Functional linear models for interval-valued data

Aggregation of large databases in a specific format is a frequently used process to make the data easily manageable. Interval-valued data is one of the data types that is generated by such an aggregation process. Using traditional methods to analyze interval-valued data results in loss of information, and thus, several interval-valued data models have been proposed to gather reliable information from such data types. On the other hand, recent technological developments have led to high dimensional and complex data in many application areas, which may not be analyzed by traditional techniques. Functional data analysis is one of the most commonly used techniques to analyze such complex datasets. While the functional extensions of much traditional statistical techniques are available, the functional form of the interval-valued data has not been studied well. This article introduces the functional forms of some well-known regression models that take interval-valued data. The proposed methods are based on the function-on-function regression model, where both the response and predictor/s are functional. Through several Monte Carlo simulations and empirical data analysis, the finite sample performance of the proposed methods is evaluated and compared with the state-of-the-art

Establishment of Dynamic Evolving Neural-Fuzzy Inference System Model for Natural Air Temperature Prediction

Air temperature (AT) prediction can play a significant role in studies related to climate change, radiation and heat flux estimation, and weather forecasting. This study applied and compared the outcomes of three advanced fuzzy inference models, i.e., dynamic evolving neural-fuzzy inference system (DENFIS), hybrid neural-fuzzy inference system (HyFIS), and adaptive neurofuzzy inference system (ANFIS) for AT prediction. Modelling was done for three stations in North Dakota (ND), USA, i.e., Robinson, Ada, and Hillsboro. The results reveal that FIS type models are well suited when handling highly variable data, such as AT, which shows a high positive correlation with average daily dew point (DP), total solar radiation (TSR), and negative correlation with average wind speed (WS). At the Robinson station, DENFIS performed the best with a coefficient of determination (R$^{2}$) of 0.96 and a modified index of agreement (md) of 0.92, followed by ANFIS with R$^{2}$ of 0.94 and md of 0.89, and HyFIS with R$^{2}$ of 0.90 and md of 0.84. A similar result was observed for the other two stations, i.e., Ada and Hillsboro stations where DENFIS performed the best with R$^{2}$: 0.953/0.960, md: 0.903/0.912, then ANFIS with R$^{2}$: 0.943/0.942, md: 0.888/0.890, and HyFIS with R$^{2}$ 0.908/0.905, md: 0.845/0.821, respectively. It can be concluded that all three models are capable of predicting AT with high efficiency by only using DP, TSR, and WS as input variables. This makes the application of these models more reliable for a meteorological variable with the need for the least number of input variables. The study can be valuable for the areas where the climatological and seasonal variations are studied and will allow providing excellent prediction results with the least error margin and without a huge expenditure

ITERATED BOOTSTRAP PROCEDURE IN INDIVIDUAL BIOEQUIVALENCE

In this paper, we propose an iterating principle in the bootstrap method to assess the individual bioequivalence under 2x4 randomized crossover design. The finite sample properties of the proposed algorithm are illustrated by an extensive simulation study and a real-world example. Our findings reveal that the proposed idea have better performance than the classical percentile bootstrap confidence limits

Machine-Learning-Based Functional Time Series Forecasting: Application to Age-Specific Mortality Rates

We propose a functional time series method to obtain accurate multi-step-ahead forecasts for age-specific mortality rates. The dynamic functional principal component analysis method is used to decompose the mortality curves into dynamic functional principal components and their associated principal component scores. Machine-learning-based multi-step-ahead forecasting strategies, which automatically learn the underlying structure of the data, are used to obtain the future realization of the principal component scores. The forecasted mortality curves are obtained by combining the dynamic functional principal components and forecasted principal component scores. The point and interval forecast accuracy of the proposed method is evaluated using six age-specific mortality datasets and compared favorably with four existing functional time series methods