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This paper proposes a Bayesian heteroscedastic matrix factorization to deal with sparse and high dimensional data. This methodology uses techniques of latent factors, considered the state-of-the-art in recommender systems based on collaborative filtering models. The proposal is to include variations among users to accommodate divergent opinions on various items, which may or may not be more generous in their critiques of the products. For this reason, tailored priors are presented for the parameters to obtain greater scalability and a specific variation for each user. We compare the results, obtained with the probabilistic matrix factorization (PMF) and our Bayesian heteroscedastic matrix factorization (BHMF), in the Netflix and the MovieLens datasets, based on the root mean square error (RMSE).

KEYWORDS: Collaborative Filtering, Latent Factors, Recommender Systems, Sparse Datas.

The standard Q-model for investment, augmented to include a liquidity variable (cash flow or retained profits) as a proxy for the nexus between investment and financial constraints, is usually applied to firm-level panel data. A relatively small number of studies apply the model to aggregate data as well. To our knowledge, however, two important econometric issues have not received proper attention: the possible nonstationarity of Q and the presence of structural breaks. Using United States (US) aggregate quarterly data, 1947:1-2022:2, we find evidence that (1) Q behaves as an I(1) variable, whereas the other variables of the equation behave
as I(0), and (2) there is a structural break around 1963:1. Accordingly, we use the “bounds testing” approach and allow the regression coefficients to change from 1963:1 onward. As a result, the coefficient of Q, which is statistically significant if the break is ignored, becomes insignificant. This finding coupled with evidence for omitted nonlinearities suggests that the model may be inadequate.

KEYWORDS: Investment, financial constraints, Q-model, structural breaks, bounds test.

Here we investigate the statistical properties of two autoregressive normal asymmetric SV models with possibly time varying means. These, although they seem very similar, it turns out, that they possess quite different statistical properties. The derived properties can be employed to develop tests or to check for up to forth order stationarity, something important for the asymptotic properties of various estimators.

KEYWORDS: Gaussian Stochastic Volatility, in Mean, static and dynamic statistical properties, financial returns.

State-space models have gained increasing popularity in econometric inference for panel surveys due to their flexibility and potential to reduce estimation errors. In this article, we apply state-space models to improve the accuracy of design-based estimates in panel surveys. While trend and seasonal components can be conveniently modeled through the state equation, the rotation pattern inherent to panel designs induces a complex correlation structure among monthly estimates. This correlation structure motivates the integration of an autoregressive (AR) model for the residuals in the observation equation. However, estimating the optimal AR parameters presents a challenge, as the parameters themselves influence the residuals they are intended to model—a self-referential problem. We propose a practical approach using the Yule-Walker equations to estimate AR parameters and introduce tools to assess their reliability. In addition, we offer heuristic insights into the method’s performance and present empirical results based on monthly labor force survey data.

KEYWORDS: State-space models, Autoregressive models, Panel data surveys.

In order to forecast time-series data that have both linear and non-linear relationships such as average temperature, humidity, precipitation, and other atmospheric elements, time-series data analysts used a variety of statistical techniques to construct their forecasts. This research article aimed to evaluate the performance of the Mann-Kentrick test model and Generalized Additive Models (GAMs) techniques in the simulation of non-stationary extremes values. The Mann-Kendall test is a nonparametric statistical method that is used to find patterns in data over time. In contrast, generalized additive models (GAM) are a parametric statistical method
used to model trends in time-series data. This study used monthly mean temperature data from the Nigerian Metrological Agency (NiMet) for the Northeastern Region of Nigeria over a 41-year period (1981 to 2022). To compare the expected performance of the models, well-known measures such as MSE, RMSE, MAE, and MAPE were employed. From the result of the trend test accuracy between Mann-Kendall’s test and Generalized Additive Models (GAM), it has shown that the Mann-Kendall’s test is good in trend detection but unable to capture nonlinear trend. Principal results with strong evidence from the plots showed that the Generalized Additive
Model (GAM) outperforms the Mann Kendall test (MK) models both in capturing nonlinear relationship and modeling the time series trend.

KEYWORDS: Evaluation, Generalized Additive Models, Extreme values, Mann-Kendall Test.

This paper presents an approach to volatility modelling and option pricing using multi-output Gaussian processes (MOGP) within the Heston framework.We employ MOGP to approximate a range of financial quantities, including implied volatility grids, options prices, and portfolio values. Our methodology offers a unified model for simultaneously handling multiple outputs, thereby enhancing computational efficiency and reducing the need for multiple separate models. In the process, we also provide a brief overview of Bayesian techniques applied to options pricing and volatility modelling, highlighting their relevance and advantages in the context of the
proposed approach. Extensive experiments demonstrate the accuracy and scalability of the MOGP model, with comparative analysis against the Fast Fourier Transform (FFT) method, showing significant improvements in computational speed and precision for pricing and risk management tasks.

