Residuals are minimized in a correlated dataset by selecting a smoothing parameter with optimum performance in the smoothing spline. The selection methods utilized in this study include Generalized Maximum Likelihood (GML), Generalized Cross-Validation (GCV), Unbiased Risk (UBR), and the Proposed Smoothing Method (PSM). The aim of this study is to compare the smoothing parameter selection ability of the four parameter selection methods for a correlated dataset with autocorrelation structure in the error term. To achieve this purpose, a Monte-Carlo simulation was conducted by utilizing program written in R-4.2.2. The performance of the parameter selection methods were evaluated using predictive Mean Squared Error (PMSE). Findings from the study indicated that GCV and GML were mostly affected by the presence of auto correlation in the residual and therefore had an asymptotically similar behavioural pattern. The estimators conformed to the asymptotic properties of the smoothing parameter selection methods considered; this is noticed in all the sample sizes and at all the smoothing parameters. The result also showed that; the most consistent and efficient among the four spline smoothing parameter selection methods considered in this study based on sample size and performance in the presence of autocorrelated residual error is the proposed smoothing method (PSM) because it does not undersmooth relative to the other smoothing method especially for small sample and medium sample size of 50 and 100.

This study aimed to examine, model, and compared the impact of investing in some social infrastructures like; transportation, communication technology, power, and educational sector indicators to the economic growth and development of Nigeria. This is important because of their incomparable contributions to the growth and development of a Nation. The data utilized in this study were sourced from the Central Bank of Nigeria (CBN) statistical bulletin, 2021 edition. The collected data were analyzed using the autoregressive distributed lag (ARDL) model. The existence of co-integration between investment in the four social infrastructures and economic growth was confirmed by the ARDL bound. The empirical findings revealed that investment in power has a positive but insignificant long-run effect on economic growth, investment in education positively and significantly affects economic growth while investment in transportation and communication technology were found to be insignificant with a negative impact on the Nigerian’ economic growth in the long-run. It was also discovered that the short-run relationship is somehow similar to the long-run relationship. The study recommends that Government should increase the budgetary allocation to the educational sector to address some of the reasons for the decline in the country’s economic growth as the results also shows that a 1% increase in budgetary allocation to the educational sector increases economic growth by over 5.1% and 1.5% in the long and short-run respectively.

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Due to the growing number of intrusions in local networks and the internet, it has become so universal that institution increasingly implements many structures that investigate information technology security violations. This study aimed to process, classify and predict the intrusion detection accuracy of some selected network attacks using the artificial neural network (ANN) technique. Five important attacks, namely; Buffer overflow, Denial of Service (DoS), User to Root Attack (U2R), Remote to Local Attack (R2L) and PROBE were chosen from the KDD CUPP’99 information and intrusion identification accuracy was investigated with artificial neural network (ANN) modeling technique. Findings from the classification show that out of the procedures utilized to establish the ANN model, 27262 of the 45528 buffer overflow are classified appropriately, 7903 of the 45528 DoS attacks are arranged appropriately, 1371 of the 45528 U2R are classified appropriately, 431 of the 45528 R2L are arranged appropriately and, 8304 of the 45528 PROBE are classified appropriately. Comprehensively, about 99.1% of the training proceedings are arranged properly, equivalent to 0.9% erroneous classification while the testing specimen assisted to confirm the model with 99.1% of the attacks were appropriately arranged by the ANN equation. This support that, comprehensively, the ANN equation is precise about the classification and prediction of the five attacks investigated in this study.