傘型迴歸函數是類似傘的形狀的迴歸函數，只要符合先上升後下降的趨勢皆為傘型迴歸函數。無母數迴歸函數中最常見的方法之一是樣條(Splines)迴歸函數。樣條為充分平滑分段多項式函數，而節點(knots)為平滑多項式函數連接的地方。在本論文中，將節點以等距離擺放並以AIC(Akaike information criterion)值得到合理的節點數。用三種方法的樣條迴歸函數去估計傘型函數。第一種為RSPL(restrictted spline regression)，也就是有形狀限制時的樣條迴歸函數。第二種是CSPL(concave spline regression)，是參考Meyer寫的樣條迴歸函數，此樣條迴歸函數為凹函數(concave function)。最後一種則稱SPL(spline regression)，為沒有形狀限制也不是凹函數的樣條函數。以IMSE為評估標準，IMSE越小，則代表此方法估計的越好。由模擬結果，在估計先上升後下降的函數時，用RSPL的方法去估計會得到最小的IMSE；而在估計凹函數時，則是CSPL會得到最小的IMSE。利用RSPL和SPL兩個方法估計由中央氣象局蒐集最近13年(1998-2010)的月均溫資料並探討最近幾年的月均溫資料趨勢是否有改變。未來假如需要估計傘型函數時，則可利用本篇所述的方法去估計。 / In this thesis, we consider the problem of estimating a regression function assuming the regression function is unimodal. The proposed method is to model the regression function as linear combination of B-spline basis functions with equally spaced knots, and the number of knots is determined using AIC (Akaike information criterion). Specific constraints are placed on the coefficients of basis functions to ensure that estimated regression function is unimodal. The coefficients are estimated using least square method. The proposed method is refered as RSPL and is compared with two other methods: SPL and CSPL, where SPL is similar to RSPL except that the coefficients of basis functions are estimated without any constraints, and CSPL gives concave regression function estimates. Simulation results show that RSPL outperforms SPL and CSPL when the true regression function is unimodal but not concave, and CSPL outperforms RSPL and SPL when the true regression function is concave. Also, RSPL is applied to temperature data to estimate temperature trend within one year.

Nous nous intéressons dans cette thèse aux méthodes d’estimation non paramétriques par noyaux récursifs ainsi qu’à leurs applications à la prévision. Nous introduisons dans un premier chapitre une famille d’estimateurs récursifs de la densité indexée par un paramètre ℓ ∈ [0, 1]. Leur comportement asymptotique en fonction de ℓ va nous amener à introduire des critères de comparaison basés sur les biais, variance et erreur quadratique asymptotiques. Pour ces critères, nous comparons les estimateurs entre eux et aussi comparons notre famille à l’estimateur non récursif de la densité de Parzen-Rosenblatt. Ensuite, nous définissons à partir de notre famille d’estimateurs de la densité, une famille d’estimateurs récursifs à noyau de la fonction de régression. Nous étudions ses propriétés asymptotiques en fonction du paramètre ℓ. Nous utilisons enfin les résultats obtenus sur l’estimation de la régression pour construire un prédicteur non paramétrique par noyau. Nous obtenons ainsi une famille de prédicteurs non paramétriques qui permettent de réduire considérablement le temps de calcul. Des exemples d’application sont donnés pour valider la performance de nos estimateurs / The aim of this thesis is to study methods of nonparametric estimation based on recursive kernel and their applications to forecasting. We introduce in the first chapter a family of recursive density estimators indexed by a parameter ℓ ∈ [0, 1]. We study their asymptotic behavior according to ℓ, and then we introduce criteria of comparison based on bias, variance and asymptotic quadratic error. For these criteria, we compare our estimators in terms of ℓ, and also compare our family to the non-recursive density estimator of Parzen-Rosenblatt. As for density, we define a family of recursive kernel estimators of regression function. We study its asymptotic properties according to the parameter ℓ. Finally, results of regression estimation are applied to define a family of nonparametric predictors that reduce considerably the computing time and examples of application are given to validate the performance of our methods

Master's thesis deals with the assessment of selected financial indicators of the company through a financial analysis and statistical methods, on the basis of which then evaluates the current situation of the company. The thesis is divided into three parts. The theoretical part contains the issues necessary for the analytical part. The analytical part is focused on the analysis of selected indicators and the subsequent application of statistical methods to predict their future development and to detect dependencies between the indexes. The last part formulates possible solutions to problems caused by financial indicators that do not reach the required values.

The thesis deals with the assessment of the economic situation of a selected company using statistical methods. The theoretical part describes the financial indicators, time series and regression analysis. The analytical part contains the calculation of selected indicators, which are subjected to statistical analysis. Based on the statistical analysis, the future development of indicators in the next two years is predicted. The last part contains suggestions that can lead to the improvement of the current situation of the company.

This thesis is focused on the use of time series and other statistical methods as a tool for examining the financial performance and financial position of the selected company. The aim is to assess the current situation of the company and on the basis of these results, draw conclusions and propose steps to improve the situation. Projections for future years will be based on knowledge of historical data.