KEYWORDS: Volatility, Bayesian Approximations, Option Pricing, Multi-GP Methodology.

Estimators based on median and Hodges-Lehmann (HL) techniques for estimating the slope parameter of simple linear regression (SLR) are robust in nature. In this paper, we develop slope estimators based on median and HL estimator of slopes obtained from quasi ranges of predictor variables. The mean and variance of the proposed estimators are obtained when errors have various symmetric distributions. Their performance is evaluated and they are compared with their competitors. Their generalized forms are discussed for the situations of multiple responses. Also, fitting of SLR model using the proposed estimators is illustrated with a data set.

KEYWORDS: Median based estimator, Quasi range, Robust, Simple linear regression, Slope parameter.

The target of this paper is to introduce the ?-order Generalized Cauchy distribution. Based on the ?-order Generalized Normal, N?(?, ?2I), emerged from Logarithmic Sobolev Inequalities (LSI) a number of ?-order distributions have been already defined. The ratio of two ?-order Generalized Normal defines the ?-order Generalized Cauchy distribution with the probability distribution function evaluated. With ? = 2 the well-known Cauchy distribution is obtained.

KEYWORDS: ?-order Generalized Normal Distribution, Laplace transformation, Cauchy distribution, Fox-Wright function.

Accurate survival predictions are crucial for cost-effectiveness evaluations in health technology assessment (HTA). However, model selection remains a challenge. Flexible survival models eliminate the need to identify the exact data-generating or best-fitting parametric model, though informed choices are still required. Using the Kaplan–Meier curve as a reference and selecting parametric survival models that minimize the squared distance to non-parametric survival estimates provides an objective approach to model selection for survival data extrapolation. This paper extends this methodology by incorporating flexible parametric models and employs
resampling methods, which are described, evaluated, and illustrated using both simulated and real-world data. Our findings demonstrate that resampling-based model selection enhances predictive accuracy, making it a valuable tool for survival extrapolation in HTA.

KEYWORDS: Flexible parametric survival models, Model selection,Mean squared error, Resampling, Health technology assessment.

Among the basic functions of government, is the provision of effective health care delivery and services. This is made possible by government efficient funding of the health-care sector. Therefore, this study tends to investigate the effectiveness of government health finance on primary health care outcome especially, infant mortality rate in Nigeria. A secondary data from Central Bank of Nigeria statistical bulletin and World Bank Indicator on Public Health Expenditure which ranges from 1990 to 2023 were used. The method of Autoregressive distributive lag (ARDL) model were employed to analyze the data. The model provided a co-integrating relationship among the variables of the study. Augmented Dickey Fuller (ADF) test statistic was significant at the 5% level of significance. The regression coefficient of constant is positive and it is statistically significant (P-value < 0.05) which implies that infant mortality rate is 46.31922 at the beginning of the study period, when other variables are not operational or held constant. Also, apart from out-of-pocket expenditure (OOP), other variables which include Public health expenditure (PHEXP), and health insurance (HI) were statistically significant in explaining infant mortality rate. With regards to effect of out-of-pocket health expenditure on households,
the study recommends a shift from out-of-pocket health payments to pre-payment mechanism of health insurance or a subsidized healthcare system as this may be the only way to reduce financial burden Nigerian citizen.

KEYWORDS: Autoregressive distributive lag model, Public health expenditure, Infant mortality rate, out-of-pocket expenditure, health insurance.

This study investigates the statistical evolution of registered motor vehicles in India and examines their relationship with the nation’s economic growth between 2001 and 2020. Using time-series data on vehicle registration, production, sales, and exports—along with gross domestic product (GDP)—the analysis reveals a strong interdependence between the automobile sector and India’s economic development. Two-wheelers remain the dominant category in production, sales, and export volumes, reflecting affordability and mobility demand in both domestic and emerging markets. Although road infrastructure has expanded, vehicle penetration has far outpaced it. Correlation and regression results demonstrate a close link between GDP growth and automobile indicators, confirming the sector’s significance as a driver of economic output, employment, and trade. The findings highlight the necessity of integrated policies that sustain sectoral growth while addressing congestion, safety, and environmental concerns.

KEYWORDS:Registered vehicles, automotive sector, GDP of India, Economic Growth.