Statistical models for the dynamics of brand equity

The purpose of this research is to propose statistical models, develop certain procedures/approaches needed to estimate these models, and when marketing data are available, provide insights about brand equity dynamics in marketing practice, especially firm-based brand equity. In this dissertation, two categories of models are explored. In Chapter II, autoregressive models with exogeneous inputs (ARX) are proposed for brand structural analysis. These models are useful when brand values are known, and the sample size is relatively small. Another category of models, state space models, are proposed when brand values are unavailable. In Chapter III and IV, an approach or a procedure is proposed or designed to guess initial parameter values for a certain iteration algorithm. Moreover, Moreover, mathematical optimization methods are introduced and integrated to estimate unknown parameters of the models for brand equity dynamics. There are at least two important findings. Firstly, the implementation of brand value structure analysis can be realized through the application of an ARX model and the assessment of a firm’s brand management performance is possible. Secondly, innovative approaches must be developed to guess the starting values for iterations and to estimate parameter values of different state space models. These findings are from this innovative and contributive research. Through brand structure analysis, a novel effort in research on brand equity dynamics, brand financial performance outcome is linked with brand equity sources, while long-term brand value is distinguished from short-term performance. The analysis helps brand managers to obtain the insights into the brand performance and the ability to focus on long-term outcomes of marketing campaigns. Moreover, innovative approaches are proposed in applying state space models for brand equity dynamics analysis. Weight least square method is used in guessing the initial parameter values for a state space model with one input series and one state series. For a state space model with two input series and two state series, as well as nonlinear constraints, a procedure is designed to guess the initial parameter values. Moreover, nonlinear mathematical optimization methods are introduced and integrated to estimate the parameter values during the implementation of the expectation-maximization algorithm.

Statistical models for the dynamics of brand equity

The purpose of this research is to propose statistical models, develop certain procedures/approaches needed to estimate these models, and when marketing data are available, provide insights about brand equity dynamics in marketing practice, especially firm-based brand equity. In this dissertation, two categories of models are explored. In Chapter II, autoregressive models with exogeneous inputs (ARX) are proposed for brand structural analysis. These models are useful when brand values are known, and the sample size is relatively small. Another category of models, state space models, are proposed when brand values are unavailable. In Chapter III and IV, an approach or a procedure is proposed or designed to guess initial parameter values for a certain iteration algorithm. Moreover, Moreover, mathematical optimization methods are introduced and integrated to estimate unknown parameters of the models for brand equity dynamics. There are at least two important findings. Firstly, the implementation of brand value structure analysis can be realized through the application of an ARX model and the assessment of a firm’s brand management performance is possible. Secondly, innovative approaches must be developed to guess the starting values for iterations and to estimate parameter values of different state space models. These findings are from this innovative and contributive research. Through brand structure analysis, a novel effort in research on brand equity dynamics, brand financial performance outcome is linked with brand equity sources, while long-term brand value is distinguished from short-term performance. The analysis helps brand managers to obtain the insights into the brand performance and the ability to focus on long-term outcomes of marketing campaigns. Moreover, innovative approaches are proposed in applying state space models for brand equity dynamics analysis. Weight least square method is used in guessing the initial parameter values for a state space model with one input series and one state series. For a state space model with two input series and two state series, as well as nonlinear constraints, a procedure is designed to guess the initial parameter values. Moreover, nonlinear mathematical optimization methods are introduced and integrated to estimate the parameter values during the implementation of the expectation-maximization algorithm.

A Comparative Analysis of Parsimonious Yield Curve Models with Focus on the Nelson-Siegel, Svensson and Bliss Versions

We shed light on computational challenges when fitting the Nelson-Siegel, Bliss and Svensson parsimonious yield curve models to observed US Treasury securities with maturities up to 30 years. As model parameters have a specific financial meaning, the stability of their estimated values over time becomes relevant when their dynamic behavior is interpreted in risk-return models. Our study is the first in the literature that compares the stability of estimated model parameters among different parsimonious models and for different approaches for predefining initial parameter values. We find that the Nelson-Siegel parameter estimates are more stable and conserve their intrinsic economical interpretation. Results reveal in addition the patterns of confounding effects in the Svensson model. To obtain the most stable and intuitive parameter estimates over time, we recommend the use of the Nelson-Siegel model by taking initial parameter values derived from the observed yields. The implications of excluding Treasury bills, constraining parameters and reducing clusters across time to maturity are also investigated.

Why Tuning the Control Parameters of Metaheuristic Algorithms Is So Important for Fair Comparison?

Although metaheuristic optimization has become a common practice, new bio-inspired algorithms often suffer from a priori ill reputation. One of the reasons is a common bad practice in metaheuristic proposals. It is essential to pay attention to the quality of conducted experiments, especially when comparing several algorithms among themselves. The comparisons should be fair and unbiased. This paper points to the importance of proper initial parameter configurations of the compared algorithms. We highlight the performance differences with several popular and recommended parameter configurations. Even though the parameter selection was mostly based on comprehensive tuning experiments, the algorithms' performance was surprisingly inconsistent, given various parameter settings. Based on the presented evidence, we conclude that paying attention to the metaheuristic algorithm's parameter tuning should be an integral part of the development and testing processes.

Performance improvement in Resampling Based Clustering

Clustering is one of powerful technique to find a biological mechanism in gene expression. This technique identify a gene that has same expression. Using bootstrap method we can improve the quality of microarray, thus resampling based clustering (RC) is consider one of the improvement. RC use K-means clustering to determine initial parameter and need thousands of iteration to converge. Performance improvement can be done at preprocess, such as normalization and changing the initial parameter. Normalization can remove or lower the bias in microarray. The result show that normalization can improve the accuracy of RC. In addition, for parameter K, a lower value will lower the accuracy of this RC.

An initialization strategy for addressing barren plateaus in parametrized quantum circuits

Parametrized quantum circuits initialized with random initial parameter values are characterized by barren plateaus where the gradient becomes exponentially small in the number of qubits. In this technical note we theoretically motivate and empirically validate an initialization strategy which can resolve the barren plateau problem for practical applications. The technique involves randomly selecting some of the initial parameter values, then choosing the remaining values so that the circuit is a sequence of shallow blocks that each evaluates to the identity. This initialization limits the effective depth of the circuits used to calculate the first parameter update so that they cannot be stuck in a barren plateau at the start of training. In turn, this makes some of the most compact ansätze usable in practice, which was not possible before even for rather basic problems. We show empirically that variational quantum eigensolvers and quantum neural networks initialized using this strategy can be trained using a gradient based method.