Master’s thesis is aimed at assessing the selected financial indicators of the company using statistical methods. Based on the results, the current situation of the company is evaluated. The thesis consists of three parts. The first part contains the necessary theoretical bases for processing the analytical part. The second part is devoted to the analysis of selected indicators, which are then applied statistical methods to the prediction of the future development of these indicators and findings, here between these indicators there is a dependence. At the end of this part, there is an evaluation of the analyzed indicators. The third part presents appropriate proposals for solutions to existing problems caused by indicators that deviate from the recommended values.

Master's thesis deals with the assessment of selected financial indicators of the production company X in order to evaluate its performance and financial situation. Based on the results of the analyzes for the period 2008 to 2015 and the application of statistical methods of time series analysis and regression analysis, prognosis of future development of monitored indicators are obtained. Subsequently, the prognosis are used for the final formulating of proposals to improve future business efficiency of the company.

The thesis is focused on assessment of fatigue behaviour of austempered ductile iron with nodular graphite. Optimal period of transformation was determined based on the best combination of stress and strain characteristics established by tensile test. Cyclic response and low-cycle fatigue life were studied under both stress-control and longitudinal strain-control mode at room temperature. For both modes, shapes of cyclic hardening curves are dependent on stress amplitude. Cyclic deformation curves (CDC) were fitted by power regression function. Results were compared with CDC established by multiple step test in both modes with verification of the influence of cyclic creep (high stress levels, stress-control mode). Experimental data of S-N curves are in agreement with the Manson-Coffin and the Basquin law. Fatigue and cyclic parameters were compared. Fatigue life time in high-cycle fatigue region was determined. Experimental data were fitted by suitable regression functions. Regression parameters and fatigue limit were established by means of each regression function. Experimental data in low- and high-cycle fatigue regions were used to construct S-N curve and to determine relevant parameters. Discontinuity of experimental data was not observed. Low-cycle fatigue behaviour was predicted. Approximation of tolerance bands was realized in high-cycle and both high and low cycle fatigue regions.

This thesis aims to familiarize the reader with the topic of life insurance, especially insurance taken out for more people. Its focus is empirical rather as combining the use of several actuarial and statistical methods through three statistical software and applications created in MS Excel using VBA. First, thesis is focused to multiple life insurance with intention to show reader the diversity of this interesting but rarely offered product in business world, especially through the application created for the purpose of this work. Sense of mentioned application lies in the fact it is able to calculate amount of the net premium for a user-selected type of insurance. Based on this outcome insurer can determine the net price corresponding to the chosen risk coverage (regardless of the amount of the costs associated with this type of insurance and required profitability). Age of insured person isn't usually part of calculation of premium for accident insurance. One of the aims of this study is to assess whether this parameter actually has or doesn't have any effect on the price of insurance. With help of SPSS and RStudio software relationship between age of insured person and amount of indemnification from daily compensation insurance has been researched. Based on the test of variable independence were detected dependencies of these variables where all of which used measure of association suggests a weak dependence amount of indemnification on the age of the insured. It surely worth insurer should consider different insurance rates for various ages of insured person. Following by examination whether the rate used to calculate premiums in case of hospitalization extra insurance corresponds to the actual risk coverage. It has been calculated the rate could be lower than currently used due to the loss experience of insurance for the past 9 years and the assumption of certain expenses and desired profit. It would be cheaper for insurance group contracts than it is today, when the insurer has done so. It could also attract new clientele. The last stated goal in this thesis is to create prognosis of the amount of indemnity paid for injuries covered by additional daily compensation insurance. Using the software EViews is analyzed this trend in the past 32 months first. Based on its outcome there is a future level forecast created for the next four years. These resulting values indicate the insurance indemnity for group contract will grow. Therefore, based on this analysis insurer should to conclude in the contract it would be appropriate to increase the premium of the insurance coverage. With these practical tasks the reader can get idea not only of problems solved in the scope of multiple life insurance and group insurance but also to become familiar with some statistical software used for analyzes carried out not only in the insurance industry. The conclusions of this thesis can also be beneficial for insurer who may adjust premium prices of analyzed insurances.

The thesis is focused on assessment of fatigue behaviour of austempered ductile iron with nodular graphite. Optimal period of transformation was determined based on the best combination of stress and strain characteristics established by tensile test. Cyclic response and low-cycle fatigue life were studied under both stress-control and longitudinal strain-control mode at room temperature. For both modes, shapes of cyclic hardening curves are dependent on stress amplitude. Cyclic deformation curves (CDC) were fitted by power regression function. Results were compared with CDC established by multiple step test in both modes with verification of the influence of cyclic creep (high stress levels, stress-control mode). Experimental data of S-N curves are in agreement with the Manson-Coffin and the Basquin law. Fatigue and cyclic parameters were compared. Fatigue life time in high-cycle fatigue region was determined. Experimental data were fitted by suitable regression functions. Regression parameters and fatigue limit were established by means of each regression function. Experimental data in low- and high-cycle fatigue regions were used to construct S-N curve and to determine relevant parameters. Discontinuity of experimental data was not observed. Low-cycle fatigue behaviour was predicted. Approximation of tolerance bands was realized in high-cycle and both high and low cycle fatigue regions.