Authors:
(1) Mattheu Bult´e, Department of Sports Science, Copenhagen University, College of Business and Economy, University of Beeveld;
(2) Healy Sorensen, Department of Sports Science, Copenhagen University.
Links table
Abstract and 1. Introduction
2. The introductory
3. GAR model (1)
3.1. Form and fixed solution
3.2. Definition
4. Estimating model parameters and 4.1. Fréchet means
4.2. Focus teacher
5. Test for the absence of serial accreditation
6. Numerical experiments
6.1. R with double noise
6.2. Distributors of single variables heavily
6.3. SPD matrix
7. Application
8. Thanks and appreciation
Approach a. General results in HADAMARD spaces
Approach b
reference
a summary
RAM in metropolitan spaces receives time index and note in time dates, equally from increasing interest due to their wide application capacity. However, the lack of a structure inherent in the metropolitan areas has often led to non -Parameter literature and free of models. To address this gap in models of a time series of random organisms, we offer an adaptation to the classic linear slope that designed for data dumped in the Hadamard space. Attention parameters in this model are the average Frécheet and a concentration teacher, both of which prove that it can be constantly estimated from the data. In addition, we propose to count the test and establish its approaches, and thus enable a hypothesis test for the absence of serial accreditation. Finally, we offer the Bootstrap procedure to obtain critical values for the testing of the test under an empty hypothesis. The theoretical results of our method, including the convergence of the two destinies, as well as the size and strength of the test, are clarified through simulation, and the benefit of the model is clarified through an analysis of a series of time of consumer enlargement expectations.
1. Introduction
Random variables in public metric spaces, which are also called random objects, receive increasing interest in modern statistical research. The preparation of the public metropolitan space does not require any algebraic structure only and is based only on the definition of the distance function. This allows the application of developed methods in areas ranging from classic settings to the most complex use cases on non -standard data. This includes the study of functional data (RAMSAY and Silverman (2005), data on Riemannian terribly, correlation matrices and their applications for functional magnetic resonance data (Petersen and Muller (2019) or adjacent prescriptions and social networks (Dubey and M¨uller (2020) among others.
One of the examples of special attention due to a wide range of applications is data that includes possibility density functions. Distributions of possibilities are a difficult example on a functional space, and therefore it is not limited to dimensions, but also non -celidy in restrictions that distinguish density functions. This leads to a number of different methods of studying these creatures: they were studied as a picture of Hilbert’s distances under the transitions (Petersen and M¨uller (2016)), as Hilbert spaces are specific with a specific addition and numerical hitting (Panaros, Zeml and Zeman (204), in addition to metric components. Srivastava and Klassen (2016)). See Petersen et al. (2022) To review these methodologies. Distributions can be found in many applications; When considering the distribution of social and economic factors within the population such as income (yoshiyuki (2017), fertility (Mazzuco and Scarpa (2015)) or death data (Chen et al. (2021)). It is also useful when considering the distributions of beliefs of economic factors (Meeks and Monti (2023), allowing economic analyzes to consider complete distributions instead of experimental expectations.
The study of random things has received a recent interest with working in standard statistical questions (DUBEY and Muller (2019, 2020); Bult´e and SkynSen (2023); HADAMARD and BACAK (2014) to calculate Fréche in such spaces.
In many of the above applications, the data may be normal again and repeatedly in a regular break and for the time series. In this case, notes may not be independent and require additional care and analyzes to take into account this accreditation. This work was mainly performed in a non -Pyramrich environment, assuming the classic weak dependence. This was done, for example, for a serial accreditation test (Jiang et al.
Although this Labor line can be applied widely, it depends on non -teacher assumptions instead of proposing a specific model to generate data. However, the temporal chains models were developed for specific random creatures by exploiting the area of space under study. One of the famous models category is those in automatic models, which were defined using the linear structure of functional spaces (BOSQ (2000); Caponra, Marinuccci (2021)) or exploiting the shade of the area of the area (ZHU and M¨uller (2022); Xavier and Manton (2006); (2021)) For example, but not limited to.
Inspired by automatic slope models, we suggest a model for automatic slope of random organisms. Depending on the interpretation of repetition in the formal linear slope as a loud, noisy group, we define a specific model by medium parameters and concentration. In order for this to be possible, we assume an additional structure and ask that the space be the area of Hadamard, and we take advantage of the area of space to determine the repetition of the time chain through geodesia. We develop the methodology and theory associated with the appreciation test and testing the hypotheses in this model. This includes the ability of intermediate and concentration parameters, and we propose a test for an automatic non -correlation test, opposite to monitor the iID sample.
The paper was organized as follows: Section 2 offers a presentation of useful concepts and results in the Hadamard spaces for the rest of the article. In Section 3, we offer an automatic slope model and provide a theory that provides a sufficient condition for a fixed solution to the repeated equation system associated with the model, and to prove the ability to identify typical parameters. We propose in the two capabilities in Section 4 to these parameters and prove the results of the rapprochement of these two destinations. In Section 5, we suggest a test of an independence -free hypothesis based on the exam statistics that describe the behavior close to the empty hypothesis and an alternative to a non -zero concentration parameter. Finally, we explain our theoretical results in section 6 with a numerical study.
