard. The present paper investigates functional expectile regression as a spatial financial risk model. Specifically, we construct a nonparametric estimator of this functional model for the functional single index regression (FSIR) structure. The asymptotic properties of this estimator are elaborated over general spatial settings. More precisely, we establish Borel-Cantelli consistency (BCC) of the constructed estimator. The latter is obtained with the precision of the convergence rate. A simulation investigation is performed to show the easy applicability of the constructed estimator in practice. Finally, real data analysis about the financial data (Euro Stoxx-50 index data) is used to illustrate the effectiveness of our methodology

Efficient Estimation of Two-Parameter Xgamma Distribution Parameters Using Ranked Set Sampling Design

An efficient method such as ranked set sampling is used for estimating the population parameters when the actual observation measurement is expensive and complicated. In this paper, we consider the problem of estimating the two-parameter xgamma (TPXG) distribution parameters under the ranked set sampling as well as the simple random sampling design. Various estimation methods, including the weighted least-square estimator, maximum likelihood estimators, least-square estimator, Cramer–von Mises, the maximum product of spacings estimators, and Anderson–Darling estimators, are considered. A comparison between the ranked set sampling and simple random sampling estimators, with the same number of measurement units, is conducted using a simulation study in terms of the bias, mean squared errors, and efficiency of estimators. The merit of the ranked set sampling estimators is examined using real data of bank customers. The results indicate that estimations using the ranked set sampling method are more efficient than the simple random sampling competitor considered in this study

Estimating the Conditional Density in Scalar-On-Function Regression Structure: <i>k</i>-N-N Local Linear Approach

In this study, the problem of conditional density estimation of a scalar response variable, given a functional covariable, is considered. A new estimator is proposed by combining the k-nearest neighbors (k-N-N) procedure with the local linear approach. Then, the uniform consistency in the number of neighbors (UNN) of the proposed estimator is established. Such result is useful in the study of some data-driven rules. As a direct application and consequence of the conditional density estimation, we derive the UNN consistency of the conditional mode function estimator. Finally, to highlight the efficiency and superiority of the obtained results, we applied our new estimator to real data and compare it to its existing competitive estimator

A Novel Parent Centric Crossover with the Log-Logistic Probabilistic Approach Using Multimodal Test Problems for Real-Coded Genetic Algorithms

In this paper, a comprehensive empirical study is conducted to evaluate the performance of a new real-coded crossover operator called Fisk crossover (FX) operator. The basic aim of the proposed study is to preserve population diversity as well as to avoid local optima. In this context, a new crossover operator is designed and developed which is linked with Log-logistic probability distribution. For its global performance, a realistic comparison is made between FX versus double Pareto crossover (DPX), Laplace crossover (LX), and simulated binary crossover (SBX) operators. Moreover, these crossover operators are also used in conjunction with three mutation operators called power mutation (PM), Makinen, Periaux, and Toivanen mutation (MPTM), and nonuniform mutation (NUM) for inclusive evaluation. The performance of probabilistic-based algorithms is tested on a set of twenty-one well-known nonlinear optimization benchmark functions with diverse features. The empirical results show a substantial dominance of FX over other crossover operators with authentication of performance index (PI). Moreover, we also examined the significance of the proposed crossover scheme by administrating ANOVA and Gabriel pairwise multiple comparison test. Finally, the statistically significant results of the proposed crossover scheme have a definite edge over the other schemes, and it is also expected that FX has a great potential to solve complex optimization problems

Energy Balance Approach to Study the Role of Perspiration in Heat Distribution of Human Skin

This paper develops a model to identify the role of perspiration in temperature distribution of human skin. The model has been solved by using the energy balance equation on the surface of human skin. The role played by thermal conductance, convection, and heat radiation during heat transfer in human skin has been considered, and the relevant laws such as Fourier law for conduction, Newton’s Law for convection, and Stefan–Boltzmann’s law for radiation have been used in the model. Pennes’ bioheat equation has been employed to estimate the heat flow in the dermal region of skin including subcutaneous tissue

Predicting temperature curve based on fast kNN local linear estimation of the conditional distribution function

Predicting the yearly curve of the temperature, based on meteorological data, is essential for understanding the impact of climate change on humans and the environment. The standard statistical models based on the big data discretization in the finite grid suffer from certain drawbacks such as dimensionality when the size of the data is large. We consider, in this paper, the predictive region problem in functional time series analysis. We study the prediction by the shortest conditional modal interval constructed by the local linear estimation of the cumulative function of $Y$Y given functional input variable $X$X . More precisely, we combine the $k$k -Nearest Neighbors procedure to the local linear algorithm to construct two estimators of the conditional distribution function. The main purpose of this paper is to compare, by a simulation study, the efficiency of the two estimators concerning the level of dependence. The feasibility of these estimators in the functional times series prediction is examined at the end of this paper. More precisely, we compare the shortest conditional modal interval predictive regions of both estimators using real meteorological data

Estimating the Conditional Density in Scalar-On-Function Regression Structure: k-N-N Local Linear Approach

In this study, the problem of conditional density estimation of a scalar response variable, given a functional covariable, is considered. A new estimator is proposed by combining the k-nearest neighbors (k-N-N) procedure with the local linear approach. Then, the uniform consistency in the number of neighbors (UNN) of the proposed estimator is established. Such result is useful in the study of some data-driven rules. As a direct application and consequence of the conditional density estimation, we derive the UNN consistency of the conditional mode function estimator. Finally, to highlight the efficiency and superiority of the obtained results, we applied our new estimator to real data and compare it to its existing competitive estimator